EVERYDAY SCIENCE THINGS - Higher Intellect · SCIENCE EVERYDAY THINGS OF volume 2: REAL-LIFE PHYSICS A SCHLAGER INFORMATION GROUP BOOK edited by NEIL SCHLAGER written by JUDSON KNIGHT

SCIENCE EVERYDAY

THINGS

OF

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SCIENCE EVERYDAY

THINGS

OF

volume 2: REAL-LIFE PHYSICS

A SCHLAGER INFORMATION GROUP BOOK

edited by NEIL SCHLAGERwritten by JUDSON KNIGHT

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SCIENCE OF EVERYDAY THINGSVOLUME 2 Real-Life physics

A Schlager Information Group BookNeil Schlager, EditorWritten by Judson Knight

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ISBN 0-7876-5631-3 (set)0-7876-5632-1 (vol. 1) 0-7876-5634-8 (vol. 3)0-7876-5633-X (vol. 2) 0-7876-5635-6 (vol. 4)

Printed in the United States of America10 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging-in-Publication Data

Knight, Judson.Science of everyday things / written by Judson Knight, Neil Schlager, editor.

p. cm.Includes bibliographical references and indexes.Contents: v. 1. Real-life chemistry – v. 2 Real-life physics.ISBN 0-7876-5631-3 (set : hardcover) – ISBN 0-7876-5632-1 (v. 1) – ISBN

0-7876-5633-X (v. 2)1. Science–Popular works. I. Schlager, Neil, 1966-II. Title.

Q162.K678 2001500–dc21 2001050121

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iiiSC IENCE OF EVERYDAY TH INGS VOLUME 2: REAL-LIFE PHYSICS

Introduction.............................................v

Advisory Board ......................................vii

GENERAL CONCEPTS

Frame of Reference. . . . . . . . . . . . . . . . . . . . . . . 3

Kinematics and Dynamics . . . . . . . . . . . . . . . 13

Density and Volume . . . . . . . . . . . . . . . . . . . . 21

Conservation Laws . . . . . . . . . . . . . . . . . . . . . 27

KINEMATICS AND PARTICLEDYNAMICS

Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Centripetal Force . . . . . . . . . . . . . . . . . . . . . . . 45

Friction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . 59

Gravity and Gravitation . . . . . . . . . . . . . . . . . 69

Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . 78

Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

FLUID MECHANICS

Fluid Mechanics. . . . . . . . . . . . . . . . . . . . . . . . 95

Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . 102

Bernoulli’s Principle . . . . . . . . . . . . . . . . . . . 112

Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

STATICS

Statics and Equilibrium . . . . . . . . . . . . . . . . 133

Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

WORK AND ENERGY

Mechanical Advantage and Simple Machines . . . . . . . . . . . . . . . . . . 157

Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

THERMODYNAMICS

Gas Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Molecular Dynamics. . . . . . . . . . . . . . . . . . . 192

Structure of Matter . . . . . . . . . . . . . . . . . . . . 203

Thermodynamics . . . . . . . . . . . . . . . . . . . . . 216

Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 236

Thermal Expansion. . . . . . . . . . . . . . . . . . . . 245

WAVE MOTION AND OSCILLATION

Wave Motion . . . . . . . . . . . . . . . . . . . . . . . . . 255

Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

Interference . . . . . . . . . . . . . . . . . . . . . . . . . . 286

Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . 301

SOUND

Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Ultrasonics. . . . . . . . . . . . . . . . . . . . . . . . . . . 319

LIGHT AND ELECTROMAGNETISM

Magnetism. . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Electromagnetic Spectrum . . . . . . . . . . . . . . 340

Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

Luminescence . . . . . . . . . . . . . . . . . . . . . . . . 365

General Subject Index ......................373

CONTENTS

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vSC IENCE OF EVERYDAY TH INGS VOLUME 2: REAL-LIFE PHYSICS

I N TRODUCT ION

Overview of the Series

Welcome to Science of Everyday Things. Our aimis to explain how scientific phenomena can beunderstood by observing common, real-worldevents. From luminescence to echolocation tobuoyancy, the series will illustrate the chief prin-ciples that underlay these phenomena andexplore their application in everyday life. Toencourage cross-disciplinary study, the entrieswill draw on applications from a wide variety offields and endeavors.

Science of Everyday Things initially compris-es four volumes:

Volume 1: Real-Life ChemistryVolume 2: Real-Life PhysicsVolume 3: Real-Life BiologyVolume 4: Real-Life Earth Science

Future supplements to the series will expandcoverage of these four areas and explore newareas, such as mathematics.

Arrangement of Real LifePhysics

This volume contains 40 entries, each covering adifferent scientific phenomenon or principle.The entries are grouped together under commoncategories, with the categories arranged, in gen-eral, from the most basic to the most complex.Readers searching for a specific topic should con-sult the table of contents or the general subjectindex.

Within each entry, readers will find the fol-lowing rubrics:

• Concept Defines the scientific principle ortheory around which the entry is focused.

• How It Works Explains the principle or the-ory in straightforward, step-by-step lan-guage.

• Real-Life Applications Describes how thephenomenon can be seen in everydayevents.

• Where to Learn More Includes books, arti-cles, and Internet sites that contain furtherinformation about the topic.

Each entry also includes a “Key Terms” sec-tion that defines important concepts discussed inthe text. Finally, each volume includes numerousillustrations, graphs, tables, and photographs.

In addition, readers will find the compre-hensive general subject index valuable in access-ing the data.

About the Editor, Author,and Advisory Board

Neil Schlager and Judson Knight would like tothank the members of the advisory board fortheir assistance with this volume. The advisorswere instrumental in defining the list of topics,and reviewed each entry in the volume for scien-tific accuracy and reading level. The advisorsinclude university-level academics as well as highschool teachers; their names and affiliations arelisted elsewhere in the volume.

NEIL SCHLAGER is the president ofSchlager Information Group Inc., an editorialservices company. Among his publications areWhen Technology Fails (Gale, 1994); HowProducts Are Made (Gale, 1994); the St. JamesPress Gay and Lesbian Almanac (St. James Press,1998); Best Literature By and About Blacks (Gale,

set_fm_v2 9/26/01 11:52 AM Page v

Introduction 2000); Contemporary Novelists, 7th ed. (St. JamesPress, 2000); and Science and Its Times (7 vols.,Gale, 2000-2001). His publications have wonnumerous awards, including three RUSA awardsfrom the American Library Association, twoReference Books Bulletin/Booklist Editors’Choice awards, two New York Public LibraryOutstanding Reference awards, and a CHOICEaward for best academic book.

Judson Knight is a freelance writer, andauthor of numerous books on subjects rangingfrom science to history to music. His work on science titles includes Science, Technology, andSociety, 2000 B.C.-A.D. 1799 (U*X*L, 2002),as well as extensive contributions to Gale’s seven-volume Science and Its Times (2000-2001).As a writer on history, Knight has publishedMiddle Ages Reference Library (2000), Ancient

Civilizations (1999), and a volume in U*X*L’s

African American Biography series (1998).

Knight’s publications in the realm of music

include Parents Aren’t Supposed to Like It (2001),

an overview of contemporary performers and

genres, as well as Abbey Road to Zapple Records: A

Beatles Encyclopedia (Taylor, 1999). His wife,

Deidre Knight, is a literary agent and president of

the Knight Agency. They live in Atlanta with their

daughter Tyler, born in November 1998.

Comments and Suggestions

Your comments on this series and suggestions for

future editions are welcome. Please write: The

Editor, Science of Everyday Things, Gale Group,

27500 Drake Road, Farmington Hills, MI 48331.

vi SC IENCE OF EVERYDAY TH INGSVOLUME 2: REAL-LIFE PHYSICS

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viiSC IENCE OF EVERYDAY TH INGS VOLUME 2: REAL-LIFE PHYSICS

T I T LEADV ISORY BOARD

William E. Acree, Jr.Professor of Chemistry, University of North Texas

Russell J. ClarkResearch Physicist, Carnegie Mellon University

Maura C. FlanneryProfessor of Biology, St. John’s University, New

York

John GoudieScience Instructor, Kalamazoo (MI) Area

Mathematics and Science Center

Cheryl HachScience Instructor, Kalamazoo (MI) Area


Michael SinclairPhysics instructor, Kalamazoo (MI) Area


Rashmi VenkateswaranSenior Instructor and Lab Coordinator,

University of OttawaOttawa, Ontario, Canada

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1

SC IENCE OF EVERYDAY TH INGSr e a l - l i f e Ph y s i c s

G ENER AL CONCEPTSGENER AL CONCEPTS

FRAME OF REFERENCE

K INEMAT ICS AND DYNAM ICS

DENS I T Y AND VOLUME

CONSERVAT ION LAWS

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3SC IENCE OF EVERYDAY TH INGS VOLUME 2: REAL-LIFE PHYSICS

F R AME OF REFERENCEFrame of Reference

CONCEPTAmong the many specific concepts the student ofphysics must learn, perhaps none is so deceptive-ly simple as frame of reference. On the surface, itseems obvious that in order to make observa-tions, one must do so from a certain point inspace and time. Yet, when the implications of thisidea are explored, the fuller complexities begin toreveal themselves. Hence the topic occurs at leasttwice in most physics textbooks: early on, whenthe simplest principles are explained—and nearthe end, at the frontiers of the most intellectuallychallenging discoveries in science.

HOW IT WORKSThere is an old story from India that aptly illus-trates how frame of reference affects an under-standing of physical properties, and indeed of thelarger setting in which those properties are man-ifested. It is said that six blind men were present-ed with an elephant, a creature of which they hadno previous knowledge, and each explained whathe thought the elephant was.

The first felt of the elephant’s side, and toldthe others that the elephant was like a wall. Thesecond, however, grabbed the elephant’s trunk,and concluded that an elephant was like a snake.The third blind man touched the smooth surfaceof its tusk, and was impressed to discover that theelephant was a hard, spear-like creature. Fourthcame a man who touched the elephant’s legs, andtherefore decided that it was like a tree trunk.However, the fifth man, after feeling of its tail,disdainfully announced that the elephant wasnothing but a frayed piece of rope. Last of all, thesixth blind man, standing beside the elephant’sslowly flapping ear, felt of the ear itself and

determined that the elephant was a sort of livingfan.

These six blind men went back to their city,and each acquired followers after the manner ofreligious teachers. Their devotees would thenargue with one another, the snake school ofthought competing with adherents of the fandoctrine, the rope philosophy in conflict with thetree trunk faction, and so on. The only personwho did not join in these debates was a seventhblind man, much older than the others, who hadvisited the elephant after the other six.

While the others rushed off with their sepa-rate conclusions, the seventh blind man hadtaken the time to pet the elephant, to walk allaround it, to smell it, to feed it, and to listen tothe sounds it made. When he returned to the cityand found the populace in a state of uproarbetween the six factions, the old man laughed tohimself: he was the only person in the city whowas not convinced he knew exactly what an ele-phant was like.

Understanding Frame of Ref-erence

The story of the blind men and the elephant,within the framework of Indian philosophy andspiritual beliefs, illustrates the principle of syad-vada. This is a concept in the Jain religion relatedto the Sanskrit word syat, which means “may be.”According to the doctrine of syadvada, no judg-ment is universal; it is merely a function of thecircumstances in which the judgment is made.

On a complex level, syadvada is an illustra-tion of relativity, a topic that will be discussedlater; more immediately, however, both syadvadaand the story of the blind men beautifully illus-


Frame ofReference

4 SC IENCE OF EVERYDAY TH INGSVOLUME 2: REAL-LIFE PHYSICS

trate the ways that frame of reference affects per-ceptions. These are concerns of fundamentalimportance both in physics and philosophy, dis-ciplines that once were closely allied until eachbecame more fully defined and developed. Evenin the modern era, long after the split betweenthe two, each in its own way has been concernedwith the relationship between subject and object.

These two terms, of course, have numerousdefinitions. Throughout this book, for instance,the word “object” is used in a very basic sense,meaning simply “a physical object” or “a thing.”Here, however, an object may be defined assomething that is perceived or observed. As soonas that definition is made, however, a flawbecomes apparent: nothing is just perceived orobserved in and of itself—there has to be some-one or something that actually perceives orobserves. That something or someone is the sub-ject, and the perspective from which the subjectperceives or observes the object is the subject’sframe of reference.

AMERICA AND CHINA: FRAME

OF REFERENCE IN PRACTICE. Anold joke—though not as old as the story of theblind men—goes something like this: “I’m glad Iwasn’t born in China, because I don’t speak Chi-nese.” Obviously, the humor revolves around thefact that if the speaker were born in China, thenhe or she would have grown up speaking Chi-nese, and English would be the foreign language.

The difference between being born in Amer-ica and speaking English on the one hand—evenif one is of Chinese descent—or of being born inChina and speaking Chinese on the other, is notjust a contrast of countries or languages. Rather,it is a difference of worlds—a difference, that is,in frame of reference.

Indeed, most people would see a huge dis-tinction between an English-speaking Americanand a Chinese-speaking Chinese. Yet to a visitorfrom another planet—someone whose frame ofreference would be, quite literally, otherworld-ly—the American and Chinese would have muchmore in common with each other than eitherwould with the visitor.

The View from Outside andInside

Now imagine that the visitor from outer space (ahandy example of someone with no precon-ceived ideas) were to land in the United States. If

the visitor landed in New York City, Chicago, orLos Angeles, he or she would conclude thatAmerica is a very crowded, fast-paced country inwhich a number of ethnic groups live in closeproximity. But if the visitor first arrived in Iowaor Nebraska, he or she might well decide that theUnited States is a sparsely populated land, eco-nomically dependent on agriculture and com-posed almost entirely of Caucasians.

A landing in San Francisco would create afalsely inflated impression regarding the numberof Asian Americans or Americans of PacificIsland descent, who actually make up only asmall portion of the national population. Thesame would be true if one first arrived in Arizonaor New Mexico, where the Native American pop-ulation is much higher than for the nation as awhole. There are numerous other examples to bemade in the same vein, all relating to the visitors’impressions of the population, economy, climate,physical features, and other aspects of a specificplace. Without consulting some outside referencepoint—say, an almanac or an atlas—it would beimpossible to get an accurate picture of the entirecountry.

The principle is the same as that in the storyof the blind men, but with an important distinc-tion: an elephant is an example of an identifiablespecies, whereas the United States is a uniqueentity, not representative of some larger class ofthing. (Perhaps the only nation remotely compa-rable is Brazil, also a vast land settled by outsidersand later populated by a number of groups.)Another important distinction between the blindmen story and the United States example is thefact that the blind men were viewing the elephantfrom outside, whereas the visitor to Americaviews it from inside. This in turn reflects a differ-ence in frame of reference relevant to the work ofa scientist: often it is possible to view a process,event, or phenomenon from outside; but some-times one must view it from inside—which ismore challenging.

Frame of Reference in Sci-ence

Philosophy (literally, “love of knowledge”) is themost fundamental of all disciplines: hence, mostpersons who complete the work for a doctoratereceive a “doctor of philosophy” (Ph.D.) degree.Among the sciences, physics—a direct offspringof philosophy, as noted earlier—is the most fun-


Frame ofReference

damental, and frame of reference is among itsmost basic concepts.

Hence, it is necessary to take a seeminglybackward approach in explaining how frame ofreference works, examining first the broad appli-cations of the principle and then drawing uponits specific relation to physics. It makes littlesense to discuss first the ways that physicistsapply frame of reference, and only then toexplain the concept in terms of everyday life. It ismore meaningful to relate frame of reference firstto familiar, or at least easily comprehensible,experiences—as has been done.

At this point, however, it is appropriate todiscuss how the concept is applied to the sci-ences. People use frame of reference every day—indeed, virtually every moment—of their lives,without thinking about it. Rare indeed is the per-son who “walks a mile in another person’sshoes”—that is, someone who tries to see eventsfrom the viewpoint of another. Physicists, on theother hand, have to be acutely aware of theirframe of reference. Moreover, they must “riseabove” their frame of reference in the sense thatthey have to take it into account in making cal-culations. For physicists in particular, and scien-tists in general, frame of reference has abundant“real-life applications.”

REAL-L IFEAPPLICATIONS

Points and Graphs

There is no such thing as an absolute frame ofreference—that is, a frame of reference that isfixed, and not dependent on anything else. If theentire universe consisted of just two points, itwould be impossible (and indeed irrelevant) tosay which was to the right of the other. Therewould be no right and left: in order to have sucha distinction, it is necessary to have a third pointfrom which to evaluate the other two points.

As long as there are just two points, there isonly one dimension. The addition of a thirdpoint—as long as it does not lie along a straightline drawn through the first two points—createstwo dimensions, length and width. From theframe of reference of any one point, then, it ispossible to say which of the other two points is tothe right.


Clearly, the judgment of right or left is rela-tive, since it changes from point to point. A moreabsolute judgment (but still not a completelyabsolute one) would only be possible from theframe of reference of a fourth point. But to con-stitute a new dimension, that fourth point couldnot lie on the same plane as the other threepoints—more specifically, it should not be possi-ble to create a single plane that encompasses allfour points.

Assuming that condition is met, however, itthen becomes easier to judge right and left. Yetright and left are never fully absolute, a fact easi-ly illustrated by substituting people for points.One may look at two objects and judge which isto the right of the other, but if one stands onone’s head, then of course right and left becomereversed.

Of course, when someone is upside-down,the correct orientation of left and right is still

LINES OF LONGITUDE ON EARTH ARE MEASURED

AGAINST THE LINE PICTURED HERE: THE “PRIME MERID-IAN” RUNNING THROUGH GREENWICH, ENGLAND. AN

IMAGINARY LINE DRAWN THROUGH THAT SPOT MARKS

THE Y-AXIS FOR ALL VERTICAL COORDINATES ON EARTH,WITH A VALUE OF 0° ALONG THE X-AXIS, WHICH IS THE

EQUATOR. THE PRIME MERIDIAN, HOWEVER, IS AN

ARBITRARY STANDARD THAT DEPENDS ON ONE’S FRAME

OF REFERENCE. (Photograph by Dennis di Cicco/Corbis. Repro-

duced by permission.)


Frame ofReference

fairly obvious. In certain situations observed byphysicists and other scientists, however, orienta-tion is not so simple. It then becomes necessaryto assign values to various points, and for this,scientists use tools such as the Cartesian coordi-nate system.

COORDINATES AND AXES.

Though it is named after the French mathemati-cian and philosopher René Descartes (1596-1650), who first described its principles, theCartesian system owes at least as much to Pierrede Fermat (1601-1665). Fermat, a brilliantFrench amateur mathematician—amateur in thesense that he was not trained in mathematics, nordid he earn a living from that discipline—greatlydeveloped the Cartesian system.

A coordinate is a number or set of numbersused to specify the location of a point on a line,on a surface such as a plane, or in space. In theCartesian system, the x-axis is the horizontal lineof reference, and the y-axis the vertical line ofreference. Hence, the coordinate (0, 0) designatesthe point where the x- and y-axes meet. All num-bers to the right of 0 on the x-axis, and above 0on the y-axis, have a positive value, while those tothe left of 0 on the x-axis, or below 0 on the y-axishave a negative value.

This version of the Cartesian system onlyaccounts for two dimensions, however; therefore,a z-axis, which constitutes a line of reference forthe third dimension, is necessary in three-dimen-sional graphs. The z-axis, too, meets the x- and y-axes at (0, 0), only now that point is designated as(0, 0, 0).

In the two-dimensional Cartesian system,the x-axis equates to “width” and the y-axis to“height.” The introduction of a z-axis adds thedimension of “depth”—though in fact, length,width, and height are all relative to the observer’sframe of reference. (Most representations of thethree-axis system set the x- and y-axes along ahorizontal plane, with the z-axis perpendicularto them.) Basic studies in physics, however, typi-cally involve only the x- and y-axes, essential toplotting graphs, which, in turn, are integral toillustrating the behavior of physical processes.

THE TRIPLE POINT. For instance,there is a phenomenon known as the “triplepoint,” which is difficult to comprehend unlessone sees it on a graph. For a chemical compoundsuch as water or carbon dioxide, there is a pointat which it is simultaneously a liquid, a solid, and

a vapor. This, of course, seems to go against com-mon sense, yet a graph makes it clear how this ispossible.

Using the x-axis to measure temperatureand the y-axis pressure, a number of surprisesbecome apparent. For instance, most peopleassociate water as a vapor (that is, steam) withvery high temperatures. Yet water can also be avapor—for example, the mist on a winter morn-ing—at relatively low temperatures and pres-sures, as the graph shows.

The graph also shows that the higher thetemperature of water vapor, the higher the pres-sure will be. This is represented by a line thatcurves upward to the right. Note that it is not astraight line along a 45° angle: up to about 68°F(20°C), temperature increases at a somewhatgreater rate than pressure does, but as tempera-ture gets higher, pressure increases dramatically.

As everyone knows, at relatively low temper-atures water is a solid—ice. Pressure, however, isrelatively high: thus on a graph, the values oftemperatures and pressure for ice lie above thevaporization curve, but do not extend to theright of 32°F (0°C) along the x-axis. To the rightof 32°F, but above the vaporization curve, are thecoordinates representing the temperature andpressure for water in its liquid state.

Water has a number of unusual properties,one of which is its response to high pressures andlow temperatures. If enough pressure is applied,it is possible to melt ice—thus transforming itfrom a solid to a liquid—at temperatures belowthe normal freezing point of 32°F. Thus, the linethat divides solid on the left from liquid on theright is not exactly parallel to the y-axis: it slopesgradually toward the y-axis, meaning that atultra-high pressures, water remains liquid eventhough it is well below the freezing point.

Nonetheless, the line between solid and liq-uid has to intersect the vaporization curve some-where, and it does—at a coordinate slightlyabove freezing, but well below normal atmos-pheric pressure. This is the triple point, andthough “common sense” might dictate that athing cannot possibly be solid, liquid, and vaporall at once, a graph illustrating the triple pointmakes it clear how this can happen.

Numbers

In the above discussion—and indeed throughoutthis book—the existence of the decimal, or base-



Frame ofReference

10, numeration system is taken for granted. Yetthat system is a wonder unto itself, involving acomplicated interplay of arbitrary and real val-ues. Though the value of the number 10 isabsolute, the expression of it (and its use withother numbers) is relative to a frame of reference:one could just as easily use a base-12 system.

Each numeration system has its own frameof reference, which is typically related to aspectsof the human body. Thus throughout the courseof history, some societies have developed a base-2 system based on the two hands or arms of aperson. Others have used the fingers on one hand(base-5) as their reference point, or all the fingersand toes (base-20). The system in use throughoutmost of the world today takes as its frame of ref-erence the ten fingers used for basic counting.

COEFFICIENTS. Numbers, of course,provide a means of assigning relative values to avariety of physical characteristics: length, mass,force, density, volume, electrical charge, and soon. In an expression such as “10 meters,” thenumeral 10 is a coefficient, a number that servesas a measure for some characteristic or property.A coefficient may also be a factor against whichother values are multiplied to provide a desiredresult.

For instance, the figure 3.141592, betterknown as pi (π), is a well-known coefficient usedin formulae for measuring the circumference orarea of a circle. Important examples of coeffi-cients in physics include those for static and slid-ing friction for any two given materials. A coeffi-cient is simply a number—not a value, as wouldbe the case if the coefficient were a measure ofsomething.

Standards of Measurement

Numbers and coefficients provide a convenientlead-in to the subject of measurement, a practicalexample of frame of reference in all sciences—and indeed, in daily life. Measurement alwaysrequires a standard of comparison: somethingthat is fixed, against which the value of otherthings can be compared. A standard may be arbi-trary in its origins, but once it becomes fixed, itprovides a frame of reference.

Lines of longitude, for instance, are meas-ured against an arbitrary standard: the “PrimeMeridian” running through Greenwich, England.An imaginary line drawn through that spotmarks the line of reference for all longitudinalmeasures on Earth, with a value of 0°. There isnothing special about Greenwich in any pro-found scientific sense; rather, its place of impor-


pres

sure

(y-a

xis)

temperature(x-axis)

triple point

(solid)(liquid)

(vapor)

THIS CARTESIAN COORDINATE GRAPH SHOWS HOW A SUBSTANCE SUCH AS WATER COULD EXPERIENCE A TRIPLE

POINT—A POINT AT WHICH IT IS SIMULTANEOUSLY A LIQUID, A SOLID, AND A VAPOR.


Frame ofReference

tance reflects that of England itself, which ruledthe seas and indeed much of the world at thetime the Prime Meridian was established.

The Equator, on the other hand, has a firmscientific basis as the standard against which alllines of latitude are measured. Yet today, thecoordinates of a spot on Earth’s surface are givenin relation to both the Equator and the PrimeMeridian.

CALIBRATION. Calibration is theprocess of checking and correcting the perform-ance of a measuring instrument or device againstthe accepted standard. America’s preeminentstandard for the exact time of day, for instance, isthe United States Naval Observatory in Washing-ton, D.C. Thanks to the Internet, people all overthe country can easily check the exact time, andcorrect their clocks accordingly.

There are independent scientific laboratoriesresponsible for the calibration of certain instru-ments ranging from clocks to torque wrenches,and from thermometers to laser beam poweranalyzers. In the United States, instruments ordevices with high-precision applications—thatis, those used in scientific studies, or by high-techindustries—are calibrated according to standardsestablished by the National Institute of Standardsand Technology (NIST).

THE VALUE OF STANDARD-

IZATION TO A SOCIETY. Standardiza-tion of weights and measures has always been animportant function of government. When Ch’inShih-huang-ti (259-210 B.C.) united China forthe first time, becoming its first emperor, he setabout standardizing units of measure as a meansof providing greater unity to the country—thusmaking it easier to rule.

More than 2,000 years later, anotherempire—Russia—was negatively affected by itsfailure to adjust to the standards of technologi-cally advanced nations. The time was the earlytwentieth century, when Western Europe wasmoving forward at a rapid pace of industrializa-tion. Russia, by contrast, lagged behind—in partbecause its failure to adopt Western standardsput it at a disadvantage.

Train travel between the West and Russiawas highly problematic, because the width ofrailroad tracks in Russia was different than inWestern Europe. Thus, adjustments had to beperformed on trains making a border crossing,and this created difficulties for passenger travel.

More importantly, it increased the cost of trans-porting freight from East to West.

Russia also used the old Julian calendar, asopposed to the Gregorian calendar adoptedthroughout much of Western Europe after 1582.Thus October 25, 1917, in the Julian calendar ofold Russia translated to November 7, 1917 in theGregorian calendar used in the West. That datewas not chosen arbitrarily: it was then that Com-munists, led by V. I. Lenin, seized power in theweakened former Russian Empire.

METHODS OF DETERMINING

STANDARDS. It is easy to understand,then, why governments want to standardizeweights and measures—as the U.S. Congress didin 1901, when it established the Bureau of Stan-dards (now NIST) as a nonregulatory agencywithin the Commerce Department. Today, NISTmaintains a wide variety of standard definitionsregarding mass, length, temperature, and soforth, against which other devices can be cali-brated.

Note that NIST keeps on hand definitionsrather than, say, a meter stick or other physicalmodel. When the French government establishedthe metric system in 1799, it calibrated the valueof a kilogram according to what is now known asthe International Prototype Kilogram, a plat-inum-iridium cylinder housed near Sèvres inFrance. In the years since then, the trend hasmoved away from such physical expressions ofstandards, and toward standards based on a con-stant figure. Hence, the meter is defined as thedistance light travels in a vacuum (an area ofspace devoid of air or other matter) during theinterval of 1/299,792,458 of a second.

METRIC VS. BRITISH. Scientistsalmost always use the metric system, not becauseit is necessarily any less arbitrary than the Britishor English system (pounds, feet, and so on), butbecause it is easier to use. So universal is the met-ric system within the scientific community that itis typically referred to simply as SI, an abbrevia-tion of the French Système Internationald’Unités—that is, “International System ofUnits.”

The British system lacks any clear frame ofreference for organizing units: there are 12 inch-es in a foot, but 3 feet in a yard, and 1,760 yardsin a mile. Water freezes at 32°F instead of 0°, as itdoes in the Celsius scale associated with the met-ric system. In contrast to the English system, the



Frame ofReference

metric system is neatly arranged according to thebase-10 numerical framework: 10 millimeters toa centimeter, 100 centimeters to a meter, 1,000meters to kilometer, and so on.

The difference between the pound and thekilogram aptly illustrates the reason scientists ingeneral, and physicists in particular, prefer themetric system. A pound is a unit of weight,meaning that its value is entirely relative to thegravitational pull of the planet on which it ismeasured. A kilogram, on the other hand, is aunit of mass, and does not change throughoutthe universe. Though the basis for a kilogrammay not ultimately be any more fundamentalthan that for a pound, it measures a qualitythat—unlike weight—does not vary according toframe of reference.

Frame of Reference in Clas-sical Physics and Astronomy

Mass is a measure of inertia, the tendency of abody to maintain constant velocity. If an object isat rest, it tends to remain at rest, or if in motion,it tends to remain in motion unless acted uponby some outside force. This, as identified by thefirst law of motion, is inertia—and the greaterthe inertia, the greater the mass.

Physicists sometimes speak of an “inertialframe of reference,” or one that has a constantvelocity—that is, an unchanging speed anddirection. Imagine if one were on a moving busat constant velocity, regularly tossing a ball in theair and catching it. It would be no more difficultto catch the ball than if the bus were standingstill, and indeed, there would be no way of deter-mining, simply from the motion of the ball itself,that the bus was moving.

But what if the inertial frame of referencesuddenly became a non-inertial frame of refer-ence—in other words, what if the bus slammedon its brakes, thus changing its velocity? Whilethe bus was moving forward, the ball was movingalong with it, and hence, there was no relativemotion between them. By stopping, the busresponded to an “outside” force—that is, itsbrakes. The ball, on the other hand, experiencedthat force indirectly. Hence, it would continue tomove forward as before, in accordance with itsown inertia—only now it would be in motionrelative to the bus.

ASTRONOMY AND RELATIVE

MOTION. The idea of relative motion plays a

powerful role in astronomy. At every moment,Earth is turning on its axis at about 1,000 MPH(1,600 km/h) and hurtling along its orbital patharound the Sun at the rate of 67,000 MPH(107,826 km/h.) The fastest any human being—that is, the astronauts taking part in the Apollomissions during the late 1960s—has traveled isabout 30% of Earth’s speed around the Sun.

Yet no one senses the speed of Earth’s move-ment in the way that one senses the movement ofa car—or indeed the way the astronauts per-ceived their speed, which was relative to theMoon and Earth. Of course, everyone experi-ences the results of Earth’s movement—thechange from night to day, the precession of theseasons—but no one experiences it directly. It issimply impossible, from the human frame of ref-erence, to feel the movement of a body as large asEarth—not to mention larger progressions onthe part of the Solar System and the universe.

FROM ASTRONOMY TO PHYS-

ICS. The human body is in an inertial frame ofreference with regard to Earth, and hence experi-ences no relative motion when Earth rotates ormoves through space. In the same way, if onewere traveling in a train alongside another trainat constant velocity, it would be impossible toperceive that either train was actually moving—unless one referred to some fixed point, such asthe trees or mountains in the background. Like-wise, if two trains were sitting side by side, andone of them started to move, the relative motionmight cause a person in the stationary train tobelieve that his or her train was the one moving.

For any measurement of velocity, and hence,of acceleration (a change in velocity), it is essen-tial to establish a frame of reference. Velocity andacceleration, as well as inertia and mass, figuredheavily in the work of Galileo Galilei (1564-1642) and Sir Isaac Newton (1642-1727), both ofwhom may be regarded as “founding fathers” ofmodern physics. Before Galileo, however, hadcome Nicholas Copernicus (1473-1543), the firstmodern astronomer to show that the Sun, andnot Earth, is at the center of “the universe”—by which people of that time meant the SolarSystem.

In effect, Copernicus was saying that theframe of reference used by astronomers for mil-lennia was incorrect: as long as they believedEarth to be the center, their calculations werebound to be wrong. Galileo and later Newton,



Frame ofReference

through their studies in gravitation, were able toprove Copernicus’s claim in terms of physics.

At the same time, without the understandingof a heliocentric (Sun-centered) universe that heinherited from Copernicus, it is doubtful thatNewton could have developed his universal lawof gravitation. If he had used Earth as the center-point for his calculations, the results would havebeen highly erratic, and no universal law wouldhave emerged.

Relativity

For centuries, the model of the universe devel-oped by Newton stood unchallenged, and eventoday it identifies the basic forces at work whenspeeds are well below that of the speed of light.However, with regard to the behavior of lightitself—which travels at 186,000 mi (299,339 km)a second—Albert Einstein (1879-1955) began toobserve phenomena that did not fit with New-tonian mechanics. The result of his studies wasthe Special Theory of Relativity, published in1905, and the General Theory of Relativity, pub-lished a decade later. Together these alteredhumanity’s view of the universe, and ultimately,of reality itself.

Einstein himself once offered this charmingexplanation of his epochal theory: “Put yourhand on a hot stove for a minute, and it seemslike an hour. Sit with a pretty girl for an hour, andit seems like a minute. That’s relativity.” Ofcourse, relativity is not quite as simple as that—though the mathematics involved is no morechallenging than that of a high-school algebraclass. The difficulty lies in comprehending howthings that seem impossible in the Newtonianuniverse become realities near the speed of light.

PLAYING TRICKS WITH TIME.

An exhaustive explanation of relativity is farbeyond the scope of the present discussion. Whatis important is the central precept: that no meas-urement of space or time is absolute, but dependson the relative motion of the observer (that is,the subject) and the observed (the object). Ein-stein further established that the movement oftime itself is relative rather than absolute, a factthat would become apparent at speeds close tothat of light. (His theory also showed that it isimpossible to surpass that speed.)

Imagine traveling on a spaceship at nearlythe speed of light while a friend remains station-

ary on Earth. Both on the spaceship and at thefriend’s house on Earth, there is a TV cameratrained on a clock, and a signal relays the imagefrom space to a TV monitor on Earth, and viceversa. What the TV monitor reveals is surprising:from your frame of reference on the spaceship, itseems that time is moving more slowly for yourfriend on Earth than for you. Your friend thinksexactly the same thing—only, from the friend’sperspective, time on the spaceship is movingmore slowly than time on Earth. How can thishappen?

Again, a full explanation—requiring refer-ence to formulae regarding time dilation, and soon—would be a rather involved undertaking.The short answer, however, is that which wasstated above: no measurement of space or time isabsolute, but each depends on the relativemotion of the observer and the observed. Putanother way, there is no such thing as absolutemotion, either in the three dimensions of space,or in the fourth dimension identified by Ein-stein, time. All motion is relative to a frame ofreference.

RELATIVITY AND ITS IMPLICA-

TIONS. The ideas involved in relativity havebeen verified numerous times, and indeed theonly reason why they seem so utterly foreign tomost people is that humans are accustomed toliving within the Newtonian framework. Einsteinsimply showed that there is no universal frame ofreference, and like a true scientist, he drew hisconclusions entirely from what the data suggest-ed. He did not form an opinion, and only thenseek the evidence to confirm it, nor did he seek toextend the laws of relativity into any realmbeyond that which they described.

Yet British historian Paul Johnson, in hisunorthodox history of the twentieth century,Modern Times (1983; revised 1992), maintainedthat a world disillusioned by World War I saw amoral dimension to relativity. Describing a set oftests regarding the behavior of the Sun’s raysaround the planet Mercury during an eclipse,the book begins with the sentence: “The modernworld began on 29 May 1919, when photographsof a solar eclipse, taken on the Island of Principeoff West Africa and at Sobral in Brazil, con-firmed the truth of a new theory of the uni-verse.”

As Johnson went on to note,“...for most peo-ple, to whom Newtonian physics... were perfectly



Frame ofReference


comprehensible, relativity never became morethan a vague source of unease. It was grasped thatabsolute time and absolute length had beendethroned.... All at once, nothing seemed certainin the spheres....At the beginning of the 1920s thebelief began to circulate, for the first time at apopular level, that there were no longer anyabsolutes: of time and space, of good and evil, ofknowledge, above all of value. Mistakenly butperhaps inevitably, relativity became confusedwith relativism.”

Certainly many people agree that the twenti-eth century—an age that saw unprecedentedmass murder under the dictatorships of AdolfHitler and Josef Stalin, among others—was char-acterized by moral relativism, or the belief thatthere is no right or wrong. And just as Newton’sdiscoveries helped usher in the Age of Reason,when thinkers believed it was possible to solveany problem through intellectual effort, it is quiteplausible that Einstein’s theory may have had thisnegative moral effect.

ABSOLUTE: Fixed; not dependent on

anything else. The value of 10 is absolute,

relating to unchanging numerical princi-

ples; on the other hand, the value of 10 dol-

lars is relative, reflecting the economy,

inflation, buying power, exchange rates

with other currencies, etc.

CALIBRATION: The process of check-

ing and correcting the performance of a

measuring instrument or device against a

commonly accepted standard.

CARTESIAN COORDINATE SYSTEM:

A method of specifying coordinates in rela-

tion to an x-axis, y-axis, and z-axis. The

system is named after the French mathe-

matician and philosopher René Descartes

(1596-1650), who first described its princi-

ples, but it was developed greatly by French

mathematician and philosopher Pierre de

Fermat (1601-1665).

COEFFICIENT: A number that serves

as a measure for some characteristic or

property. A coefficient may also be a factor

against which other values are multiplied

to provide a desired result.

COORDINATE: A number or set of

numbers used to specify the location of a

point on a line, on a surface such as a

plane, or in space.

FRAME OF REFERENCE: The per-

spective of a subject in observing an object.

OBJECT: Something that is perceived

or observed by a subject.

RELATIVE: Dependent on something

else for its value or for other identifying

qualities. The fact that the United States

has a constitution is an absolute, but the

fact that it was ratified in 1787 is relative:

that date has meaning only within the

Western calendar.

SUBJECT: Something (usually a per-

son) that perceives or observes an object

and/or its behavior.

X-AXIS: The horizontal line of refer-

ence for points in the Cartesian coordinate

system.

Y-AXIS: The vertical line of reference

for points in the Cartesian coordinate sys-

tem.

Z-AXIS: In a three-dimensional version

of the Cartesian coordinate system, the z-

axis is the line of reference for points in the

third dimension. Typically the x-axis

equates to “width,” the y-axis to “height,”

and the z-axis to “depth”—though in fact

length, width, and height are all relative to

the observer’s frame of reference.

KEY TERMS


Frame ofReference

If so, this was certainly not Einstein’s inten-tion. Aside from the fact that, as stated, he did notset out to describe anything other than the phys-ical behavior of objects, he continued to believethat there was no conflict between his ideas and abelief in an ordered universe: “Relativity,” he oncesaid, “teaches us the connection between the dif-ferent descriptions of one and the same reality.”

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Fleisher, Paul. Relativity and Quantum Mechanics: Princi-ples of Modern Physics. Minneapolis, MN: LernerPublications, 2002.

“Frame of Reference” (Web site).<http://www.physics.reading.ac.uk/units/flap/glos-sary/ff/frameref.html> (March 21, 2001).

“Inertial Frame of Reference” (Web site).<http://id.mind.net/~zona/mstm/physics/mechan-ics/framesOfReference /inertialFrame.html> (March21, 2001).

Johnson, Paul. Modern Times: The World from the Twen-ties to the Nineties. Revised edition. New York:HarperPerennial, 1992.

King, Andrew. Plotting Points and Position. Illustrated byTony Kenyon. Brookfield, CT: Copper Beech Books,1998.

Parker, Steve. Albert Einstein and Relativity. New York:Chelsea House, 1995.

Robson, Pam. Clocks, Scales, and Measurements. NewYork: Gloucester Press, 1993.

Rutherford, F. James; Gerald Holton; and Fletcher G.Watson. Project Physics. New York: Holt, Rinehart,and Winston, 1981.

Swisher, Clarice. Relativity: Opposing Viewpoints. SanDiego, CA: Greenhaven Press, 1990.




K INEMAT ICS ANDDYNAM ICSKinematics and Dynamics

CONCEPTWebster’s defines physics as “a science that dealswith matter and energy and their interactions.”Alternatively, physics can be described as thestudy of matter and motion, or of matter inmo-tion. Whatever the particulars of the definition,physics is among the most fundamental of disci-plines, and hence, the rudiments of physics areamong the most basic building blocks for think-ing about the world. Foundational to an under-standing of physics are kinematics, the explana-tion of how objects move, and dynamics, thestudy of why they move. Both are part of a largerbranch of physics called mechanics, the study ofbodies in motion. These are subjects that maysound abstract, but in fact, are limitless in theirapplications to real life.

HOW IT WORKS

The Place of Physics in theSciences

Physics may be regarded as the queen of the sci-ences, not because it is “better” than chemistry orastronomy, but because it is the foundation onwhich all others are built. The internal and inter-personal behaviors that are the subject of thesocial sciences (psychology, anthropology, sociol-ogy, and so forth) could not exist without thebiological framework that houses the humanconsciousness. Yet the human body and otherelements studied by the biological and medicalsciences exist within a larger environment, theframework for earth sciences, such as geology.

Earth sciences belong to a larger grouping ofphysical sciences, each more fundamental in con-cerns and broader in scope. Earth, after all, is but

one corner of the realm studied by astronomy;and before a universe can even exist, there mustbe interactions of elements, the subject of chem-istry. Yet even before chemicals can react, theyhave to do so within a physical framework—therealm of the most basic science—physics.

The Birth of Physics inGreece

THE FIRST HYPOTHESIS. In-deed, physics stands in relation to the sciences asphilosophy does to thought itself: without phi-losophy to provide the concept of concepts, itwould be impossible to develop a consistentworldview in which to test ideas. It is no accident,then, that the founder of the physical scienceswas also the world’s first philosopher, Thales (c.625?-547? B.C.) of Miletus in Greek Asia Minor(now part of Turkey.) Prior to Thales’s time, reli-gious figures and mystics had made statementsregarding ethics or the nature of deity, but nonehad attempted statements concerning the funda-mental nature of reality.

For instance, the Bible offers a story ofEarth’s creation in the Book of Genesis whichwas well-suited to the understanding of people inthe first millennium before Christ. But the writerof the biblical creation story made no attempt toexplain how things came into being. He was con-cerned, rather, with showing that God had willedthe existence of all physical reality by callingthings into being—for example, by saying, “Letthere be light.”

Thales, on the other hand, made a genuinephilosophical and scientific statement when hesaid that “Everything is water.” This was the firsthypothesis, a statement capable of being scientif-


Kinematicsand Dynamics

MATHEMATICS, MEASURE-

MENT, AND MATTER. In the two cen-turies after Thales’s death, several other thinkersadvanced understanding of physical reality inone way or another. Pythagoras (c. 580-c. 500B.C.) taught that everything could be quantified,or related to numbers. Though he entangled thisidea with mysticism and numerology, the con-cept itself influenced the idea that physicalprocesses could be measured. Likewise, therewere flaws at the heart of the paradoxes put forthby Zeno of Elea (c. 495-c. 430 B.C.), who set outto prove that motion was impossible—yet he wasalso the first thinker to analyze motion seriously.

In one of Zeno’s paradoxes, he referred to anarrow being shot from a bow. At every momentof its flight, it could be said that the arrow was atrest within a space equal to its length. Though itwould be some 2,500 years before slow-motionphotography, in effect he was asking his listenersto imagine a snapshot of the arrow in flight. If itwas at rest in that “snapshot,” he asked, so tospeak, and in every other possible “snapshot,”when did the arrow actually move? These para-doxes were among the most perplexing questionsof premodern times, and remain a subject ofinquiry even today.

In fact, it seems that Zeno unwittingly (forthere is no reason to believe that he deliberatelydeceived his listeners) inserted an error in hisparadoxes by treating physical space as though itwere composed of an infinite number of points.In the ideal world of geometric theory, a pointtakes up no space, and therefore it is correct tosay that a line contains an infinite number ofpoints; but this is not the case in the real world,where a “point” has some actual length. Hence, ifthe number of points on Earth were limitless, sotoo would be Earth itself.

Zeno’s contemporary Leucippus (c. 480-c.420 B.C.) and his student Democritus (c. 460-370B.C.) proposed a new and highly advanced modelfor the tiniest point of physical space: the atom. Itwould be some 2,300 years, however, beforephysicists returned to the atomic model.

Aristotle’s Flawed Physics

The study of matter and motion began to takeshape with Aristotle (384-322 B.C.); yet, thoughhis Physics helped establish a framework for thediscipline, his errors are so profound that anypraise must be qualified. Certainly, Aristotle was


ically tested for accuracy. Thales’s pronounce-ment did not mean he believed all things werenecessarily made of water, literally. Rather, heappears to have been referring to a general ten-dency of movement: that the whole world is in afluid state.

ATTEMPTING TO UNDER-

STAND PHYSICAL REALITY. Whilewe can respect Thales’s statement for its trulyearth-shattering implications, we may be temptedto read too much into it. Nonetheless, it is strik-ing that he compared physical reality to water. Onthe one hand, there is the fact that water is essen-tial to all life, and pervades Earth—but that is asubject more properly addressed by the realms ofchemistry and the biological sciences. Perhaps ofmore interest to the physicist is the allusion to afluid nature underlying all physical reality.

The physical realm is made of matter, whichappears in four states: solid, liquid, gas, and plas-ma. The last of these is not the same as bloodplasma: containing many ionized atoms or mol-ecules which exhibit collective behavior, plasmais the substance from which stars, for instance,are composed. Though not plentiful on Earth,within the universe it may be the most commonof all four states. Plasma is akin to gas, but differ-ent in molecular structure; the other three statesdiffer at the molecular level as well.

Nonetheless, it is possible for a substancesuch as water—genuine H2O, not the figurativewater of Thales—to exist in liquid, gas, or solidform, and the dividing line between these is notalways fixed. In fact, physicists have identified aphenomenon known as the triple point: at a cer-tain temperature and pressure, a substance canbe solid, liquid, and gas all at once!

The above statement shows just how chal-lenging the study of physical reality can be, andindeed, these concepts would be far beyond thescope of Thales’s imagination, had he been pre-sented with them. Though he almost certainlydeserves to be called a “genius,” he lived in aworld that viewed physical processes as a productof the gods’ sometimes capricious will. Thebehavior of the tides, for instance, was attributedto Poseidon. Though Thales’s statement beganthe process of digging humanity out from underthe burden of superstition that had impeded sci-entific progress for centuries, the road forwardwould be a long one.


Kinematicsand

Dynamics

one of the world’s greatest thinkers, who origi-nated a set of formalized realms of study. How-ever, in Physics he put forth an erroneous expla-nation of matter and motion that still prevailedin Europe twenty centuries later.

Actually, Aristotle’s ideas disappeared in thelate ancient period, as learning in general came toa virtual halt in Europe. That his writings—which on the whole did much more to advancethe progress of science than to impede it—sur-vived at all is a tribute to the brilliance of Arab,rather than European, civilization. Indeed, it wasin the Arab world that the most important scien-tific work of the medieval period took place.Only after about 1200 did Aristotelian thinkingonce again enter Europe, where it replaced acrude jumble of superstitions that had been sub-stituted for learning.

THE FOUR ELEMENTS. Accord-ing to Aristotelian physics, all objects consisted,in varying degrees, of one or more elements: air,fire, water, and earth. In a tradition that wentback to Thales, these elements were not necessar-ily pure: water in the everyday world was com-posed primarily of the element water, but alsocontained smaller amounts of the other ele-ments. The planets beyond Earth were said to bemade up of a “fifth element,” or quintessence, ofwhich little could be known.

The differing weights and behaviors of theelements governed the behavior of physicalobjects. Thus, water was lighter than earth, forinstance, but heavier than air or fire. It was due tothis difference in weight, Aristotle reasoned, thatcertain objects fall faster than others: a stone, forinstance, because it is composed primarily ofearth, will fall much faster than a leaf, which hasmuch less earth in it.

Aristotle further defined “natural” motion asthat which moved an object toward the center ofthe Earth, and “violent” motion as anything thatpropelled an object toward anything other thanits “natural” destination. Hence, all horizontal orupward motion was “violent,” and must be thedirect result of a force. When the force wasremoved, the movement would end.

ARISTOTLE’S MODEL OF THE

UNIVERSE. From the fact that Earth’s cen-ter is the destination of all “natural” motion, it iseasy to comprehend the Aristotelian cosmology,or model of the universe. Earth itself was in thecenter, with all other bodies (including the Sun)


revolving around it. Though in constant move-ment, these heavenly bodies were always in their“natural” place, because they could only move onthe firmly established—almost groove-like—paths of their orbits around Earth. This in turnmeant that the physical properties of matter andmotion on other planets were completely differ-ent from the laws that prevailed on Earth.

Of course, virtually every precept within theAristotelian system is incorrect, and Aristotlecompounded the influence of his errors by pro-moting a disdain for quantification. Specifically,he believed that mathematics had little value fordescribing physical processes in the real world,and relied instead on pure observation withoutattempts at measurement.

Moving Beyond Aristotle

Faulty as Aristotle’s system was, however, it pos-sessed great appeal because much of it seemed tofit with the evidence of the senses. It is not at allimmediately apparent that Earth and the otherplanets revolve around the Sun, nor is it obviousthat a stone and a leaf experience the same accel-eration as they fall toward the ground. In fact,quite the opposite appears to be the case: aseveryone knows, a stone falls faster than a leaf.Therefore, it would seem reasonable—on the

ARISTOTLE. (The Bettmann Archive. Reproduced by permission.)



surface of it, at least—to accept Aristotle’s con-clusion that this difference results purely from adifference in weight.

Today, of course, scientists—and indeed,even people without any specialized scientificknowledge—recognize the lack of merit in theAristotelian system. The stone does fall fasterthan the leaf, but only because of air resistance,not weight. Hence, if they fell in a vacuum (aspace otherwise entirely devoid of matter, includ-ing air), the two objects would fall at exactly thesame rate.

As with a number of truths about matterand motion, this is not one that appears obvious,yet it has been demonstrated. To prove this high-ly nonintuitive hypothesis, however, required anapproach quite different from Aristotle’s—anapproach that involved quantification and theseparation of matter and motion into variouscomponents. This was the beginning of realprogress in physics, and in a sense may be regard-ed as the true birth of the discipline. In the yearsthat followed, understanding of physics wouldgrow rapidly, thanks to advancements of manyindividuals; but their studies could not have beenpossible without the work of one extraordinarythinker who dared to question the Aristotelianmodel.


Kinematics: How ObjectsMove

By the sixteenth century, the Aristotelian world-view had become so deeply ingrained that fewEuropean thinkers would have considered thepossibility that it could be challenged. Professorsall over Europe taught Aristotle’s precepts to theirstudents, and in this regard the University of Pisain Italy was no different. Yet from its classroomswould emerge a young man who not only ques-tioned, but ultimately overturned the Aris-totelian model: Galileo Galilei (1564-1642.)

Challenges to Aristotle had been slowlygrowing within the scientific communities of theArab and later the European worlds during thepreceding millennium. Yet the ideas that mostinfluenced Galileo in his break with Aristotlecame not from a physicist but from anastronomer, Nicolaus Copernicus (1473-1543.) Itwas Copernicus who made a case, based purelyon astronomical observation, that the Sun andnot Earth was at the center of the universe.

Galileo embraced this model of the cosmos,but was later forced to renounce it on ordersfrom the pope in Rome. At that time, of course,the Catholic Church remained the single mostpowerful political entity in Europe, and itsendorsement of Aristotelian views—whichphilosophers had long since reconciled withChristian ideas—is a measure of Aristotle’simpact on thinking.

GALILEO’S REVOLUTION IN

PHYSICS. After his censure by the Church,Galileo was placed under house arrest and wasforbidden to study astronomy. Instead he turnedto physics—where, ironically, he struck the blowthat would destroy the bankrupt scientific systemendorsed by Rome. In 1638, he published Dis-courses and Mathematical Demonstrations Con-cerning Two New Sciences Pertaining to Mathe-matics and Local Motion, a work usually referredto as Two New Sciences. In it, he laid the ground-work for physics by emphasizing a new methodthat included experimentation, demonstration,and quantification of results.

In this book—highly readable for a work ofphysics written in the seventeenth century—Galileo used a dialogue, an established formatamong philosophers and scientists of the past.


GALILEO. (Archive Photos, Inc. Reproduced by permission.)


Kinematicsand

Dynamics

The character of Salviati argued for Galileo’sideas and Simplicio for those of Aristotle, whilethe genial Sagredo sat by and made occasionalcomments. Through Salviati, Galileo chose tochallenge Aristotle on an issue that to most peo-ple at the time seemed relatively settled: the claimthat objects fall at differing speeds according totheir weight.

In order to proceed with his aim, Galileo hadto introduce a number of innovations, andindeed, he established the subdiscipline of kine-matics, or how objects move. Aristotle had indi-cated that when objects fall, they fall at the samerate from the moment they begin to fall untilthey reach their “natural” position. Galileo, onthe other hand, suggested an aspect of motion,unknown at the time, that became an integralpart of studies in physics: acceleration.

Scalars and Vectors

Even today, many people remain confused as towhat acceleration is. Most assume that accelera-tion means only an increase in speed, but in factthis represents only one of several examples ofacceleration. Acceleration is directly related tovelocity, often mistakenly identified with speed.

In fact, speed is what scientists today wouldcall a scalar quantity, or one that possesses mag-nitude but no specific direction. Speed is the rateat which the position of an object changes over agiven period of time; thus people say “miles (orkilometers) per hour.” A story problem concern-ing speed might state that “A train leaves NewYork City at a rate of 60 miles (96.6 km/h). Howfar will it have traveled in 73 minutes?”

Note that there is no reference to direction,whereas if the story problem concerned veloci-ty—a vector, that is, a quantity involving bothmagnitude and direction—it would includesome crucial qualifying phrase after “New YorkCity”: “for Boston,” perhaps, or “northward.” Inpractice, the difference between speed and veloc-ity is nearly as large as that between a math prob-lem and real life: few people think in terms ofdriving 60 miles, for instance, without also con-sidering the direction they are traveling.

RESULTANTS. One can apply thesame formula with velocity, though the process ismore complicated. To obtain change in distance,one must add vectors, and this is best done bymeans of a diagram. You can draw each vector asan arrow on a graph, with the tail of each vector

at the head of the previous one. Then it is possi-ble to draw a vector from the tail of the first tothe head of the last. This is the sum of the vec-tors, known as a resultant, which measures thenet change.

Suppose, for instance, that a car travels east 4mi (6.44 km), then due north 3 mi (4.83 km).This may be drawn on a graph with four unitsalong the x axis, then 3 units along the y axis,making two sides of a triangle. The number ofsides to the resulting shape is always one morethan the number of vectors being added; the finalside is the resultant. From the tail of the first seg-ment, a diagonal line drawn to the head of thelast will yield a measurement of 5 units—theresultant, which in this case would be equal to 5mi (8 km) in a northeasterly direction.

VELOCITY AND ACCELERA-

TION. The directional component of velocitymakes it possible to consider forms of motionother than linear, or straight-line, movement.Principal among these is circular, or rotationalmotion, in which an object continually changesdirection and thus, velocity. Also significant isprojectile motion, in which an object is thrown,shot, or hurled, describing a path that is a combi-nation of horizontal and vertical components.

Furthermore, velocity is a key component inacceleration, which is defined as a change invelocity. Hence, acceleration can mean one of fivethings: an increase in speed with no change indirection (the popular, but incorrect, definitionof the overall concept); a decrease in speed withno change in direction; a decrease or increase ofspeed with a change in direction; or a change indirection with no change in speed. If a car speedsup or slows down while traveling in a straightline, it experiences acceleration. So too does anobject moving in rotational motion, even if itsspeed does not change, because its direction willchange continuously.

Dynamics: Why Objects Move

GALILEO’S TEST. To return toGalileo, he was concerned primarily with a spe-cific form of acceleration, that which occurs dueto the force of gravity. Aristotle had provided anexplanation of gravity—if a highly flawed one—with his claim that objects fall to their “natural”position; Galileo set out to develop the first trulyscientific explanation concerning how objects fallto the ground.




According to Galileo’s predictions, two metalballs of differing sizes would fall with the samerate of acceleration. To test his hypotheses, how-ever, he could not simply drop two balls from arooftop—or have someone else do so while hestood on the ground—and measure their rate offall. Objects fall too fast, and lacking sophisticat-ed equipment available to scientists today, he hadto find another means of showing the rate atwhich they fell.

This he did by resorting to a method Aristo-tle had shunned: the use of mathematics as ameans of modeling the behavior of objects. Thisis such a deeply ingrained aspect of science todaythat it is hard to imagine a time when anyonewould have questioned it, and that very fact is atribute to Galileo’s achievement. Since he couldnot measure speed, he set out to find an equationrelating total distance to total time. Through adetailed series of steps, Galileo discovered that inuniform or constant acceleration from rest—thatis, the acceleration he believed an object experi-ences due to gravity—there is a proportionalrelationship between distance and time.

With this mathematical model, Galileocould demonstrate uniform acceleration. He didthis by using an experimental model for whichobservation was easier than in the case of twofalling bodies: an inclined plane, down which herolled a perfectly round ball. This allowed him toextrapolate that in free fall, though velocity wasgreater, the same proportions still applied andtherefore, acceleration was constant.

POINTING THE WAY TOWARD

NEWTON. The effects of Galileo’s system wereenormous: he demonstrated mathematically thatacceleration is constant, and established a methodof hypothesis and experiment that became thebasis of subsequent scientific investigation. Hedid not, however, attempt to calculate a figure forthe acceleration of bodies in free fall; nor did heattempt to explain the overall principle of gravity,or indeed why objects move as they do—the focusof a subdiscipline known as dynamics.

At the end of Two New Sciences, Sagredooffered a hopeful prediction: “I really believethat... the principles which are set forth in this lit-tle treatise will, when taken up by speculativeminds, lead to another more remarkableresult....” This prediction would come true withthe work of a man who, because he lived in asomewhat more enlightened time—and because

he lived in England, where the pope had nopower—was free to explore the implications ofhis physical studies without fear of Rome’s inter-vention. Born in the very year Galileo died, hisname was Sir Isaac Newton (1642-1727.)

NEWTON’S THREE LAWS OF

MOTION. In discussing the movement of theplanets, Galileo had coined the term inertia todescribe the tendency of an object in motion toremain in motion, and an object at rest to remainat rest. This idea would be the starting point ofNewton’s three laws of motion, and Newtonwould greatly expand on the concept of inertia.

The three laws themselves are so significantto the understanding of physics that they aretreated separately elsewhere in this volume; herethey are considered primarily in terms of theirimplications regarding the larger topic of matterand motion.

Introduced by Newton in his Principia(1687), the three laws are:

• First law of motion: An object at rest willremain at rest, and an object in motion willremain in motion, at a constant velocityunless or until outside forces act upon it.

• Second law of motion: The net force actingupon an object is a product of its mass mul-tiplied by its acceleration.

• Third law of motion: When one objectexerts a force on another, the second objectexerts on the first a force equal in magni-tude but opposite in direction.

These laws made final the break with Aristo-tle’s system. In place of “natural” motion, Newtonpresented the concept of motion at a uniformvelocity—whether that velocity be a state of restor of uniform motion. Indeed, the closest thing to“natural” motion (that is, true “natural” motion)is the behavior of objects in outer space. There,free from friction and away from the gravitation-al pull of Earth or other bodies, an object set inmotion will remain in motion forever due to itsown inertia. It follows from this observation, inci-dentally, that Newton’s laws were and are univer-sal, thus debunking the old myth that the physicalproperties of realms outside Earth are fundamen-tally different from those of Earth itself.

MASS AND GRAVITATIONAL

ACCELERATION. The first law establishesthe principle of inertia, and the second law makesreference to the means by which inertia is meas-ured: mass, or the resistance of an object to a



Kinematicsand

Dynamics


change in its motion—including a change invelocity. Mass is one of the most fundamentalnotions in the world of physics, and it too is thesubject of a popular misconception—one whichconfuses it with weight. In fact, weight is a force,equal to mass multiplied by the acceleration dueto gravity.

It was Newton, through a complicated seriesof steps he explained in his Principia, who madepossible the calculation of that acceleration—anact of quantification that had eluded Galileo. Thefigure most often used for gravitational accelera-tion at sea level is 32 ft (9.8 m) per secondsquared. This means that in the first second, anobject falls at a velocity of 32 ft per second, but its

velocity is also increasing at a rate of 32 ft per sec-ond per second. Hence, after 2 seconds, its veloc-ity will be 64 ft (per second; after 3 seconds 96 ftper second, and so on.

Mass does not vary anywhere in the uni-verse, whereas weight changes with any change inthe gravitational field. When United States astro-naut Neil Armstrong planted the American flagon the Moon in 1969, the flagpole (and indeedArmstrong himself) weighed much less than onEarth. Yet it would have required exactly the sameamount of force to move the pole (or, again,Armstrong) from side to side as it would have onEarth, because their mass and therefore theirinertia had not changed.

ACCELERATION: A change in velocity.

DYNAMICS: The study of why objects

move as they do; compare with kinematics.

FORCE: The product of mass multi-

plied by acceleration.

HYPOTHESIS: A statement capable of

being scientifically tested for accuracy.

INERTIA: The tendency of an object in

motion to remain in motion, and of an

object at rest to remain at rest.

KINEMATICS: The study of how

objects move; compare with dynamics.

MASS: A measure of inertia, indicating

the resistance of an object to a change in its

motion—including a change in velocity.

MATTER: The material of physical real-

ity. There are four basic states of matter:

solid, liquid, gas, and plasma.

MECHANICS: The study of bodies in

motion.

RESULTANT: The sum of two or more

vectors, which measures the net change in

distance and direction.

SCALAR: A quantity that possesses

only magnitude, with no specific direction.

Mass, time, and speed are all scalars. The

opposite of a scalar is a vector.

SPEED: The rate at which the position

of an object changes over a given period of

time.

VACUUM: Space entirely devoid of

matter, including air.

VECTOR: A quantity that possesses

both magnitude and direction. Velocity,

acceleration, and weight (which involves

the downward acceleration due to gravity)

are examples of vectors. Its opposite is a

scalar.

VELOCITY: The speed of an object in a

particular direction.

WEIGHT: A measure of the gravitation-

al force on an object; the product of mass

multiplied by the acceleration due to grav-

ity. (The latter is equal to 32 ft or 9.8 m per

second per second, or 32 ft/9.8 m per sec-

ond squared.)

KEY TERMS



Beyond Mechanics

The implications of Newton’s three laws go farbeyond what has been described here; but again,these laws, as well as gravity itself, receive a muchmore thorough treatment elsewhere in this vol-ume. What is important in this context is thegradually unfolding understanding of matter andmotion that formed the basis for the study ofphysics today.

After Newton came the Swiss mathematicianand physicist Daniel Bernoulli (1700-1782), whopioneered another subdiscipline, fluid dynamics,which encompasses the behavior of liquids andgases in contact with solid objects. Air itself is anexample of a fluid, in the scientific sense of theterm. Through studies in fluid dynamics, itbecame possible to explain the principles of airresistance that cause a leaf to fall more slowlythan a stone—even though the two are subject toexactly the same gravitational acceleration, andwould fall at the same speed in a vacuum.

EXTENDING THE REALM OF

PHYSICAL STUDY. The work of Galileo,Newton, and Bernoulli fit within one of fivemajor divisions of classical physics: mechanics,or the study of matter, motion, and forces. Theother principal divisions are acoustics, or studiesin sound; optics, the study of light; thermody-namics, or investigations regarding the relation-ships between heat and other varieties of energy;and electricity and magnetism. (These subjects,and subdivisions within them, also receive exten-sive treatment elsewhere in this book.)

Newton identified one type of force, gravita-tion, but in the period leading up to the time ofScottish physicist James Clerk Maxwell (1831-1879), scientists gradually became aware of a newfundamental interaction in the universe. Build-ing on studies of numerous scientists, Maxwellhypothesized that electricity and magnetism arein fact differing manifestations of a second vari-ety of force, electromagnetism.

MODERN PHYSICS. The term clas-sical physics, used above, refers to the subjects ofstudy from Galileo’s time through the end of thenineteenth century. Classical physics deals pri-marily with subjects that can be discerned by thesenses, and addressed processes that could beobserved on a large scale. By contrast, modern

physics, which had its beginnings with the workof Max Planck (1858-1947), Albert Einstein(1879-1955), Niels Bohr (1885-1962), and othersat the beginning of the twentieth century,addresses quite a different set of topics.

Modern physics is concerned primarily withthe behavior of matter at the molecular, atomic,or subatomic level, and thus its truths cannot begrasped with the aid of the senses. Nor is classicalphysics much help in understanding modernphysics. The latter, in fact, recognizes two forcesunknown to classical physicists: weak nuclearforce, which causes the decay of some subatomicparticles, and strong nuclear force, which bindsthe nuclei of atoms with a force 1 trillion (1012)times as great as that of the weak nuclear force.

Things happen in the realm of modernphysics that would have been inconceivable toclassical physicists. For instance, according toquantum mechanics—first developed byPlanck—it is not possible to make a measurementwithout affecting the object (e.g., an electron)being measured.Yet even atomic, nuclear, and par-ticle physics can be understood in terms of theireffects on the world of experience: challenging asthese subjects are, they still concern—thoughwithin a much more complex framework—thephysical fundamentals of matter and motion.

WHERE TO LEARN MORE

Ballard, Carol. How Do We Move? Austin, TX: RaintreeSteck-Vaughn, 1998.


Fleisher, Paul. Objects in Motion: Principles of ClassicalMechanics. Minneapolis, MN: Lerner Publications,2002.

Hewitt, Sally. Forces Around Us. New York: Children’sPress, 1998.

Measure for Measure: Sites That Do the Work for You(Web site). <http://www.wolinskyweb.com/meas-ure.html> (March 7, 2001).

Motion, Energy, and Simple Machines (Web site).<http://www.necc.mass.edu/MRVIS/MR3_13/start.html> (March 7, 2001).

Physlink.com (Web site). <http://www.physlink.com>(March 7, 2001).


Wilson, Jerry D. Physics: Concepts and Applications, sec-ond edition. Lexington, MA: D. C. Heath, 1981.




D ENS I T Y AND VOLUMEDensity and Volume

CONCEPTDensity and volume are simple topics, yet inorder to work within any of the hard sciences, itis essential to understand these two types ofmeasurement, as well as the fundamental quanti-ty involved in conversions between them—mass.Measuring density makes it possible to distin-guish between real gold and fake gold, and mayalso give an astronomer an important clueregarding the internal composition of a planet.

HOW IT WORKSThere are four fundamental standards by whichmost qualities in the physical world can be meas-ured: length, mass, time, and electric current.The volume of a cube, for instance, is a unit oflength cubed: the length is multiplied by thewidth and multiplied by the height. Width andheight, however, are not distinct standards ofmeasurement: they are simply versions of length,distinguished by their orientation. Whereaslength is typically understood as a distance alongan x-axis in one-dimensional space, width adds asecond dimension, and height a third.

Of particular concern within this essay arelength and mass, since volume is measured interms of length, and density in terms of the ratiobetween mass and volume. Elsewhere in thisbook, the distinction between mass and weighthas been presented numerous times from thestandpoint of a person whose mass and weight aremeasured on Earth, and again on the Moon. Mass,of course, does not change, whereas weight does,due to the difference in gravitational force exertedby Earth as compared with that of its satellite, theMoon. But consider instead the role of the funda-

mental quality, mass, in determining this signifi-cantly less fundamental property of weight.

According to the second law of motion,weight is a force equal to mass multiplied byacceleration. Acceleration, in turn, is equal tochange in velocity divided by change in time.Velocity, in turn, is equal to distance (a form oflength) divided by time. If one were to expressweight in terms of l, t, and m, with these repre-senting, respectively, the fundamental propertiesof length, time, and mass, it would be expressed as

—clearly, a much more complicated formu-la than that of mass!

Mass

So what is mass? Again, the second law ofmotion, derived by Sir Isaac Newton (1642-1727), is the key: mass is the ratio of force toacceleration. This topic, too, is discussed innumerous places throughout this book; what isactually of interest here is a less precise identifi-cation of mass, also made by Newton.

Before formulating his laws of motion, New-ton had used a working definition of mass as thequantity of matter an object possesses. This is notof much value for making calculations or meas-urements, unlike the definition in the second law.Nonetheless, it serves as a useful reminder ofmatter’s role in the formula for density.

Matter can be defined as a physical sub-stance not only having mass, but occupyingspace. It is composed of atoms (or in the case ofsubatomic particles, it is part of an atom), and is

M • Dt 2


Density andVolume


convertible with energy. The form or state ofmatter itself is not important: on Earth it is pri-marily observed as a solid, liquid, or gas, but itcan also be found (particularly in other parts ofthe universe) in a fourth state, plasma.

Yet there are considerable differences amongtypes of matter—among various elements andstates of matter. This is apparent if one imaginesthree gallon jugs, one containing water, the sec-ond containing helium, and the third containingiron filings. The volume of each is the same, butobviously, the mass is quite different.

The reason, of course, is that at a molecularlevel, there is a difference in mass between thecompound H2O and the elements helium andiron. In the case of helium, the second-lightest ofall elements after hydrogen, it would take a greatdeal of helium for its mass to equal that of iron.In fact, it would take more than 43,000 gallons ofhelium to equal the mass of the iron in one gal-lon jug!

Density

Rather than comparing differences in molecularmass among the three substances, it is easier toanalyze them in terms of density, or mass divid-

ed by volume. It so happens that the three itemsrepresent the three states of matter on Earth: liq-uid (water), solid (iron), and gas (helium). Forthe most part, solids tend to be denser than liq-uids, and liquids denser than gasses.

One of the interesting things about density,as distinguished from mass and volume, is that ithas nothing to do with the amount of material. Akilogram of iron differs from 10 kilograms ofiron both in mass and volume, but the density ofboth samples is the same. Indeed, as discussedbelow, the known densities of various materialsmake it possible to determine whether a sampleof that material is genuine.

Volume

Mass, because of its fundamental nature, issometimes hard to comprehend, and densityrequires an explanation in terms of mass and vol-ume. Volume, on the other hand, appears to bequite straightforward—and it is, when one isdescribing a solid of regular shape. In other situ-ations, however, volume is more complicated.

As noted earlier, the volume of a cube can beobtained simply by multiplying length by widthby height. There are other means for measuring

HOW DOES A GIGANTIC STEEL SHIP, SUCH AS THE SUPERTANKER PICTURED HERE, STAY AFLOAT, EVEN THOUGH IT

HAS A WEIGHT DENSITY FAR GREATER THAN THE WATER BELOW IT? THE ANSWER LIES IN ITS CURVED HULL, WHICH

CONTAINS A LARGE AMOUNT OF OPEN SPACE AND ALLOWS THE SHIP TO SPREAD ITS AVERAGE DENSITY TO A LOWER

LEVEL THAN THE WATER. (Photograph by Vince Streano/Corbis. Reproduced by permission.)


Density andVolume


the volume of other straight-sided objects, such

as a pyramid. That formula applies, indeed, for

any polyhedron (a three-dimensional closed

solid bounded by a set number of plane figures)

that constitutes a modified cube in which the

lengths of the three dimensions are unequal—

that is, an oblong shape.

For a cylinder or sphere, volume measure-

ments can be obtained by applying formulae

involving radius (r) and the constant π, roughly

equal to 3.14. The formula for volume of a cylinder

is V = πr2h, where h is the height. A sphere’s volume

can be obtained by the formula (4/3)πr3. Even the

volume of a cone can be easily calculated: it is one-

third that of a cylinder of equal base and height.


Measuring Volume

What about the volume of a solid that is irregu-lar in shape? Some irregularly shaped objects,such as a scooter, which consists primarily of oneround wheel and a number of oblong shapes, canbe measured by separating them into regularshapes. Calculus may be employed with morecomplex problems to obtain the volume of anirregular shape—but the most basic method issimply to immerse the object in water. This pro-cedure involves measuring the volume of thewater before and after immersion, and calculat-ing the difference. Of course, the object being

SINCE SCIENTISTS KNOW EARTH’S MASS AS WELL AS ITS VOLUME, THEY ARE EASILY ABLE TO COMPUTE ITS DENSI-TY—APPROXIMATELY 5 G/CM3. (Corbis. Reproduced by permission.)


Density andVolume

measured cannot be water-soluble; if it is, its vol-

ume must be measured in a non-water-based liq-

uid such as alcohol.

Measuring liquid volumes is easy, given the

fact that liquids have no definite shape, and will

simply take the shape of the container in which

they are placed. Gases are similar to liquids in the

sense that they expand to fit their container;

however, measurement of gas volume is a more

involved process than that used to measure either

liquids or solids, because gases are highly respon-

sive to changes in temperature and pressure.

If the temperature of water is raised from its

freezing point to its boiling point (32° to 212°F or

0 to 100°C), its volume will increase by only 2%.

If its pressure is doubled from 1 atm (defined as

normal air pressure at sea level—14.7 pounds-

per-square-inch or 1.013 x 105 Pa) to 2 atm, vol-

ume will decrease by only 0.01%.

Yet, if air were heated from 32° to 212°F, its

volume would increase by 37%; and if its pres-

sure were doubled from 1 atm to 2, its volume

would decrease by 50%. Not only do gases

respond dramatically to changes in temperature

and pressure, but also, gas molecules tend to be

non-attractive toward one another—that is, they

do not tend to stick together. Hence, the concept

of “volume” involving gas is essentially meaning-

less, unless its temperature and pressure are

known.

Buoyancy: Volume and Density

Consider again the description above, of an

object with irregular shape whose volume is

measured by immersion in water. This is not the

only interesting use of water and solids when

dealing with volume and density. Particularly

intriguing is the concept of buoyancy expressed

in Archimedes’s principle.

More than twenty-two centuries ago, the

Greek mathematician, physicist, and inventor

Archimedes (c. 287-212 B.C.) received orders

from the king of his hometown—Syracuse, a

Greek colony in Sicily—to weigh the gold in the

royal crown. According to legend, it was while

bathing that Archimedes discovered the principle

that is today named after him. He was so excited,

legend maintains, that he jumped out of his bath

and ran naked through the streets of Syracuseshouting “Eureka!” (I have found it).

What Archimedes had discovered was, inshort, the reason why ships float: because thebuoyant, or lifting, force of an object immersedin fluid is equal to the weight of the fluid dis-placed by the object.

HOW A STEEL SHIP FLOATS

ON WATER. Today most ships are made ofsteel, and therefore, it is even harder to under-stand why an aircraft carrier weighing manythousands of tons can float. After all, steel has aweight density (the preferred method for meas-uring density according to the British system ofmeasures) of 480 pounds per cubic foot, and adensity of 7,800 kilograms-per-cubic-meter. Bycontrast, sea water has a weight density of 64pounds per cubic foot, and a density of 1,030kilograms-per-cubic-meter.

This difference in density should mean thatthe carrier would sink like a stone—and indeed itwould, if all the steel in it were hammered flat. Asit is, the hull of the carrier (or indeed of any sea-worthy ship) is designed to displace or move aquantity of water whose weight is greater thanthat of the vessel itself. The weight of the displacedwater—that is, its mass multiplied by the down-ward acceleration due to gravity—is equal to thebuoyant force that the ocean exerts on the ship. Ifthe ship weighs less than the water it displaces, itwill float; but if it weighs more, it will sink.

Put another way, when the ship is placed inthe water, it displaces a certain quantity of waterwhose weight can be expressed in terms of Vdg—volume multiplied by density multiplied by thedownward acceleration due to gravity. The densi-ty of sea water is a known figure, as is g (32 ft or9.8 m/sec2); thus the only variable for the waterdisplaced is its volume.

For the buoyant force on the ship, g will ofcourse be the same, and the value of V will be thesame as for the water. In order for the ship tofloat, then, its density must be much less thanthat of the water it has displaced. This can beachieved by designing the ship in order to maxi-mize displacement. The steel is spread over aslarge an area as possible, and the curved hull,when seen in cross section, contains a relativelylarge area of open space. Obviously, the densityof this space is much less than that of water; thus,the average density of the ship is greatly reduced,which enables it to float.



Density andVolume


Comparing Densities

As noted several times, the densities of numerous

materials are known quantities, and can be easily

compared. Some examples of density, all

expressed in terms of kilograms per cubic meter,

are:

• Hydrogen: 0.09 kg/m3

• Air: 1.3 kg/m3

• Oak: 720 kg/m3

• Ethyl alcohol: 790 kg/m3

• Ice: 920 kg/m3

• Pure water: 1,000 kg/m3

• Concrete: 2,300 kg/m3

• Iron and steel: 7,800 kg/m3

• Lead: 11,000 kg/m3

• Gold: 19,000 kg/m3

Note that pure water (as opposed to seawater, which is 3% denser) has a density of 1,000kilograms per cubic meter, or 1 gram per cubiccentimeter. This value is approximate; however,at a temperature of 39.2°F (4°C) and under nor-mal atmospheric pressure, it is exact, and so,water is a useful standard for measuring the spe-cific gravity of other substances.

SPECIFIC GRAVITY AND THE

DENSITIES OF PLANETS. Specificgravity is the ratio between the densities of twoobjects or substances, and it is expressed as anumber without units of measure. Due to thevalue of 1 g/cm3 for water, it is easy to determinethe specific gravity of a given substance, whichwill have the same number value as its density.For example, the specific gravity of concrete,which has a density of 2.3 g/cm3, is 2.3. The spe-

ARCHIMEDES’S PRINCIPLE: A rule

of physics which holds that the buoyant

force of an object immersed in fluid is

equal to the weight of the fluid displaced

by the object. It is named after the Greek

mathematician, physicist, and inventor

Archimedes (c. 287-212 B.C.), who first

identified it.

BUOYANCY: The tendency of an object

immersed in a fluid to float. This can be

explained by Archimedes’s principle.

DENSITY: The ratio of mass to vol-

ume—in other words, the amount of mat-

ter within a given area.

MASS: According to the second law of

motion, mass is the ratio of force to acceler-

ation. Mass may likewise be defined, though

much less precisely, as the amount of mat-

ter an object contains. Mass is also the

product of volume multiplied by density.

MATTER: Physical substance that occu-

pies space, has mass, is composed of atoms

(or in the case of subatomic particles, is

part of an atom), and is convertible into

energy.

SPECIFIC GRAVITY: The density of

an object or substance relative to the densi-

ty of water; or more generally, the ratio

between the densities of two objects or

substances.

VOLUME: The amount of three-

dimensional space an object occupies. Vol-

ume is usually expressed in cubic units of

length.

WEIGHT DENSITY: The proper term

for density within the British system of

weights and measures. The pound is a unit

of weight rather than of mass, and thus

British units of density are usually ren-

dered in terms of weight density—that is,

pounds-per-cubic-foot. By contrast, the

metric or international units measure mass

density (referred to simply as “density”),

which is rendered in terms of kilograms-

per-cubic-meter, or grams-per-cubic-

centimeter.

KEY TERMS


Density andVolume

cific gravities of gases are usually determined incomparison to the specific gravity of dry air.

Most rocks near the surface of Earth have aspecific gravity of somewhere between 2 and 3,while the specific gravity of the planet itself isabout 5. How do scientists know that the densityof Earth is around 5 g/cm3? The computation isfairly simple, given the fact that the mass and vol-ume of the planet are known. And given the factthat most of what lies close to Earth’s surface—sea water, soil, rocks—has a specific gravity wellbelow 5, it is clear that Earth’s interior must con-tain high-density materials, such as nickel oriron. In the same way, calculations regarding thedensity of other objects in the Solar System pro-vide a clue as to their interior composition.

ALL THAT GLITTERS. Closer tohome, a comparison of density makes it possibleto determine whether a piece of jewelry allegedto be solid gold is really genuine. To determinethe answer, one must drop it in a beaker of waterwith graduated units of measure clearly marked.(Here, figures are given in cubic centimeters,since these are easiest to use in this context.)

Suppose the item has a mass of 10 grams.The density of gold is 19 g/cm3, and since V =m/d = 10/19, the volume of water displaced bythe gold should be 0.53 cm3. Suppose thatinstead, the item displaced 0.91 cm3 of water.Clearly, it is not gold, but what is it?

Given the figures for mass and volume, itsdensity would be equal to m/V = 10/0.91 = 11g/cm3—which happens to be the density of lead.If on the other hand the amount of water dis-placed were somewhere between the values for

pure gold and pure lead, one could calculate

what portion of the item was gold and which

lead. It is possible, of course, that it could contain

some other metal, but given the high specific

gravity of lead, and the fact that its density is rel-

atively close to that of gold, lead is a favorite gold

substitute among jewelry counterfeiters.

WHERE TO LEARN MORE


Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Sciencefor Curious Minds. Illustrated by Ann HumphreyWilliams. Hauppauge, N.Y.: Barron’s, 2000.

“Density and Specific Gravity” (Web site).<http://www.tpub.com/fluid/ch1e.htm> (March 27,2001).

“Density, Volume, and Cola” (Web site).<http://student.biology.arizona.edu/sciconn/densi-ty/density_coke.html> (March 27, 2001).

“The Mass Volume Density Challenge” (Web site).<http://science-math-technology.com/mass_vol-ume_density.html> (March 27, 2001).

“Metric Density and Specific Gravity” (Web site).<http://www.essex1.com/people/speer/density.html>(March 27, 2001).

“Mineral Properties: Specific Gravity” The Mineral andGemstone Kingdom (Web site). <http://www.miner-als.net/resource/property/sg.htm> (March 27, 2001).

Robson, Pam. Clocks, Scales and Measurements. NewYork: Gloucester Press, 1993.

“Volume, Mass, and Density” (Web site).<http://www.nyu.edu/pages/mathmol/modules/water/density_intro.html> (March 27, 2001).

Willis, Shirley. Tell Me How Ships Float. Illustrated by theauthor. New York: Franklin Watts, 1999.




CONSERVAT ION L AWSConservation Laws

CONCEPTThe term “conservation laws” might sound atfirst like a body of legal statutes geared towardprotecting the environment. In physics, however,the term refers to a set of principles describingcertain aspects of the physical universe that arepreserved throughout any number of reactionsand interactions. Among the properties con-served are energy, linear momentum, angularmomentum, and electrical charge. (Mass, too, isconserved, though only in situations well belowthe speed of light.) The conservation of theseproperties can be illustrated by examples asdiverse as dropping a ball (energy); the motion ofa skater spinning on ice (angular momentum);and the recoil of a rifle (linear momentum).

HOW IT WORKSThe conservation laws describe physical proper-ties that remain constant throughout the variousprocesses that occur in the physical world. Inphysics,“to conserve” something means “to resultin no net loss of” that particular component. Foreach such component, the input is the same asthe output: if one puts a certain amount of ener-gy into a physical system, the energy that resultsfrom that system will be the same as the energyput into it.

The energy may, however, change forms. Inaddition, the operations of the conservation lawsare—on Earth, at least—usually affected by anumber of other forces, such as gravity, friction,and air resistance. The effects of these forces,combined with the changes in form that takeplace within a given conserved property, some-times make it difficult to perceive the working ofthe conservation laws. It was stated above that

the resulting energy of a physical system will bethe same as the energy that was introduced to it.Note, however, that the usable energy output of asystem will not be equal to the energy input. Thisis simply impossible, due to the factors men-tioned above—particularly friction.

When one puts gasoline into a motor, forinstance, the energy that the motor puts out willnever be as great as the energy contained in thegasoline, because part of the input energy isexpended in the operation of the motor itself.Similarly, the angular momentum of a skater onice will ultimately be dissipated by the resistantforce of friction, just as that of a Frisbee thrownthrough the air is opposed both by gravity andair resistance—itself a specific form of friction.

In each of these cases, however, the propertyis still conserved, even if it does not seem so tothe unaided senses of the observer. Because themotor has a usable energy output less than theinput, it seems as though energy has been lost. Infact, however, the energy has only changed forms,and some of it has been diverted to areas otherthan the desired output. (Both the noise and theheat of the motor, for instance, represent uses ofenergy that are typically considered undesirable.)Thus, upon closer study of the motor—itself anexample of a system—it becomes clear that theresulting energy, if not the desired usable output,is the same as the energy input.

As for the angular momentum examples inwhich friction, or air resistance, plays a part, heretoo (despite all apparent evidence to the con-trary) the property is conserved. This is easier tounderstand if one imagines an object spinning inouter space, free from the opposing force of fric-tion. Thanks to the conservation of angular


ConservationLaws


momentum, an object set into rotation in spacewill continue to spin indefinitely. Thus, if anastronaut in the 1960s, on a spacewalk from hiscapsule, had set a screwdriver spinning in theemptiness of the exosphere, the screwdriverwould still be spinning today!

Energy and Mass

Among the most fundamental statements in allof science is the conservation of energy: a systemisolated from all outside factors will maintain thesame total amount of energy, even though ener-gy transformations from one form or anothertake place.

Energy is manifested in many varieties,including thermal, electromagnetic, sound,chemical, and nuclear energy, but all these aremerely reflections of three basic types of energy.There is potential energy, which an object pos-sesses by virtue of its position; kinetic energy,which it possesses by virtue of its motion; andrest energy, which it possesses by virtue of itsmass.

The last of these three will be discussed inthe context of the relationship between energyand mass; at present the concern is with potential

and kinetic energy. Every system possesses a cer-tain quantity of both, and the sum of its poten-tial and kinetic energy is known as mechanicalenergy. The mechanical energy within a systemdoes not change, but the relative values of poten-tial and kinetic energy may be altered.

A SIMPLE EXAMPLE OF ME-

CHANICAL ENERGY. If one held a base-ball at the top of a tall building, it would have acertain amount of potential energy. Once it wasdropped, it would immediately begin losingpotential energy and gaining kinetic energy pro-portional to the potential energy it lost. The rela-tionship between the two forms, in fact, isinverse: as the value of one variable decreases,that of the other increases in exact proportion.

The ball cannot keep falling forever, losingpotential energy and gaining kinetic energy. Infact, it can never gain an amount of kinetic ener-gy greater than the potential energy it possessedin the first place. At the moment before it hits theground, the ball’s kinetic energy is equal to thepotential energy it possessed at the top of thebuilding. Correspondingly, its potential energy iszero—the same amount of kinetic energy it pos-sessed before it was dropped.

AS THIS HUNTER FIRES HIS RIFLE, THE RIFLE PRODUCES A BACKWARD “KICK” AGAINST HIS SHOULDER. THIS KICK,WITH A VELOCITY IN THE OPPOSITE DIRECTION OF THE BULLET’S TRAJECTORY, HAS A MOMENTUM EXACTLY THE SAME

AS THAT OF THE BULLET ITSELF: HENCE MOMENTUM IS CONSERVED. (Photograph by Tony Arruza/Corbis. Reproduced by

permission.)


ConservationLaws

Then, as the ball hits the ground, the energyis dispersed. Most of it goes into the ground, anddepending on the rigidity of the ball and theground, this energy may cause the ball to bounce.Some of the energy may appear in the form ofsound, produced as the ball hits bottom, andsome will manifest as heat. The total energy,however, will not be lost: it will simply havechanged form.

REST ENERGY. The values formechanical energy in the above illustrationwould most likely be very small; on the otherhand, the rest or mass energy of the baseballwould be staggering. Given the weight of 0.333pounds for a regulation baseball, which on Earthconverts to 0.15 kg in mass, it would possessenough energy by virtue of its mass to provide ayear’s worth of electrical power to more than150,000 American homes. This leads to two obvi-ous questions: how can a mere baseball possessall that energy? And if it does, how can the ener-gy be extracted and put to use?

The answer to the second question is, “Byaccelerating it to something close to the speed oflight”—which is more than 27,000 times fasterthan the fastest speed ever achieved by humans.(The astronauts on Apollo 10 in May 1969reached nearly 25,000 MPH (40,000 km/h),which is more than 33 times the speed of soundbut still insignificant when compared to thespeed of light.) The answer to the first questionlies in the most well-known physics formula ofall time: E = mc2

In 1905, Albert Einstein (1879-1955) pub-lished his Special Theory of Relativity, which hefollowed a decade later with his General Theoryof Relativity. These works introduced the worldto the above-mentioned formula, which holdsthat energy is equal to mass multiplied by thesquared speed of light. This formula gained itswidespread prominence due to the many impli-cations of Einstein’s Relativity, which quite liter-ally changed humanity’s perspective on the uni-verse. Most concrete among those implicationswas the atom bomb, made possible by the un-derstanding of mass and energy achieved by Einstein.

In fact, E = mc2 is the formula for rest ener-gy, sometimes called mass energy. Though restenergy is “outside” of kinetic and potential ener-gy in the sense that it is not defined by the above-described interactions within the larger system of


mechanical energy, its relation to the other formscan be easily shown. All three are defined interms of mass. Potential energy is equal to mgh,where m is mass, g is gravity, and h is height.Kinetic energy is equal to 1⁄2 mv2, where v is veloc-ity. In fact—using a series of steps that will not bedemonstrated here—it is possible to directlyrelate the kinetic and rest energy formulae.

The kinetic energy formula describes thebehavior of objects at speeds well below thespeed of light, which is 186,000 mi (297,600 km)per second. But at speeds close to that of thespeed of light, 1⁄2 mv2 does not accurately reflectthe energy possessed by the object. For instance,if v were equal to 0.999c (where c represents thespeed of light), then the application of the for-mula 1⁄2 mv2 would yield a value equal to less than3% of the object’s real energy. In order to calcu-late the true energy of an object at 0.999c, itwould be necessary to apply a different formulafor total energy, one that takes into account thefact that, at such a speed, mass itself becomesenergy.

AS SURYA BONALY GOES INTO A SPIN ON THE ICE, SHE

DRAWS IN HER ARMS AND LEG, REDUCING THE MOMENT

OF INERTIA. BECAUSE OF THE CONSERVATION OF ANGU-LAR MOMENTUM, HER ANGULAR VELOCITY WILL

INCREASE, MEANING THAT SHE WILL SPIN MUCH FASTER.(Bolemian Nomad Picturemakers/Corbis. Reproduced by permission.)


ConservationLaws

CONSERVATION OF MASS.

Mass itself is relative at speeds approaching c,and, in fact, becomes greater and greater the clos-er an object comes to the speed of light. This mayseem strange in light of the fact that there is, afterall, a law stating that mass is conserved. But massis only conserved at speeds well below c: as anobject approaches 186,000 mi (297,600 km) persecond, the rules are altered.

The conservation of mass states that totalmass is constant, and is unaffected by factorssuch as position, velocity, or temperature, in anysystem that does not exchange any matter with itsenvironment. Yet, at speeds close to c, the mass ofan object increases dramatically.

In such a situation, the mass would be equalto the rest, or starting mass, of the object dividedby 8(1 – (v2/c2), where v is the object’s speed ofrelative motion. The denominator of this equa-tion will always be less than one, and the greaterthe value of v, the smaller the value of thedenominator. This means that at a speed of c, thedenominator is zero—in other words, theobject’s mass is infinite! Obviously, this is notpossible, and indeed, what the formula actuallyshows is that no object can travel faster than thespeed of light.

Of particular interest to the present discus-sion, however, is the fact, established by relativitytheory, that mass can be converted into energy.Hence, as noted earlier, a baseball or indeed anyobject can be converted into energy—and sincethe formula for rest energy requires that the massbe multiplied by c2, clearly, even an object of vir-tually negligible mass can generate a staggeringamount of energy. This conversion of mass toenergy happens well below the speed of light, ina very small way, when a stick of dynamiteexplodes. A portion of that stick becomes energy,and the fact that this portion is equal to just 6parts out of 100 billion indicates the vast propor-tions of energy available from converted mass.

Other Conservation Laws

In addition to the conservation of energy, as wellas the limited conservation of mass, there arelaws governing the conservation of momentum,both for an object in linear (straight-line)motion, and for one in angular (rotational)motion. Momentum is a property that a movingbody possesses by virtue of its mass and velocity,which determines the amount of force and time

required to stop it. Linear momentum is equal tomass multiplied by velocity, and the conservationof linear momentum law states that when thesum of the external force vectors acting on aphysical system is equal to zero, the total linearmomentum of the system remains unchanged, orconserved.

Angular momentum, or the momentum ofan object in rotational motion, is equal to mr2ω,where m is mass, r is the radius of rotation, andω (the Greek letter omega) stands for angularvelocity. According to the conservation of angu-lar momentum law, when the sum of the externaltorques acting on a physical system is equal tozero, the total angular momentum of the systemremains unchanged. Torque is a force appliedaround an axis of rotation. When playing the oldgame of “spin the bottle,” for instance, one isapplying torque to the bottle and causing it torotate.

ELECTRIC CHARGE. The conser-vation of both linear and angular momentum arebest explained in the context of real-life exam-ples, provided below. Before going on to thoseexamples, however, it is appropriate here to dis-cuss a conservation law that is outside the realmof everyday experience: the conservation of elec-tric charge, which holds that for an isolated sys-tem, the net electric charge is constant.

This law is “outside the realm of everydayexperience” such that one cannot experience itthrough the senses, but at every moment, it ishappening everywhere. Every atom has positive-ly charged protons, negatively charged electrons,and uncharged neutrons. Most atoms are neu-tral, possessing equal numbers of protons andelectrons; but, as a result of some disruption, anatom may have more protons than electrons, andthus, become positively charged. Conversely, itmay end up with a net negative charge due to agreater number of electrons. But the protons orelectrons it released or gained did not simplyappear or disappear: they moved from one partof the system to another—that is, from one atomto another atom, or to several other atoms.

Throughout these changes, the charge ofeach proton and electron remains the same, andthe net charge of the system is always the sum ofits positive and negative charges. Thus, it isimpossible for any electrical charge in the uni-verse to be smaller than that of a proton or elec-tron. Likewise, throughout the universe, there is



ConservationLaws

always the same number of negative and positiveelectrical charges: just as energy changes form,the charges simply change position.

There are also conservation laws describingthe behavior of subatomic particles, such as thepositron and the neutrino. However, the mostsignificant of the conservation laws are thoseinvolving energy (and mass, though with the lim-itations discussed above), linear momentum,angular momentum, and electrical charge.


Conservation of LinearMomentum: Rifles and Rockets

FIRING A RIFLE. The conservationof linear momentum is reflected in operations assimple as the recoil of a rifle when it is fired, andin those as complex as the propulsion of a rocketthrough space. In accordance with the conserva-tion of momentum, the momentum of a systemmust be the same after it undergoes an operationas it was before the process began. Before firing,the momentum of a rifle and bullet is zero, andtherefore, the rifle-bullet system must return tothat same zero-level of momentum after it isfired. Thus, the momentum of the bullet must bematched—and “cancelled” within the systemunder study—by a corresponding backwardmomentum.

When a person shooting a gun pulls the trig-ger, it releases the bullet, which flies out of thebarrel toward the target. The bullet has mass andvelocity, and it clearly has momentum; but this isonly half of the story. At the same time it is fired,the rifle produces a “kick,” or sharp jolt, againstthe shoulder of the person who fired it. Thisbackward kick, with a velocity in the oppositedirection of the bullet’s trajectory, has a momen-tum exactly the same as that of the bullet itself:hence, momentum is conserved.

But how can the rearward kick have thesame momentum as that of the bullet? After all,the bullet can kill a person, whereas, if one holdsthe rifle correctly, the kick will not even cause anyinjury. The answer lies in several properties oflinear momentum. First of all, as noted earlier,momentum is equal to mass multiplied by veloc-ity; the actual proportions of mass and velocity,

however, are not important as long as the back-ward momentum is the same as the forwardmomentum. The bullet is an object of relativelysmall mass and high velocity, whereas the rifle ismuch larger in mass, and hence, its rearwardvelocity is correspondingly small.

In addition, there is the element of impulse,or change in momentum. Impulse is the productof force multiplied by change or interval in time.Again, the proportions of force and time intervaldo not matter, as long as they are equal to themomentum change—that is, the difference inmomentum that occurs when the rifle is fired. Toavoid injury to one’s shoulder, clearly force mustbe minimized, and for this to happen, time inter-val must be extended.

If one were to fire the rifle with the stock(the rear end of the rifle) held at some distancefrom one’s shoulder, it would kick back andcould very well produce a serious injury. This isbecause the force was delivered over a very shorttime interval—in other words, force was maxi-mized and time interval minimized. However, ifone holds the rifle stock firmly against one’sshoulder, this slows down the delivery of thekick, thus maximizing time interval and mini-mizing force.

ROCKETING THROUGH SPACE.

Contrary to popular belief, rockets do not moveby pushing against a surface such as a launchpad.If that were the case, then a rocket would havenothing to propel it once it had been launched,and certainly there would be no way for a rocketto move through the vacuum of outer space.Instead, what propels a rocket is the conservationof momentum.

Upon ignition, the rocket sends exhaustgases shooting downward at a high rate of veloc-ity. The gases themselves have mass, and thus,they have momentum. To balance this downwardmomentum, the rocket moves upward—though,because its mass is greater than that of the gasesit expels, it will not move at a velocity as high asthat of the gases. Once again, the upward or for-ward momentum is exactly the same as thedownward or backward momentum, and linearmomentum is conserved.

Rather than needing something to pushagainst, a rocket in fact performs best in outerspace, where there is nothing—neither launch-pad nor even air—against which to push. Notonly is “pushing” irrelevant to the operation of



ConservationLaws


CONSERVATION LAWS: A set of

principles describing physical properties

that remain constant—that is, are con-

served—throughout the various processes

that occur in the physical world. The most

significant of these laws concerns the con-

servation of energy (as well as, with quali-

fications, the conservation of mass); con-

servation of linear momentum; conserva-

tion of angular momentum; and conserva-

tion of electrical charge.

CONSERVATION OF ANGULAR MO-

MENTUM: A physical law stating that

when the sum of the external torques act-

ing on a physical system is equal to zero,

the total angular momentum of the system

remains unchanged. Angular momentum

is the momentum of an object in rotation-

al motion, and torque is a force applied

around an axis of rotation.

CONSERVATION OF ELECTRICAL

CHARGE: A physical law which holds

that for an isolated system, the net electri-

cal charge is constant.

CONSERVATION OF ENERGY: A

law of physics stating that within a system

isolated from all other outside factors, the

total amount of energy remains the same,

though transformations of energy from

one form to another take place.

CONSERVATION OF LINEAR MO-

MENTUM: A physical law stating that

when the sum of the external force vectors

acting on a physical system is equal to zero,

the total linear momentum of the system

remains unchanged—or is conserved.

CONSERVATION OF MASS: A phys-

ical principle stating that total mass is con-

stant, and is unaffected by factors such as

position, velocity, or temperature, in any

system that does not exchange any matter

with its environment. Unlike the other

conservation laws, however, conservation

of mass is not universally applicable, but

applies only at speeds significant lower

than that of light—186,000 mi (297,600

km) per second. Close to the speed of light,

mass begins converting to energy.

CONSERVE: In physics, “to conserve”

something means “to result in no net loss

of” that particular component. It is possi-

ble that within a given system, the compo-

nent may change form or position, but as

long as the net value of the component

remains the same, it has been conserved.

FRICTION: The force that resists

motion when the surface of one object

comes into contact with the surface of

another.

MOMENTUM: A property that a mov-

ing body possesses by virtue of its mass and

velocity, which determines the amount of

force and time required to stop it.

SYSTEM: In physics, the term “system”

usually refers to any set of physical interac-

tions isolated from the rest of the universe.

Anything outside of the system, including

all factors and forces irrelevant to a discus-

sion of that system, is known as the envi-

ronment.

KEY TERMS


ConservationLaws

the rocket, but the rocket moves much more effi-ciently without the presence of air resistance. Inthe same way, on the relatively frictionless surfaceof an ice-skating rink, conservation of linearmomentum (and hence, the process that makespossible the flight of a rocket through space) iseasy to demonstrate.

If, while standing on the ice, one throws anobject in one direction, one will be pushed in theopposite direction with a corresponding level ofmomentum. However, since a person’s mass ispresumably greater than that of the objectthrown, the rearward velocity (and, therefore,distance) will be smaller.

Friction, as noted earlier, is not the onlyforce that counters conservation of linearmomentum on Earth: so too does gravity, andthus, once again, a rocket operates much better inspace than it does when under the influence ofEarth’s gravitational field. If a bullet is fired at abottle thrown into the air, the linear momentumof the spent bullet and the shattered pieces ofglass in the infinitesimal moment just after thecollision will be the same as that of the bullet andthe bottle a moment before impact. An instantlater, however, gravity will accelerate the bulletand the pieces downward, thus leading to achange in total momentum.

Conservation of AngularMomentum: Skaters andOther Spinners

As noted earlier, angular momentum is equal tomr2ω, where m is mass, r is the radius of rotation,and ω stands for angular velocity. In fact, the firsttwo quantities, mr2, are together known asmoment of inertia. For an object in rotation,moment of inertia is the property wherebyobjects further from the axis of rotation movefaster, and thus, contribute a greater share to theoverall kinetic energy of the body.

One of the most oft-cited examples of angu-lar momentum—and of its conservation—involves a skater or ballet dancer executing aspin. As the skater begins the spin, she has one legplanted on the ice, with the other stretchedbehind her. Likewise, her arms are outstretched,thus creating a large moment of inertia. Butwhen she goes into the spin, she draws in her

arms and leg, reducing the moment of inertia. Inaccordance with conservation of angularmomentum, mr2ω will remain constant, andtherefore, her angular velocity will increase,meaning that she will spin much faster.

CONSTANT ORIENTATION. Themotion of a spinning top and a Frisbee in flightalso illustrate the conservation of angularmomentum. Particularly interesting is the ten-dency of such an object to maintain a constantorientation. Thus, a top remains perfectly verticalwhile it spins, and only loses its orientation oncefriction from the floor dissipates its velocity andbrings it to a stop. On a frictionless surface, how-ever, it would remain spinning—and thereforeupright—forever.

A Frisbee thrown without spin does not pro-vide much entertainment; it will simply fall tothe ground like any other object. But if it is tossedwith the proper spin, delivered from the wrist,conservation of angular momentum will keep itin a horizontal position as it flies through the air.Once again, the Frisbee will eventually bebrought to ground by the forces of air resistanceand gravity, but a Frisbee hurled through emptyspace would keep spinning for eternity.

WHERE TO LEARN MORE


“Conservation Laws: An Online Physics Textbook” (Website).<http://www.lightandmatter.com/area1book2.html>(March 12, 2001).

“Conservation Laws: The Most Powerful Laws of Physics”(Web site).<http://webug.physics.uiuc.edu/courses/phys150/fall99/slides/lect0 7/> (March 12, 2001).

“Conservation of Energy.” NASA (Web site).<http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.html> (March 12, 2001).

Elkana, Yehuda. The Discovery of the Conservation ofEnergy. With a foreword by I. Bernard Cohen. Cam-bridge, MA: Harvard University Press, 1974.

“Momentum and Its Conservation” (Web site).<http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/momtoc. html> (March 12, 2001).


Suplee, Curt. Everyday Science Explained. Washington,D.C.: National Geographic Society, 1996.



35


K I NEMAT ICS ANDPART ICLE DYNAM ICS

K INEMAT ICS ANDPART ICLE DYNAM ICS

MOMENTUM

CENTR IPETAL FORCE

FR ICT ION

LAWS OF MOT ION

GRAV I T Y

PROJECT I LE MOT ION

TORQUE



MOMENTUMMomentum

CONCEPTThe faster an object is moving—whether it be abaseball, an automobile, or a particle of matter—the harder it is to stop. This is a reflection ofmomentum, or specifically, linear momentum,which is equal to mass multiplied by velocity.Like other aspects of matter and motion,momentum is conserved, meaning that when thevector sum of outside forces equals zero, no netlinear momentum within a system is ever lost orgained. A third important concept is impulse, theproduct of force multiplied by length in time.Impulse, also defined as a change in momentum,is reflected in the proper methods for hitting abaseball with force or surviving a car crash.

HOW IT WORKSLike many other aspects of physics, the word“momentum” is a part of everyday life. The com-mon meaning of momentum, however, unlikemany other physics terms, is relatively consistentwith its scientific meaning. In terms of formula,momentum is equal to the product of mass andvelocity, and the greater the value of that prod-uct, the greater the momentum.

Consider the term “momentum” outside theworld of physics, as applied, for example, in therealm of politics. If a presidential candidate seesa gain in public-opinion polls, then wins a debateand embarks on a whirlwind speaking tour, themedia comments that he has “gained momen-tum.” As with momentum in the framework ofphysics, what these commentators mean is thatthe candidate will be hard to stop—or to carrythe analogy further, that he is doing enough ofthe right things (thus gaining “mass”), and doingthem quickly enough, thereby gaining velocity.

Momentum and Inertia

It might be tempting to confuse momentum withanother physical concept, inertia. Inertia, asdefined by the second law of motion, is the ten-dency of an object in motion to remain inmotion, and of an object at rest to remain at rest.Momentum, by definition, involves a body inmotion, and can be defined as the tendency of abody in motion to continue moving at a constantvelocity.

Not only does momentum differ from iner-tia in that it relates exclusively to objects inmotion, but (as will be discussed below) thecomponent of velocity in the formula formomentum makes it a vector—that is, a quanti-ty that possesses both magnitude and direction.There is at least one factor that momentum veryclearly has in common with inertia: mass, ameasure of inertia indicating the resistance of anobject to a change in its motion.

Mass and Weight

Unlike velocity, mass is a scalar, a quantity thatpossesses magnitude without direction. Mass isoften confused with weight, a vector quantityequal to its mass multiplied by the downwardacceleration due to gravity. The weight of anobject changes according to the gravitationalforce of the planet or other celestial body onwhich it is measured. Hence, the mass of a personon the Moon would be the same as it is on Earth,whereas the person’s weight would be consider-ably less, due to the smaller gravitational pull ofthe Moon.

Given the unchanging quality of mass asopposed to weight, as well as the fact that scien-tists themselves prefer the much simpler metric


Momentum


system, metric units will generally be used in the

following discussion. Where warranted, of

course, conversion to English or British units (for

example, the pound, a unit of weight) will be

provided. However, since the English unit of

mass, the slug, is even more unfamiliar to most

Americans than its metric equivalent, the kilo-

gram, there is little point in converting kilos into

slugs.

Velocity and Speed

Not only is momentum often confused with

inertia, and mass with weight, but in the everyday

world the concepts of velocity and speed tend to

be blurred. Speed is the rate at which the position

of an object changes over a given period of time,

expressed in terms such as “50 MPH.” It is a

scalar quantity.

Velocity, by contrast, is a vector. If one were

to say “50 miles per hour toward the northeast,”

this would be an expression of velocity. Vectors

are typically designated in bold, without italics;

thus velocity is typically abbreviated v. Scalars,

on the other hand, are rendered in italics. Hence,

the formula for momentum is usually shown

as mv.

Linear Momentum and ItsConservation

Momentum itself is sometimes designated as p. Itshould be stressed that the form of momentumdiscussed here is strictly linear, or straight-line,momentum, in contrast to angular momentum,more properly discussed within the frameworkof rotational motion.

Both angular and linear momentum abideby what are known as conservation laws. Theseare statements concerning quantities that, undercertain conditions, remain constant or unchang-ing. The conservation of linear momentum lawstates that when the sum of the external forcevectors acting on a physical system is equal tozero, the total linear momentum of the systemremains unchanged—or conserved.

The conservation of linear momentum isreflected both in the recoil of a rifle and in thepropulsion of a rocket through space. When arifle is fired, it produces a “kick”—that is, a sharpjolt to the shoulder of the person who has firedit—corresponding to the momentum of the bul-let. Why, then, does the “kick” not knock a per-son’s shoulder off the way a bullet would? Becausethe rifle’s mass is much greater than that of thebullet, meaning that its velocity is much smaller.

WHEN BILLIARD BALLS COLLIDE, THEIR HARDNESS RESULTS IN AN ELASTIC COLLISION—ONE IN WHICH KINETIC ENER-GY IS CONSERVED. (Photograph by John-Marshall Mantel/Corbis. Reproduced by permission.)


MomentumAs for rockets, they do not—contrary topopular belief—move by pushing against a sur-face, such as a launch pad. If that were the case,then a rocket would have nothing to propel itonce it is launched, and certainly there would beno way for a rocket to move through the vacuumof outer space. Instead, as it burns fuel, the rock-et expels exhaust gases that exert a backwardmomentum, and the rocket itself travels forwardwith a corresponding degree of momentum.

Systems

Here, “system” refers to any set of physical inter-actions isolated from the rest of the universe.Anything outside of the system, including all fac-tors and forces irrelevant to a discussion of thatsystem, is known as the environment. In thepool-table illustration shown earlier, the interac-tion of the billiard balls in terms of momentumis the system under discussion.

It is possible to reduce a system even furtherfor purposes of clarity: hence, one might specifythat the system consists only of the pool balls, theforce applied to them, and the resulting momen-tum interactions. Thus, we will ignore the fric-tion of the pool table’s surface, and the assump-tion will be that the balls are rolling across a fric-tionless plane.

Impulse

For an object to have momentum, some forcemust have set it in motion, and that force musthave been applied over a period of time. Like-wise, when the object experiences a collision orany other event that changes its momentum, thatchange may be described in terms of a certainamount of force applied over a certain period oftime. Force multiplied by time interval isimpulse, expressed in the formula F • δt, where Fis force, δ (the Greek letter delta) means “achange” or “change in...”; and t is time.

As with momentum itself, impulse is a vec-tor quantity. Whereas the vector component ofmomentum is velocity, the vector quantity inimpulse is force. The force component ofimpulse can be used to derive the relationshipbetween impulse and change in momentum.According to the second law of motion, F = m a;that is, force is equal to mass multiplied by accel-eration. Acceleration can be defined as a change


in velocity over a change or interval in time.Expressed as a formula, this is

.

Thus, force is equal to

,

an equation that can be rewritten as Fδt = mδv.In other words, impulse is equal to change inmomentum.

This relationship between impulse andmomentum change, derived here in mathematicalterms, will be discussed below in light of severalwell-known examples from the real world. Notethat the metric units of impulse and momentumare actually interchangeable, though they are typ-ically expressed in different forms, for the purposeof convenience. Hence, momentum is usually ren-dered in terms of kilogram-meters-per-second (kg • m/s), whereas impulse is typically shown asnewton-seconds (N • s). In the English system,momentum is shown in units of slug-feet per-

m ∆v∆t ))

=a ∆v∆t

WHEN PARACHUTISTS LAND, THEY KEEP THEIR KNEES

BENT AND OFTEN ROLL OVER—ALL IN AN EFFORT TO

LENGTHEN THE PERIOD OF THE FORCE OF IMPACT, THUS

REDUCING ITS EFFECTS. (Photograph by James A. Sugar/Corbis.

Reproduced by permission.)


Momentum another so that they collide head-on. Due to theproperties of clay as a substance, the two lumpswill tend to stick. Assuming the lumps are not of equal mass, they will continue traveling in the same direction as the lump with greatermomentum.

As they meet, the two lumps form a largermass MV that is equal to the sum of their twoindividual masses. Once again, MV = m1v1 +m2v2. The M in MV is the sum of the smaller val-ues m, and the V is the vector sum of velocity.Whereas M is larger than m1 or m2—the reasonbeing that scalars are simply added like ordinarynumbers—V is smaller than v1 or v2. This lowernumber for net velocity as compared to particlevelocity will always occur when two objects aremoving in opposite directions. (If the objects aremoving in the same direction, V will have a valuebetween that of v1 and v2.)

To add the vector sum of the two lumps incollision, it is best to make a diagram showing thebodies moving toward one another, with arrowsillustrating the direction of velocity. By conven-tion, in such diagrams the velocity of an objectmoving to the right is rendered as a positivenumber, and that of an object moving to the leftis shown with a negative number. It is thereforeeasier to interpret the results if the object withthe larger momentum is shown moving to theright.

The value of V will move in the same direc-tion as the lump with greater momentum. Butsince the two lumps are moving in oppositedirections, the momentum of the smaller lumpwill cancel out a portion of the greater lump’smomentum—much as a negative number, whenadded to a positive number of greater magni-tude, cancels out part of the positive number’svalue. They will continue traveling in the direc-tion of the lump with greater momentum, nowwith a combined mass equal to the arithmeticsum of their masses, but with a velocity muchsmaller than either had before impact.

BILLIARD BALLS. The game of poolprovides an example of a collision in which oneobject, the cue ball, is moving, while the other—known as the object ball—is stationary. Due tothe hardness of pool balls, and their tendency notto stick to one another, this is also an example ofan almost perfectly elastic collision—one inwhich kinetic energy is conserved.


second, and impulse in terms of the pound-second.


When Two Objects Collide

Two moving objects, both possessing momen-tum by virtue of their mass and velocity, collidewith one another. Within the system created bytheir collision, there is a total momentum MVthat is equal to their combined mass and the vec-tor sum of their velocity.

This is the case with any system: the totalmomentum is the sum of the various individualmomentum products. In terms of a formula, thisis expressed as MV = m1v1 + m2v2 + m3v3 +... andso on. As noted earlier, the total momentum willbe conserved; however, the actual distribution ofmomentum within the system may change.

TWO LUMPS OF CLAY. Considerthe behavior of two lumps of clay, thrown at one

AS SAMMY SOSA’S BAT HITS THIS BALL, IT APPLIES A

TREMENDOUS MOMENTUM CHANGE TO THE BALL. AFTER

CONTACT WITH THE BALL, SOSA WILL CONTINUE HIS

SWING, THEREBY CONTRIBUTING TO THE MOMENTUM

CHANGE AND ALLOWING THE BALL TO TRAVEL FARTHER.(AFP/Corbis. Reproduced by permission.)


MomentumThe colliding lumps of clay, on the otherhand, are an excellent example of an inelastic col-lision, or one in which kinetic energy is not con-served. The total energy in a given system, such asthat created by the two lumps of clay in collision,is conserved; however, kinetic energy may betransformed, for instance, into heat energyand/or sound energy as a result of collision.Whereas inelastic collisions involve soft, stickyobjects, elastic collisions involve rigid, non-stickyobjects.

Kinetic energy and momentum both involvecomponents of velocity and mass: p (momen-tum) is equal to mv, and KE (kinetic energy)equals 1⁄2 mv2. Due to the elastic nature of pool-ball collisions, when the cue ball strikes theobject ball, it transfers its velocity to the latter.Their masses are the same, and therefore theresulting momentum and kinetic energy of theobject ball will be the same as that possessed bythe cue ball prior to impact.

If the cue ball has transferred all of its veloc-ity to the object ball, does that mean it hasstopped moving? It does. Assuming that theinteraction between the cue ball and the objectball constitutes a closed system, there is no othersource from which the cue ball can acquire veloc-ity, so its velocity must be zero.

It should be noted that this illustration treatspool-ball collisions as though they were 100%elastic, though in fact, a portion of kinetic ener-gy in these collisions is transformed into heat andsound. Also, for a cue ball to transfer all of itsvelocity to the object ball, it must hit it straight-on. If the balls hit off-center, not only will theobject ball move after impact, but the cue ballwill continue to move—roughly at 90° to a linedrawn through the centers of the two balls at themoment of impact.

Impulse: Breaking or Build-ing the Impact

When a cue ball hits an object ball in pool, it issafe to assume that a powerful impact is desired.The same is true of a bat hitting a baseball. Butwhat about situations in which a powerfulimpact is not desired—as for instance when carsare crashing? There is, in fact, a relationshipbetween impulse, momentum change, transfer ofkinetic energy, and the impact—desirable orundesirable—experienced as a result.

Impulse, again, is equal to momentumchange—and also equal to force multiplied bytime interval (or change in time). This meansthat the greater the force and the greater theamount of time over which it is applied, thegreater the momentum change. Even more inter-esting is the fact that one can achieve the samemomentum change with differing levels of forceand time interval. In other words, a relatively lowdegree of force applied over a relatively long peri-od of time would produce the same momentumchange as a relatively high amount of force over arelatively short period of time.

The conservation of kinetic energy in a col-lision is, as noted earlier, a function of the relativeelasticity of that collision. The question ofwhether KE is transferred has nothing to do withimpulse. On the other hand, the question of howKE is transferred—or, even more specifically, theinterval over which the transfer takes place—isvery much related to impulse.

Kinetic energy, again, is equal to 1⁄2 mv2. If amoving car were to hit a stationary car head-on,it would transfer a quantity of kinetic energy tothe stationary car equal to one-half its ownmass multiplied by the square of its velocity.(This, of course, assumes that the collision isperfectly elastic, and that the mass of the cars isexactly equal.) A transfer of KE would alsooccur if two moving cars hit one another head-on, especially in a highly elastic collision.Assuming one car had considerably greatermass and velocity than the other, a high degreeof kinetic energy would be transferred—whichcould have deadly consequences for the peoplein the car with less mass and velocity. Even withcars of equal mass, however, a high rate of accel-eration can bring about a potentially lethaldegree of force.

CRUMPLE ZONES IN CARS. Ina highly elastic car crash, two automobiles wouldbounce or rebound off one another. This wouldmean a dramatic change in direction—a reversal,in fact—hence, a sudden change in velocity andtherefore momentum. In other words, the figurefor mδv would be high, and so would that forimpulse, Fδt.

On the other hand, it is possible to have ahighly inelastic car crash, accompanied by asmall change in momentum. It may seem logicalto think that, in a crash situation, it would be bet-ter for two cars to bounce off one another than



Momentum


ACCELERATION: A change velocity.

Acceleration can be expressed as a formula

δv/δt—that is, change in velocity divided

by change, or interval, in time.

CONSERVATION OF LINEAR

MOMENTUM: A physical law, which

states that when the sum of the external

force vectors acting on a physical system is

equal to zero, the total linear momentum

of the system remains unchanged—or is

conserved.


something (for example, momentum or

kinetic energy) means “to result in no net

loss of” that particular component. It is

possible that within a given system, one

type of energy may be transformed into

another type, but the net energy in the sys-

tem will remain the same.

ELASTIC COLLISION: A collision in

which kinetic energy is conserved. Typical-

ly elastic collisions involve rigid, non-sticky

objects such as pool balls. At the other

extreme is an inelastic collision.

IMPULSE: The amount of force and

time required to cause a change in

momentum. Impulse is the product of

force multiplied by a change, or interval, in

time (Fδt): the greater the momentum,

the greater the force needed to change it,

and the longer the period of time over

which it must be applied.

INELASTIC COLLISION: A collision

in which kinetic energy is not conserved.

(The total energy is conserved: kinetic

energy itself, however, may be transformed

into heat energy or sound energy.) Typical-

ly, inelastic collisions involve non-rigid,

sticky objects—for instance, lumps of clay.

At the other extreme is an elastic collision.




KINETIC ENERGY: The energy an

object possesses by virtue of its motion.



KEY TERMS

for them to crumple together. In fact, however,the latter option is preferable. When the carscrumple rather than rebounding, they do notexperience a reversal in direction. They do expe-rience a change in speed, of course, but themomentum change is far less than it would be ifthey rebounded.

Furthermore, crumpling lengthens theamount of time during which the change invelocity occurs, and thus reduces impulse. Buteven with the reduced impulse of this momen-tum change, it is possible to further reduce theeffect of force, another aspect of impact. Remem-ber that mδv = Fδt: the value of force and timeinterval do not matter, as long as their product isequal to the momentum change. Because F and

δt are inversely proportional, an increase inimpact time will reduce the effects of force.

For this reason, car manufacturers actuallydesign and build into their cars a feature knownas a crumple zone. A crumple zone—and thereare usually several in a single automobile—is asection in which the materials are put together insuch a way as to ensure that they will crumplewhen the car experiences a collision. Of course,the entire car cannot be one big crumple zone—this would be fatal for the driver and riders; how-ever, the incorporation of crumple zones at keypoints can greatly reduce the effect of the force acar and its occupants must endure in a crash.

Another major reason for crumple zones isto keep the passenger compartment of the car


Momentum


intact. Many injuries are caused when the bodyof the car intrudes on the space of the occu-pants—as, for instance, when the floor buckles,or when the dashboard is pushed deep into thepassenger compartment. Obviously, it is pre-ferable to avoid this by allowing the fender to collapse.

REDUCING IMPULSE: SAVING

LIVES, BONES, AND WATER BAL-

LOONS. An airbag is another way of mini-mizing force in a car accident, in this case byreducing the time over which the occupantsmove forward toward the dashboard or wind-shield. The airbag rapidly inflates, and just asrapidly begins to deflate, within the split-secondthat separates the car’s collision and a person’s

collision with part of the car. As it deflates, it isreceding toward the dashboard even as the dri-ver’s or passenger’s body is being hurled towardthe dashboard. It slows down impact, extendingthe amount of time during which the force is dis-tributed.

By the same token, a skydiver or paratroop-er does not hit the ground with legs outstretched:he or she would be likely to suffer a broken boneor worse from such a foolish stunt. Rather, as aparachutist prepares to land, he or she keepsknees bent, and upon impact immediately rollsover to the side. Thus, instead of experiencing theforce of impact over a short period of time, theparachutist lengthens the amount of time thatforce is experienced, which reduces its effects.

motion—including a change in velocity. A

kilogram is a unit of mass, whereas a

pound is a unit of weight.

MOMENTUM: A property that a mov-

ing body possesses by virtue of its mass and

velocity, which determines the amount of

force and time (impulse) required to stop

it. Momentum—actually linear momen-

tum, as opposed to the angular momen-

tum of an object in rotational motion—is

equal to mass multiplied by velocity.


only magnitude, with no specific direc-

tion—as contrasted with a vector, which

possesses both magnitude and direction.

Scalar quantities are usually expressed in

italicized letters, thus: m (mass).



time.







ronment.


both magnitude and direction—as con-

trasted with a scalar, which possesses mag-

nitude without direction. Vector quantities

are usually expressed in bold, non-itali-

cized letters, thus: F (force). They may also

be shown by placing an arrow over the let-

ter designating the specific property, as for

instance v for velocity.

VECTOR SUM: A calculation that

yields the net result of all the vectors

applied in a particular situation. In the case

of momentum, the vector component is

velocity. The best method is to make a dia-

gram showing bodies in collision, with

arrows illustrating the direction of velocity.

On such a diagram, motion to the right is

assigned a positive value, and to the left a

negative value.



KEY TERMS CONT INUED


Momentum The same principle applies if one werecatching a water balloon. In order to keep it frombursting, one needs to catch the balloon inmidair, then bring it to a stop slowly by “travel-ing” with it for a few feet before reducing itsmomentum down to zero. Once again, there isno way around the fact that one is attempting tobring about a substantial momentum change—achange equal in value to the momentum of theobject in movement. Nonetheless, by increasingthe time component of impulse, one reduces theeffects of force.

In old Superman comics, the “Man of Steel”often caught unfortunate people who had fallen,or been pushed, out of tall buildings. The car-toons usually showed him, at a stationary posi-tion in midair, catching the person before he orshe could hit the ground. In fact, this would notsave their lives: the force component of the sud-den momentum change involved in being caughtwould be enough to kill the person. Of course, itis a bit absurd to quibble over scientific accuracyin Superman, but in order to make the situationmore plausible, the “Man of Steel” should havebeen shown catching the person, then slowly fol-lowing through on the trajectory of the falltoward earth.

THE CRACK OF THE BAT:

INCREASING IMPULSE. But what if—to once again turn the tables—a strong force isdesired? This time, rather than two pool ballsstriking one another, consider what happenswhen a batter hits a baseball. Once more, the cor-relation between momentum change and impulsecan create an advantage, if used properly.

As the pitcher hurls the ball toward homeplate, it has a certain momentum; indeed, a pitchthrown by a major-league player can send theball toward the batter at speeds around 100 MPH(160 km/h)—a ball having considerable momen-tum). In order to hit a line drive or “knock theball out of the park,” the batter must thereforecause a significant change in momentum.

Consider the momentum change in terms ofthe impulse components. The batter can onlyapply so much force, but it is possible to magnifyimpulse greatly by increasing the amount of timeover which the force is delivered. This is known in

sports—and it applies as much in tennis or golf asin baseball—as “following through.” By increas-ing the time of impact, the batter has increasedimpulse and thus, momentum change. Obvious-ly, the mass of the ball has not been altered; thedifference, then, is a change in velocity.

How is it possible that in earlier examples,the effects of force were decreased by increasingthe time interval, whereas in the baseball illustra-tion, an increase in time interval resulted in amore powerful impact? The answer relates to dif-ferences in direction and elasticity. The baseballand the bat are colliding head-on in a relativelyelastic situation; by contrast, crumpling cars areinelastic. In the example of a person catching awater balloon, the catcher is moving in the samedirection as the balloon, thus reducing momen-tum change. Even in the case of the paratrooper,the ground is stationary; it does not move towardthe parachutist in the way that the baseballmoves toward the bat.

WHERE TO LEARN MORE


Bonnet, Robert L. and Dan Keen. Science Fair Projects:Physics. Illustrated by Frances Zweifel. New York:Sterling, 1999.

Fleisher, Paul. Objects in Motion: Principles of ClassicalMechanics. Minneapolis, MN: Lerner Publications,2002.

Gardner, Robert. Experimenting with Science in Sports.New York: F. Watts, 1993.

“Lesson 1: The Impulse Momentum Change Theorem”(Web site)<http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u411a.html> (March 19, 2001).

“Momentum” (Web site).<http://id.mind.net/~zona/mstm/physics/mechan-ics/momentum/momentum.html> (March 19, 2001).

Physlink.com (Web site). <http://www.physlink.com>(March 7, 2001).


Schrier, Eric and William F. Allman. Newton at the Bat:The Science in Sports. New York: Charles Scribner’sSons, 1984.

Zubrowski, Bernie. Raceways: Having Fun with Balls andTracks. Illustrated by Roy Doty. New York: WilliamMorrow, 1985.




C ENTR IPETAL FORCECentripetal Force

CONCEPTMost people have heard of centripetal and cen-trifugal force. Though it may be somewhat diffi-cult to keep track of which is which, chances areanyone who has heard of the two conceptsremembers that one is the tendency of objects inrotation to move inward, and the other is the ten-dency of rotating objects to move outward. Itmay come as a surprise, then, to learn that thereis no such thing, strictly speaking, as centrifugal(outward) force. There is only centripetal(inward) force and the inertia that makes objectsin rotation under certain situations move out-ward, for example, a car making a turn, themovement of a roller coaster— even the spinningof a centrifuge.

HOW IT WORKSLike many other principles in physics, centripetalforce ultimately goes back to a few simple pre-cepts relating to the basics of motion. Consideran object in uniform circular motion: an objectmoves around the center of a circle so that itsspeed is constant or unchanging.

The formula for speed—or rather, averagespeed—is distance divided by time; hence, peo-ple say, for instance, “miles (or kilometers) perhour.” In the case of an object making a circle,distance is equal to the circumference, or dis-tance around, the circle. From geometry, weknow that the formula for calculating the cir-cumference of a circle is 2πr, where r is theradius, or the distance from the circumference tothe center. The figure π may be rendered as3.141592..., though in fact, it is an irrationalnumber: the decimal figures continue foreverwithout repetition or pattern.

From the above, it can be discerned that theformula for the average speed of an object movingaround a circle is 2πr divided by time. Further-more, we can see that there is a proportional rela-tionship between radius and average speed. If theradius of a circle is doubled, but an object at thecircle’s periphery makes one complete revolutionin the same amount of time as before, this meansthat the average speed has doubled as well. Thiscan be shown by setting up two circles, one with aradius of 2, the other with a radius of 4, and usingsome arbitrary period of time—say, 2 seconds.

The above conclusion carries with it aninteresting implication with regard to speeds atdifferent points along the radius of a circle.Rather than comparing two points movingaround the circumferences of two different cir-cles—one twice as big as the other—in the sameperiod of time, these two points could be on thesame circle: one at the periphery, and one exact-ly halfway along the radius. Assuming they bothtraveled a complete circle in the same period oftime, the proportional relationship describedearlier would apply. This means, then, that thefurther out on the circle one goes, the greater theaverage speed.

Velocity = Speed + Direction

Speed is a scalar, meaning that it has magnitudebut no specific direction; by contrast, velocity is avector—a quantity with both a magnitude (thatis, speed) and a direction. For an object in circu-lar motion, the direction of velocity is the sameas that in which the object is moving at any givenpoint. Consider the example of the city ofAtlanta, Georgia, and Interstate-285, one of sev-eral instances in which a city is surrounded by a“loop” highway. Local traffic reporters avoid giv-


CentripetalForce

means that it is experiencing acceleration. As withthe subject of centripetal force and “centrifugalforce,” most people have a mistaken view of accel-eration, believing that it refers only to an increasein speed. In fact, acceleration is a change in veloc-ity, and can thus refer either to a change in speedor direction. Nor must that change be a positiveone; in other words, an object undergoing a reduc-tion in speed is also experiencing acceleration.

The acceleration of an object in rotationalmotion is always toward the center of the circle.This may appear to go against common sense,which should indicate that acceleration moves inthe same direction as velocity, but it can, in fact,be proven in a number of ways. One methodwould be by the addition of vectors, but a“hands-on” demonstration may be more enlight-ening than an abstract geometrical proof.

It is possible to make a simple accelerometer,a device for measuring acceleration, with a lit can-dle inside a glass. The candle should be standingat a 90°-angle to the bottom of the glass, attachedto it by hot wax as you would affix a burning can-dle to a plate. When you hold the candle level, theflame points upward; but if you spin the glass in acircle, the flame will point toward the center ofthat circle—in the direction of acceleration.

Mass � Acceleration = Force

Since we have shown that acceleration exists foran object spinning around a circle, it is then pos-sible for us to prove that the object experiencessome type of force. The proof for this assertionlies in the second law of motion, which definesforce as the product of mass and acceleration:hence, where there is acceleration and mass, theremust be force. Force is always in the direction ofacceleration, and therefore the force is directedtoward the center of the circle.

In the above paragraph, we assumed theexistence of mass, since all along the discussionhas concerned an object spinning around a circle.By definition, an object—that is, an item of mat-ter, rather than an imaginary point—possessesmass. Mass is a measure of inertia, which can beexplained by the first law of motion: an object inmotion tends to remain in motion, at the samespeed and in the same direction (that is, at thesame velocity) unless or until some outside forceacts on it. This tendency to maintain velocity isinertia. Put another way, it is inertia that causesan object standing still to remain motionless, and


ing mere directional coordinates for spots on thathighway (for instance, “southbound on 285”),because the area where traffic moves southdepends on whether one is moving clockwise orcounterclockwise. Hence, reporters usually say“southbound on the outer loop.”

As with cars on I-285, the direction of thevelocity vector for an object moving around acircle is a function entirely of its position and thedirection of movement—clockwise or counter-clockwise—for the circle itself. The direction ofthe individual velocity vector at any given pointmay be described as tangential; that is, describinga tangent, or a line that touches the circle at justone point. (By definition, a tangent line cannotintersect the circle.)

It follows, then, that the direction of an objectin movement around a circle is changing; hence,its velocity is also changing—and this in turn

TYPICALLY, A CENTRIFUGE CONSISTS OF A BASE; A

ROTATING TUBE PERPENDICULAR TO THE BASE; AND

VIALS ATTACHED BY MOVABLE CENTRIFUGE ARMS TO THE

ROTATING TUBE. THE MOVABLE ARMS ARE HINGED AT

THE TOP OF THE ROTATING TUBE, AND THUS CAN MOVE

UPWARD AT AN ANGLE APPROACHING 90° TO THE TUBE.WHEN THE TUBE BEGINS TO SPIN, CENTRIPETAL FORCE

PULLS THE MATERIAL IN THE VIALS TOWARD THE CEN-TER. (Photograph by Charles D. Winters. National Audubon Society

Collection/Photo Researchers, Inc. Reproduced by permission.)


CentripetalForce


likewise, it is inertia which dictates that a movingobject will “try” to keep moving.

Centripetal Force

Now that we have established the existence of aforce in rotational motion, it is possible to give ita name: centripetal force, or the force that causesan object in uniform circular motion to movetoward the center of the circular path. This is nota “new” kind of force; it is merely force as appliedin circular or rotational motion, and it isabsolutely essential. Hence, physicists speak of a“centripetal force requirement”: in the absence ofcentripetal force, an object simply cannot turn.Instead, it will move in a straight line.

The Latin roots of centripetal together mean

“seeking the center.” What, then, of centrifugal, a

word that means “fleeing the center”? It would be

correct to say that there is such a thing as cen-

trifugal motion; but centrifugal force is quite a

different matter. The difference between cen-

tripetal force and a mere centrifugal tendency—

a result of inertia rather than of force—can be

explained by referring to a familiar example.


Riding in a Car

When you are riding in a car and the car acceler-

ates, your body tends to move backward against

A CLOTHOID LOOP IN A ROLLER COASTER IN HAINES CITY, FLORIDA. AT THE TOP OF A LOOP, YOU FEEL LIGHTER

THAN NORMAL; AT THE BOTTOM, YOU FEEL HEAVIER. (The Purcell Team/Corbis. Reproduced by permission.)


CentripetalForce

the seat. Likewise, if the car stops suddenly, yourbody tends to move forward, in the direction ofthe dashboard. Note the language here: “tends tomove” rather than “is pushed.” To say that some-thing is pushed would imply that a force has beenapplied, yet what is at work here is not a force,but inertia—the tendency of an object in motionto remain in motion, and an object at rest toremain at rest.

A car that is not moving is, by definition, atrest, and so is the rider. Once the car begins mov-ing, thus experiencing a change in velocity, therider’s body still tends to remain in the fixed posi-tion. Hence, it is not a force that has pushed therider backward against the seat; rather, force haspushed the car forward, and the seat moves up tomeet the rider’s back. When stopping, once again,there is a sudden change in velocity from a certainvalue down to zero. The rider, meanwhile, is con-tinuing to move forward due to inertia, and thus,his or her body has a tendency to keep moving inthe direction of the now-stationary dashboard.

This may seem a bit too simple to anyonewho has studied inertia, but because the humanmind has such a strong inclination to perceiveinertia as a force in itself, it needs to be clarifiedin the most basic terms. This habit is similar tothe experience you have when sitting in a vehiclethat is standing still, while another vehicle along-side moves backward. In the first split-second ofawareness, your mind tends to interpret thebackward motion of the other car as forwardmotion on the part of the car in which you aresitting—even though your own car is standingstill.

Now we will consider the effects of cen-tripetal force, as well as the illusion of centrifugalforce. When a car turns to the left, it is undergo-ing a form of rotation, describing a 90°-angle orone-quarter of a circle. Once again, your bodyexperiences inertia, since it was in motion alongwith the car at the beginning of the turn, andthus you tend to move forward. The car, at thesame time, has largely overcome its own inertiaand moved into the leftward turn. Thus the cardoor itself is moving to the left. As the doormeets the right side of your body, you have thesensation of being pushed outward against thedoor, but in fact what has happened is that thedoor has moved inward.

The illusion of centrifugal force is so deeplyingrained in the popular imagination that it war-

rants further discussion below. But while on thesubject of riding in an automobile, we need toexamine another illustration of centripetal force.It should be noted in this context that for a car tomake a turn at all, there must be friction betweenthe tires and the road. Friction is the force thatresists motion when the surface of one objectcomes into contact with the surface of another;yet ironically, while opposing motion, frictionalso makes relative motion possible.

Suppose, then, that a driver applies thebrakes while making a turn. This now adds aforce tangential, or at a right angle, to the cen-tripetal force. If this force is greater than the cen-tripetal force—that is, if the car is moving toofast—the vehicle will slide forward rather thanmaking the turn. The results, as anyone who hasever been in this situation will attest, can be dis-astrous.

The above highlights the significance of thecentripetal force requirement: without a suffi-cient degree of centripetal force, an object simplycannot turn. Curves are usually banked to maxi-mize centripetal force, meaning that the roadwaytilts inward in the direction of the curve. Thisbanking causes a change in velocity, and hence, inacceleration, resulting in an additional quantityknown as reaction force, which provides thevehicle with the centripetal force necessary formaking the turn.

The formula for calculating the angle atwhich a curve should be banked takes intoaccount the car’s speed and the angle of thecurve, but does not include the mass of the vehi-cle itself. As a result, highway departments postsigns stating the speed at which vehicles shouldmake the turn, but these signs do not need toinclude specific statements regarding the weightof given models.

The Centrifuge

To return to the subject of “centrifugal force”—which, as noted earlier, is really just centrifugalmotion—you might ask,“If there is no such thingas centrifugal force, how does a centrifuge work?”Used widely in medicine and a variety of sciences,a centrifuge is a device that separates particleswithin a liquid. One application, for instance, isto separate red blood cells from plasma.

Typically a centrifuge consists of a base; arotating tube perpendicular to the base; and twovials attached by movable centrifuge arms to the



CentripetalForce


rotating tube. The movable arms are hinged atthe top of the rotating tube, and thus can moveupward at an angle approaching 90° to the tube.When the tube begins to spin, centripetal forcepulls the material in the vials toward the center.

Materials that are denser have greater iner-tia, and thus are less responsive to centripetalforce. Hence, they seem to be pushed outward,but in fact what has happened is that the lessdense material has been pulled inward. This leadsto the separation of components, for instance,with plasma on the top and red blood cells on thebottom. Again, the plasma is not as dense, andthus is more easily pulled toward the center ofrotation, whereas the red blood cells respond less,and consequently remain on the bottom.

The centrifuge was invented in 1883 by Carlde Laval (1845-1913), a Swedish engineer, whoused it to separate cream from milk. During the1920s, the chemist Theodor Svedberg (1884-1971), who was also Swedish, improved onLaval’s work to create the ultracentrifuge, usedfor separating very small particles of similarweight.

In a typical ultracentrifuge, the vials are nolarger than 0.2 in (0.6 cm) in diameter, and thesemay rotate at speeds of up to 230,000 revolutionsper minute. Most centrifuges in use by industryrotate in a range between 1,000 and 15,000 revo-lutions per minute, but others with scientificapplications rotate at a much higher rate, and canproduce a force more than 25,000 times as greatas that of gravity.

In 1994, researchers at the University of Col-orado created a sort of super-centrifuge for sim-ulating stresses applied to dams and other largestructures. The instrument has just one cen-trifuge arm, measuring 19.69 ft (6 m), attachedto which is a swinging basket containing a scalemodel of the structure to be tested. If the modelis 1/50 the size of the actual structure, then thecentrifuge is set to create a centripetal force 50times that of gravity.

The Colorado centrifuge has also been usedto test the effects of explosions on buildings.Because the combination of forces—centripetal,gravity, and that of the explosion itself—is sogreat, it takes a very small quantity of explosive tomeasure the effects of a blast on a model of thebuilding.

Industrial uses of the centrifuge include thatfor which Laval invented it—separation of creamfrom milk—as well as the separation of impuri-ties from other substances. Water can be removedfrom oil or jet fuel with a centrifuge, and like-wise, waste-management agencies use it to sepa-rate solid materials from waste water prior topurifying the water itself.

Closer to home, a washing machine on spincycle is a type of centrifuge. As the wet clothesspin, the water in them tends to move outward,separating from the clothes themselves. An evensimpler, more down-to-earth centrifuge can becreated by tying a fairly heavy weight to a ropeand swinging it above one’s head: once again, theweight behaves as though it were pushed outward,though in fact, it is only responding to inertia.

Roller Coasters and Cen-tripetal Force

People ride roller coasters, of course, for the thrillthey experience, but that thrill has more to dowith centripetal force than with speed. By the late twentieth century, roller coasters capable of speeds above 90 MPH (144 km/h) began toappear in amusement parks around America; butprior to that time, the actual speeds of a rollercoaster were not particularly impressive. Seldom,if ever, did they exceed that of a car moving downthe highway. On the other hand, the accelerationand centripetal force generated on a roller coast-er are high, conveying a sense of weightlessness(and sometimes the opposite of weightlessness)that is memorable indeed.

Few parts of a roller coaster ride are straightand flat—usually just those segments that markthe end of one ride and the beginning of anoth-er. The rest of the track is generally composed ofdips and hills, banked turns, and in some cases,clothoid loops. The latter refers to a geometricshape known as a clothoid, rather like a teardropupside-down.

Because of its shape, the clothoid has a muchsmaller radius at the top than at the bottom—akey factor in the operation of the roller coasterride through these loops. In days past, roller-coaster designers used perfectly circular loops,which allowed cars to enter them at speeds thatwere too high, built too much force and resultedin injuries for riders. Eventually, engineers recog-nized the clothoid as a means of providing a safe,fun ride.


CentripetalForce

As you move into the clothoid loop, then up,then over, and down, you are constantly chang-ing position. Speed, too, is changing. On the wayup the loop, the roller coaster slows due to adecrease in kinetic energy, or the energy that anobject possesses by virtue of its movement. At thetop of the loop, the roller coaster has gained agreat deal of potential energy, or the energy anobject possesses by virtue of its position, and itskinetic energy is at zero. But once it starts goingdown the other side, kinetic energy—and with itspeed—increases rapidly once again.

Throughout the ride, you experience twoforces, gravity, or weight, and the force (due tomotion) of the roller coaster itself, known asnormal force. Like kinetic and potential energy—which rise and fall correspondingly with dips andhills—normal force and gravitational force arelocked in a sort of “competition” throughout theroller-coaster rider. For the coaster to have its

proper effect, normal force must exceed that ofgravity in most places.

The increase in normal force on a roller-coaster ride can be attributed to acceleration andcentripetal motion, which cause you to experi-ence something other than gravity. Hence, at thetop of a loop, you feel lighter than normal, and atthe bottom, heavier. In fact, there has been noreal change in your weight: it is, like the idea of“centrifugal force” discussed earlier, a matter ofperception.

WHERE TO LEARN MORE

Aylesworth, Thomas G. Science at the Ball Game. NewYork: Walker, 1977.


Buller, Laura and Ron Taylor. Forces of Nature. Illustra-tions by John Hutchinson and Stan North. New York:Marshall Cavendish, 1990.



CENTRIFUGAL: A term describing the

tendency of objects in uniform circular

motion to move away from the center of

the circular path. Though the term “cen-

trifugal force” is often used, it is inertia,

rather than force, that causes the object to

move outward.

CENTRIPETAL FORCE: The force

that causes an object in uniform circular

motion to move toward the center of the

circular path.









Mass, time, and speed are all scalars. A

scalar is contrasted with a vector.



time.

TANGENTIAL: Movement along a tan-

gent, or a line that touches a circle at just

one point and does not intersect the circle.

UNIFORM CIRCULAR MOTION:

The motion of an object around the center

of a circle in such a manner that speed is

constant or unchanging.


both magnitude and direction. Velocity,

acceleration, and weight (which involves

the downward acceleration due to gravity)

are examples of vectors. It is contrasted

with a scalar.



KEY TERMS


CentripetalForce

“Centrifugal Force—Rotational Motion.” National Aero-nautics and Space Administration (Web site).<http://observe.ivv.nasa.gov/nasa/space/centrifugal/centrifugal3.html> (March 5, 2001).

“Circular and Satellite Motion” (Web site).<http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/circtoc.html> (March 5, 2001).

Cobb, Vicki. Why Doesn’t the Earth Fall Up? And OtherNot Such Dumb Questions About Motion. Illustratedby Ted Enik. New York: Lodestar Books, 1988.

Lefkowitz, R. J. Push! Pull! Stop! Go! A Book About Forces

and Motion. Illustrated by June Goldsborough. NewYork: Parents’ Magazine Press, 1975.

“Rotational Motion.” Physics Department, University ofGuelph (Web site).<http://www.physics.uoguelph.ca/tutorials/torque/>(March 4, 2001).

Schaefer, Lola M. Circular Movement. Mankato, MN:Pebble Books, 2000.

Snedden, Robert. Forces. Des Plaines, IL: HeinemannLibrary, 1999.

Whyman, Kathryn. Forces in Action. New York: Glouces-ter Press, 1986.




F R I C T IONFriction

CONCEPTFriction is the force that resists motion when thesurface of one object comes into contact with thesurface of another. In a machine, friction reducesthe mechanical advantage, or the ratio of outputto input: an automobile, for instance, uses one-quarter of its energy on reducing friction. Yet, itis also friction in the tires that allows the car tostay on the road, and friction in the clutch thatmakes it possible to drive at all. From matches tomachines to molecular structures, friction is oneof the most significant phenomena in the physi-cal world.

HOW IT WORKSThe definition of friction as “the force that resistsmotion when the surface of one object comesinto contact with the surface of another” doesnot exactly identify what it is. Rather, the state-ment describes the manifestation of friction interms of how other objects respond. A lesssophisticated version of such a definition wouldexplain electricity, for instance, as “the force thatruns electrical appliances.” The reason why fric-tion cannot be more firmly identified is simple:physicists do not fully understand what it is.

Much the same could be said of force,defined by Sir Isaac Newton’s (1642-1727) sec-ond law of motion as the product of mass multi-plied acceleration. The fact is that force is so fun-damental that it defies full explanation, except interms of the elements that compose it, and com-pared to force, friction is relatively easy to identi-fy. In fact, friction plays a part in the total forcethat must be opposed in order for movement totake place in many situations. So, too, does grav-

ity—and gravity, unlike force itself, is much easi-er to explain. Since gravity plays a role in friction,it is worthwhile to review its essentials.

Newton’s first law of motion identifies iner-tia, a tendency of objects in the physical universethat is sometimes mistaken for friction. When anobject is in motion or at rest, the first law states,it will remain in that state at a constant velocity(which is zero for an object at rest) unless or untilan outside force acts on it. This tendency toremain in a given state of motion is inertia.

Inertia is not a force: on the contrary, a verysmall quantity of force may accelerate an object,thus overcoming its inertia. Inertia is, however, acomponent of force, since mass is a measure ofinertia. In the case of gravitational force, mass ismultiplied by the acceleration due to gravity,which is equal to 32 ft (9.8 m)/sec2. People ineveryday life are familiar with another term forgravitational force: weight.

Weight, in turn, is an all-important factor infriction, as revealed in the three laws governingthe friction between an object at rest and the sur-face on which it sits. According to the first ofthese, friction is proportional to the weight of theobject. The second law states that friction is notdetermined by the surface area of the object—that is, the area that touches the surface on whichthe object rests. In fact, the contact area betweenobject and surface is a dependant variable, afunction of weight.

The second law might seem obvious if onewere thinking of a relatively elastic object—say, agarbage bag filled with newspapers sitting on thefinished concrete floor of a garage. Clearly asmore newspapers are added, thus increasing the


Frictionweight, its surface area would increase as well.But what if one were to compare a large card-board box (the kind, for instance, in which tele-visions or computers are shipped) with an ordi-nary concrete block of the type used in founda-tions for residential construction? Obviously, theblock has more friction against the concretefloor; but at the same time, it is clear that despiteits greater weight, the block has less surface areathan the box. How can this be?

The answer is that “surface area” is quite lit-erally more than meets the eye. Friction itselfoccurs at a level invisible to the naked eye, andinvolves the adhesive forces between moleculeson surfaces pushed together by the force ofweight. This is similar to the manner in which,when viewed through a high-powered lens, twocomplementary patches of Velcro™ are revealedas a forest of hooks on the one hand, and a sea ofloops on the other.

On a much more intensified level, that ofmolecular structure, the surfaces of objectsappear as mountains and valleys. Nothing, infact, is smooth when viewed on this scale, andhence, from a molecular perspective, it becomesclear that two objects in contact actually touchone another only in places. An increase of weight,however, begins pushing objects together, caus-ing an increase in the actual—that is, the molec-ular—area of contact. Hence area of contact isproportional to weight.

Just as the second law regarding friction statesthat surface area does not determine friction (butrather, weight determines surface area), the thirdlaw holds that friction is independent of the speedat which an object is moving along a surface—provided that speed is not zero. The reason forthis provision is that an object with no speed (thatis, one standing perfectly still) is subject to themost powerful form of friction, static friction.

The latter is the friction that an object at restmust overcome to be set in motion; however, thisshould not be confused with inertia, which is rel-atively easy to overcome through the use of force.Inertia, in fact, is far less complicated than staticfriction, involving only mass rather than weight.Nor is inertia affected by the composition of thematerials touching one another.

As stated earlier, friction is proportional toweight, which suggests that another factor isinvolved. And indeed there is another factor,known as coefficient of friction. The latter, desig-


nated by the Greek letter mu (µ), is constant forany two types of surface in contact with oneanother, and provides a means of comparing thefriction between them to that between other sur-faces. For instance, the coefficient of static fric-tion for wood on wood is 0.5; but for metal onmetal with lubrication in between, it is only 0.03.A rubber tire on dry concrete yields the highestcoefficient of static friction, 1.0, which is desir-able in that particular situation.

Coefficients are much lower for the secondtype of friction, sliding friction, the frictionalresistance experienced by a body in motion.Whereas the earlier figures measured the relativeresistance to putting certain objects into motion,the sliding-friction coefficient indicates the rela-tive resistance against those objects once they aremoving. To use the same materials mentionedabove, the coefficient of sliding friction for woodon wood is 0.3; for two lubricated metals 0.03 (nochange); and for a rubber tire on dry concrete 0.7.

Finally, there is a third variety of friction,one in which coefficients are so low as to be neg-

THE RAISED TREAD ON AN AUTOMOBILE’S TIRES, COU-PLED WITH THE ROUGHENED ROAD SURFACE, PROVIDES

SUFFICIENT FRICTION FOR THE DRIVER TO BE ABLE TO

TURN THE CAR AND TO STOP. (Photograph by Martyn God-

dard/Corbis. Reproduced by permission.)


Friction REAL-L IFEAPPLICATIONS

Self-Motivation ThroughFriction

Friction, in fact, always opposes movement; why,then, is friction necessary—as indeed it is—forwalking, and for keeping a car on the road? Theanswer relates to the differences between frictionand inertia alluded to earlier. In situations ofstatic friction, it is easy to see how a person mightconfuse friction with inertia, since both serve tokeep an object from moving. In situations of slid-ing or rolling friction, however, it is easier to seethe difference between friction and inertia.

Whereas friction is always opposed to move-ment, inertia is not. When an object is not mov-ing, its inertia does oppose movement—butwhen the object is in motion, then inertia resistsstopping. In the absence of friction or otherforces, inertia allows an object to remain inmotion forever. Imagine a hockey player hitting apuck across a very, very large rink. Because icehas a much smaller coefficient of friction withregard to the puck than does dirt or asphalt, thepuck will travel much further. Still, however, theice has some friction, and, therefore, the puckwill come to a stop at some point.

Now suppose that instead of ice, the surfaceand objects in contact with it were friction-free,possessing a coefficient of zero. Then what wouldhappen if the player hit the puck? Assuming forthe purposes of this thought experiment, that therink covered the entire surface of Earth, it wouldtravel and travel and travel, ultimately goingaround the planet. It would never stop, becausethere would be no friction to stop it, and there-fore inertia would have free rein.

The same would be true if one were to firm-ly push the hockey player with enough force(small in the absence of friction) to set him inmotion: he would continue riding around theplanet indefinitely, borne by his skates. But whatif instead of being set in motion, the hockey play-er tried to set himself in motion by the action ofhis skates against the rink’s surface?

He would be unable to move even a hair’sbreadth. The fact is that while static friction oppos-es the movement of an object from a position ofrest to a state of motion, it may—assuming it canbe overcome to begin motion at all—be indispen-sable to that movement. As with the skater in per-


ligible: rolling friction, or the frictional resistance

that a wheeled object experiences when it rolls

over a relatively smooth, flat surface. In ideal cir-

cumstances, in fact, there would be absolutely no

resistance between a wheel and a road. However,

there exists no ideal—that is, perfectly rigid—

wheel or road; both objects “give” in response to

the other, the wheel by flattening somewhat and

the road by experiencing indentation.

Up to this point, coefficients of friction have

been discussed purely in comparative terms, but in

fact, they serve a function in computing frictional

force—that is, the force that must be overcome to

set an object in motion, or to keep it in motion.

Frictional force is equal to the coefficient of fric-

tion multiplied by normal force—that is, the per-

pendicular force that one object or surface exerts

on another. On a horizontal plane, normal force is

equal to gravity and hence weight. In this equa-

tion, the coefficient of friction establishes a limit to

frictional force: in order to move an object in a

given situation, one must exert a force in excess of

the frictional force that keeps it from moving.

ACTOR JACK BUCHANAN LIT THIS MATCH USING A SIM-PLE DISPLAY OF FRICTION: DRAGGING THE MATCH

AGAINST THE BACK OF THE MATCHBOX. (Photograph by Hul-

ton-Deutsch Collection/Corbis. Reproduced by permission.)


Frictionpetual motion across the rink, the absence of fric-tion means that inertia is “in control;” with fric-tion, however, it is possible to overcome inertia.

Friction in Driving a Car

The same principle applies to a car’s tires: if theywere perfectly smooth—and, to make mattersworse, the road were perfectly smooth as well—the vehicle would keep moving forward when thedriver attempted to stop. For this reason, tires aredesigned with raised tread to maintain a highdegree of friction, gripping the road tightly anddispersing water when the roadway is wet.

The force of friction, in fact, pervades theentire operation of a car, and makes it possiblefor the tires themselves to turn. The turningforce, or torque, that the driver exerts on thesteering wheel is converted into forces that drivethe tires, and these in turn use friction to providetraction. Between steering wheel and tires, ofcourse, are a number of steps, with the enginerotating the crankshaft and transmitting powerto the clutch, which applies friction to translatethe motion of the crankshaft to the gearbox.

When the driver of a car with a manualtransmission presses down on the clutch pedal,this disengages the clutch itself. A clutch is a cir-cular mechanism containing (among otherthings) a pressure plate, which lifts off the clutchplate. As a result, the flywheel—the instrumentthat actually transmits force from the crank-shaft—is disengaged from the transmissionshaft. With the clutch thus disengaged, the driverchanges gears, and after the driver releases theclutch pedal, springs return the pressure plateand the clutch plate to their place against the fly-wheel. The flywheel then turns the transmissionshaft.

Controlled friction in the clutch makes thisoperation possible; likewise the synchromeshwithin the gearbox uses friction to bring thegearwheels into alignment. This is a complicatedprocess, but at the heart of it is an engagement ofgear teeth in which friction forces them to cometo the same speed.

Friction is also essential to stopping a car—not just with regard to the tires, but also withrespect to the brakes. Whether they are diskbrakes or drum brakes, two elements must cometogether with a force more powerful than theengine’s, and friction provides that needed force.In disk brakes, brake pads apply friction to both

sides of the spinning disks, and in drum brakes,brake shoes transmit friction to the inside of aspinning drum. This braking force is then trans-mitted to the tires, which apply friction to theroad and thus stop the car.

Efficiency and Friction

The automobile is just one among many exam-ples of a machine that could not operate withoutfriction. The same is true of simple machinessuch as screws, as well as nails, pliers, bolts, andforceps. At the heart of this relationship is a par-adox, however, because friction inevitablyreduces the efficiency of machines: a car, as notedearlier, exerts fully one-quarter of its power sim-ply on overcoming the force of friction bothwithin its engine and from air resistance as ittravels down the road.

In scientific terms, efficiency or mechanicaladvantage is measured by the ratio of force out-put to force input. Clearly, in most situations it isideal to maximize output and minimize input,and over the years inventors have dreamed ofcreating a mechanism—a perpetual motionmachine—to do just that. In this idealizedmachine, one would apply a certain amount ofenergy to set it into operation, and then it wouldnever stop; hence the ratio of output to inputwould be nearly infinite.

Unfortunately, the perpetual motionmachine is a dream every bit as elusive as themythical Fountain of Youth. At least this is trueon Earth, where friction will always cause a sys-tem to lose kinetic energy, or the energy of move-ment. No matter what the design, the machinewill eventually lose energy and stop; however,this is not true in outer space, where friction isvery small—though it still exists. In space itmight truly be possible to set a machine inmotion and let inertia do the rest; thus perhapsperpetual motion actually is more than a dream.

It should also be noted that mechanicaladvantage is not always desirable. A screw is ahighly inefficient machine: one puts much moreforce into screwing it in than the screw will exertonce it is in place. Yet this is exactly the purposeof a screw: an “efficient” one, or one that workedits way back out of the place into which it hadbeen screwed, would in fact be of little use.

Once again, it is friction that provides ascrew with its strangely efficient form of ineffi-ciency. Nonetheless, friction, in spite of the



Friction


advantages discussed above, is as undesirable as itis desirable. With friction, there is always some-thing lost; however, there is a physical law thatenergy does not simply disappear; it just changesform. In the case of friction, the energy thatcould go to moving the machine is instead trans-lated into sound—or even worse, heat.

When Sparks Fly

In movement involving friction, moleculesvibrate, bringing about a rise in temperature. Thiscan be easily demonstrated by simply rubbingone’s hands together quickly, as a person is apt todo when cold: heat increases. For a machine com-posed of metal parts, this increase in temperaturecan be disastrous, leading to serious wear anddamage. This is why various forms of lubricantare applied to systems subject to friction.

An automobile uses grease and oil, as well asball bearings, which are tiny uniform balls ofmetal that imitate the behavior of oil-based sub-stances on a large scale. In a molecule of oil—whether it is a petroleum-related oil or the typeof oil that comes from living things—positiveand negative electrical charges are distributedthroughout the molecule. By contrast, in waterthe positive charges are at one end of the mole-cule and the negative at the other. This creates atight bond as the positive end of one water mol-ecule adheres to the negative end of another.With oil, the relative absence of attractionbetween molecules means that each is in effect atiny ball separate from the others. The ball-likemolecules “roll” between metal elements, provid-ing the buffer necessary to reduce friction.

Yet for every statement one can make con-cerning friction, there is always another state-ment with which to counter it. Earlier it wasnoted that the wheel, because it reduced frictiongreatly, provided an enormous technologicalboost to societies. Yet long before the wheel—hundreds of thousands of years ago—an evenmore important technological breakthroughoccurred when humans made a discovery thatdepended on maximizing friction: fire, or ratherthe means of making fire. Unlike the wheel, fireoccurs in nature, and can spring from a numberof causes, but when human beings harnessed themeans of making fire on their own, they had torely on the heat that comes from friction.

By the early nineteenth century, inventorshad developed an easy method of creating fire by

using a little stick with a phosphorus tip. Thisstick, of course, is known as a match. In a strike-anywhere match, the head contains all the chem-icals needed to create a spark. To ignite this typeof match, one need only create frictional heat byrubbing it against a surface, such as sandpaper,with a high coefficient of friction.

The chemicals necessary for ignition in safe-ty matches, on the other hand, are dispersedbetween the match head and a treated strip, usu-ally found on the side of the matchbox or match-book. The chemicals on the tip and those on thestriking surface must come into contact for igni-tion to occur, but once again, there must be fric-tion between the match head and the strikingpad. Water reduces friction with its heavy bond,as it does with a car’s tires on a rainy day, whichexplains why matches are useless when wet.

The Outer Limits of Friction

Clearly friction is a complex subject, and the dis-coveries of modern physics only promise to addto that complexity. In a February 1999 onlinearticle for Physical Review Focus, Dana Macken-zie reported that “Engineers hope to makemicroscopic engines and gears as ordinary in ourlives as microscopic circuits are today. But beforethis dream becomes a reality, they will have todeal with laws of friction that are very differentfrom those that apply to ordinary-sizedmachines.”

The earlier statement that friction is propor-tional to weight, in fact, applies only in the realmof classical physics. The latter term refers to thestudies of physicists up to the end of the nine-teenth century, when the concerns were chieflythe workings of large objects whose operationscould be discerned by the senses. Modernphysics, on the other hand, focuses on atomicand molecular structures, and addresses physicalbehaviors that could not have been imaginedprior to the twentieth century.

According to studies conducted by AlanBurns and others at Sandia National Laborato-ries in Albuquerque, New Mexico, molecularinteractions between objects in very close prox-imity create a type of friction involving repulsionrather than attraction. This completely upsets themodel of friction understood for more than acentury, and indicates new frontiers of discoveryconcerning the workings of friction at a molecu-lar level.


Friction

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-

Wesley, 1991.

Buller, Laura and Ron Taylor. Forces of Nature. Illustra-

tions by John Hutchinson and Stan North. New York:

Marshall Cavendish, 1990.

Dixon, Malcolm and Karen Smith. Forces and Movement.Mankato, MN: Smart Apple Media, 1998.

“Friction.” How Stuff Works (Web site).<http://www.howstuffworks.com/search/index.htm?words=friction> (March 8, 2001).

“Friction and Interactions” (Web site).<http://www.cord.edu/dept/physics/p128/lec-ture99_12.html> (March 8, 2001).



COEFFICIENT OF FRICTION: A fig-

ure, constant for a particular pair of sur-

faces in contact, that can be multiplied by

the normal force between them to calculate

the frictional force they experience.






another. Varieties including sliding fric-

tion, static friction, and rolling friction.

The degree of friction between two specif-

ic surfaces is proportional to coefficient of

friction.

FRICTIONAL FORCE: The force nec-

essary to set an object in motion, or to keep

it in motion; equal to normal force multi-

plied by coefficient of friction.







MECHANICAL ADVANTAGE: The

ratio of force output to force input in a

machine.

NORMAL FORCE: The perpendicular

force with which two objects press against

one another. On a plane without any

incline (which would add acceleration in

addition to that of gravity) normal force is

the same as weight.

ROLLING FRICTION: The frictional

resistance that a circular object experiences

when it rolls over a relatively smooth, flat

surface. With a coefficient of friction much

smaller than that of sliding friction, rolling

friction involves by far the least amount

of resistance among the three varieties of

friction.

SLIDING FRICTION: The frictional

resistance experienced by a body in

motion. Here the coefficient of friction is

greater than that for rolling friction, but

less than for static friction.



time.

STATIC FRICTION: The frictional

resistance that a stationary object must

overcome before it can go into motion. Its

coefficient of friction is greater than that of

sliding friction, and thus largest among the

three varieties of friction.



WEIGHT: A measure of the gravitational

force on an object; the product of mass mul-

tiplied by the acceleration due to gravity.

KEY TERMS


Friction Levy, Matthys and Richard Panchyk. Engineering theCity: How Infrastructure Works. Chicago: ChicagoReview Press, 2000.

Macaulay, David. The New Way Things Work. Boston:Houghton Mifflin, 1998.

Mackenzie, Dana. “Friction of Molecules.” Physical ReviewFocus (Web site). <http://focus.aps.org/v3/st9.html(March 8, 2001).

Rutherford, F. James; Gerald Holton; and Fletcher G.

Watson. Project Physics. New York: Holt, Rinehart,

and Winston, 1981.

Skateboard Science (Web site). <http://www.exploratori-

um.edu/skateboarding/ (March 8, 2001).

Suplee, Curt. Everyday Science Explained. Washington,

D.C.: National Geographic Society, 1996.




L AWS OF MOT IONLaws of Motion

CONCEPTIn all the universe, there are few ideas more fun-damental than those expressed in the three lawsof motion. Together these explain why it is rela-tively difficult to start moving, and then to stopmoving; how much force is needed to start orstop in a given situation; and how one forcerelates to another. In their beauty and simplicity,these precepts are as compelling as a poem, andlike the best of poetry, they identify somethingthat resonates through all of life. The applica-tions of these three laws are literally endless: fromthe planets moving through the cosmos to thefirst seconds of a car crash to the action that takesplace when a person walks. Indeed, the laws ofmotion are such a part of daily life that termssuch as inertia, force, and reaction extend intothe realm of metaphor, describing emotionalprocesses as much as physical ones.

HOW IT WORKSThe three laws of motion are fundamental tomechanics, or the study of bodies in motion.These laws may be stated in a number of ways,assuming they contain all the components iden-tified by Sir Isaac Newton (1642-1727). It is onhis formulation that the following are based:

The Three Laws of Motion

• First law of motion: An object at rest willremain at rest, and an object in motion willremain in motion, at a constant velocityunless or until outside forces act upon it.

• Second law of motion: The net force actingupon an object is a product of its mass mul-tiplied by its acceleration.

• Third law of motion: When one object

exerts a force on another, the second objectexerts on the first a force equal in magni-tude but opposite in direction.

Laws of Man vs. Laws ofNature

These, of course, are not “laws” in the sense thatpeople normally understand that term. Humanlaws, such as injunctions against stealing or park-ing in a fire lane, are prescriptive: they state howthe world should be. Behind the prescriptivestatements of civic law, backing them up and giv-ing them impact, is a mechanism—police,courts, and penalties—for ensuring that citizensobey.

A scientific law operates in exactly the oppo-site fashion. Here the mechanism for ensuringthat nature “obeys” the law comes first, and the“law” itself is merely a descriptive statement con-cerning evident behavior. With human or civiclaw, it is clearly possible to disobey: hence, thejustice system exists to discourage disobedience.In the case of scientific law, disobedience is clear-ly impossible—and if it were not, the law wouldhave to be amended.

This is not to say, however, that scientificlaws extend beyond their own narrowly definedlimits. On Earth, the intrusion of outsideforces—most notably friction—prevents objectsfrom behaving perfectly according to the first lawof motion. The common-sense definition of fric-tion calls to mind, for instance, the action that amatch makes as it is being struck; in its broaderscientific meaning, however, friction can bedefined as any force that resists relative motionbetween two bodies in contact.


Laws ofMotion


The operations of physical forces on Earthare continually subject to friction, and thisincludes not only dry bodies, but liquids, forinstance, which are subject to viscosity, or inter-nal friction. Air itself is subject to viscosity, whichprevents objects from behaving perfectly inaccordance with the first law of motion. Otherforces, most notably that of gravity, also comeinto play to stop objects from moving endlesslyonce they have been set in motion.

The vacuum of outer space presents scien-tists with the most perfect natural laboratory fortesting the first law of motion: in theory, if theywere to send a spacecraft beyond Earth’s orbital

radius, it would continue travelling indefinitely.But even this craft would likely run into anotherobject, such as a planet, and would then be drawninto its orbit. In such a case, however, it can besaid that outside forces have acted upon it, andthus the first law of motion stands.

The orbit of a satellite around Earth illus-trates both the truth of the first law, as well as theforces that limit it. To break the force of gravity, apowered spacecraft has to propel the satellite intothe exosphere. Yet once it has reached the fric-tionless vacuum, the satellite will move indefi-nitely around Earth without need for the motivepower of an engine—it will get a “free ride,”

THE CARGO BAY OF THE SPACE SHUTTLE DISCOVERY, shown just after releasing a satellite. Oncereleased into the frictionless vacuum around Earth, the satellite will move indefinitelyaround Earth without need for the motive power of an engine. The planet’s gravity keeps itat a fixed height, and at that height, it could theoretically circle Earth forever. (Corbis. Repro-



Laws ofMotion


thanks to the first law of motion. Unlike thehypothetical spacecraft described above, howev-er, it will not go spinning into space, because it isstill too close to Earth. The planet’s gravity keepsit at a fixed height, and at that height, it couldtheoretically circle Earth forever.

The first law of motion deserves such partic-ular notice, not simply because it is the first law.Nonetheless, it is first for a reason, because itestablishes a framework for describing the behav-ior of an object in motion. The second law iden-tifies a means of determining the force necessaryto move an object, or to stop it from moving, andthe third law provides a picture of what happenswhen two objects exert force on one another.

The first law warrants special attentionbecause of misunderstandings concerning it,which spawned a debate that lasted nearly twen-ty centuries. Aristotle (384-322 B.C.) was the firstscientist to address seriously what is now knownas the first law of motion, though in fact, thatterm would not be coined until about two thou-sand years after his death. As its title suggests, hisPhysics was a seminal work, a book in which Aris-totle attempted to give form to, and thus definethe territory of, studies regarding the operationof physical processes. Despite the great philoso-pher’s many achievements, however, Physics is ahighly flawed work, particularly with regard towhat became known as his theory of impetus—that is, the phenomena addressed in the first lawof motion.

Aristotle’s Mistake

According to Aristotle, a moving object requiresa continual application of force to keep it mov-ing: once that force is no longer applied, it ceasesto move. You might object that, when a ball is inflight, the force necessary to move it has alreadybeen applied: a person has thrown the ball, and itis now on a path that will eventually be stoppedby the force of gravity. Aristotle, however, wouldhave maintained that the air itself acts as a forceto keep the ball in flight, and that when the balldrops—of course he had no concept of “gravity”as such—it is because the force of the air on theball is no longer in effect.

These notions might seem patently absurdto the modern mind, but they went virtuallyunchallenged for a thousand years. Then in thesixth century A.D., the Byzantine philosopherJohannes Philoponus (c. 490-570) wrote a cri-

tique of Physics. In what sounds very much like aprecursor to the first law of motion, Philoponusheld that a body will keep moving in the absenceof friction or opposition.

He further maintained that velocity is pro-portional to the positive difference between forceand resistance—in other words, that the forcepropelling an object must be greater than theresistance. As long as force exceeds resistance,Philoponus held, a body will remain in motion.This in fact is true: if you want to push a refriger-ator across a carpeted floor, you have to exertenough force not only to push the refrigerator, butalso to overcome the friction from the floor itself.

The Arab philosophers Ibn Sina (Avicenna;980-1037) and Ibn Bâjja (Avempace; fl. c. 1100)defended Philoponus’s position, and the Frenchscholar Peter John Olivi (1248-1298) became thefirst Western thinker to critique Aristotle’s state-ments on impetus. Real progress on the subject,however, did not resume until the time of JeanBuridan (1300-1358), a French physicist whowent much further than Philoponus had eightcenturies earlier.

In his writing, Buridan offered an amazinglyaccurate analysis of impetus that prefigured allthree laws of motion. It was Buridan’s positionthat one object imparts to another a certainamount of power, in proportion to its velocityand mass, that causes the second object to movea certain distance. This, as will be shown below,was amazingly close to actual fact. He was alsocorrect in stating that the weight of an objectmay increase or decrease its speed, depending onother circumstances, and that air resistance slowsan object in motion.

The true breakthrough in understanding thelaws of motion, however, came as the result ofwork done by three extraordinary men whoselives stretched across nearly 250 years. First cameNicolaus Copernicus (1473-1543), whoadvanced what was then a heretical notion: thatEarth, rather than being the center of the uni-verse, revolved around the Sun along with theother planets. Copernicus made his case purelyin terms of astronomy, however, with no directreference to physics.

Galileo’s Challenge: TheCopernican Model

Galileo Galilei (1564-1642) likewise embraced aheliocentric (Sun-centered) model of the uni-


Laws ofMotion

verse—a position the Church forced him torenounce publicly on pain of death. As a result ofhis censure, Galileo realized that in order to provethe Copernican model, it would be necessary toshow why the planets remain in motion as theydo. In explaining this, he coined the term inertiato describe the tendency of an object in motion toremain in motion, and an object at rest to remainat rest. Galileo’s observations, in fact, formed thefoundation for the laws of motion.

In the years that followed Galileo’s death,some of the world’s greatest scientific mindsbecame involved in the effort to understand theforces that kept the planets in motion around theSun. Among them were Johannes Kepler (1571-1630), Robert Hooke (1635-1703), and EdmundHalley (1656-1742). As a result of a disputebetween Hooke and Sir Christopher Wren (1632-1723) over the subject, Halley brought the ques-tion to his esteemed friend Isaac Newton. As itturned out, Newton had long been consideringthe possibility that certain laws of motion exist-ed, and these he presented in definitive form inhis Principia (1687).

The impact of the Newton’s book, whichincluded his observations on gravity, was nothingshort of breathtaking. For the next three centuries,human imagination would be ruled by the New-tonian framework, and only in the twentieth cen-tury would the onset of new ideas reveal its limita-tions. Yet even today, outside the realm of quan-tum mechanics and relativity theory—in otherwords, in the world of everyday experience—Newton’s laws of motion remain firmly in place.


The First Law of Motion in aCar Crash

It is now appropriate to return to the first law ofmotion, as formulated by Newton: an object at rest will remain at rest, and an object in motionwill remain in motion, at a constant velocity unlessor until outside forces act upon it. Examples of thisfirst law in action are literally unlimited.

One of the best illustrations, in fact, involvessomething completely outside the experience ofNewton himself: an automobile. As a car movesdown the highway, it has a tendency to remain inmotion unless some outside force changes its

velocity. The latter term, though it is commonlyunderstood to be the same as speed, is in factmore specific: velocity can be defined as thespeed of an object in a particular direction.

In a car moving forward at a fixed rate of 60MPH (96 km/h), everything in the car—driver,passengers, objects on the seats or in the trunk—is also moving forward at the same rate. If thatcar then runs into a brick wall, its motion will bestopped, and quite abruptly. But though itsmotion has stopped, in the split seconds after thecrash it is still responding to inertia: rather thanbouncing off the brick wall, it will continueplowing into it.

What, then, of the people and objects in thecar? They too will continue to move forward inresponse to inertia. Though the car has beenstopped by an outside force, those inside experi-ence that force indirectly, and in the fragment oftime after the car itself has stopped, they contin-ue to move forward—unfortunately, straight intothe dashboard or windshield.

It should also be clear from this exampleexactly why seatbelts, headrests, and airbags inautomobiles are vitally important. Attorneys mayfile lawsuits regarding a client’s injuries fromairbags, and homespun opponents of the seatbeltmay furnish a wealth of anecdotal evidence con-cerning people who allegedly died in an accidentbecause they were wearing seatbelts; nonetheless,the first law of motion is on the side of these pro-tective devices.

The admittedly gruesome illustration of acar hitting a brick wall assumes that the driverhas not applied the brakes—an example of anoutside force changing velocity—or has done sotoo late. In any case, the brakes themselves, ifapplied too abruptly, can present a hazard, andagain, the significant factor here is inertia. Likethe brick wall, brakes stop the car, but there isnothing to stop the driver and/or passengers.Nothing, that is, except protective devices: theseat belt to keep the person’s body in place, theairbag to cushion its blow, and the headrest toprevent whiplash in rear-end collisions.

Inertia also explains what happens to a carwhen the driver makes a sharp, sudden turn.Suppose you are is riding in the passenger seat ofa car moving straight ahead, when suddenly thedriver makes a quick left turn. Though the car’stires turn instantly, everything in the vehicle—itsframe, its tires, and its contents—is still respond-



Laws ofMotion

ing to inertia, and therefore “wants” to move for-ward even as it is turning to the left.

As the car turns, the tires may respond to thisshift in direction by squealing: their rubber sur-faces were moving forward, and with the suddenturn, the rubber skids across the pavement like ahard eraser on fine paper. The higher the originalspeed, of course, the greater the likelihood the tireswill squeal. At very high speeds, it is possible thecar may seem to make the turn “on two wheels”—that is, its two outer tires. It is even possible thatthe original speed was so high, and the turn sosharp, that the driver loses control of the car.

Here inertia is to blame: the car simply can-not make the change in velocity (which, again,refers both to speed and direction) in time. Evenin less severe situations, you are likely to feel thatyou have been thrown outward against the rider’sside door. But as in the car-and-brick-wall illus-tration used earlier, it is the car itself that firstexperiences the change in velocity, and thus itresponds first. You, the passenger, then, are mov-ing forward even as the car has turned; therefore,rather than being thrown outward, you are sim-ply meeting the leftward-moving door even asyou push forward.

From Parlor Tricks to SpaceShips

It would be wrong to conclude from the car-related illustrations above that inertia is alwaysharmful. In fact it can help every bit as much asit can potentially harm, a fact shown by two quitedifferent scenarios.

The beneficial quality to the first scenariomay be dubious: it is, after all, a mere parlor trick,albeit an entertaining one. In this famous stunt,with which most people are familiar even if theyhave never seen it, a full table setting is placed ona table with a tablecloth, and a skillful practition-er manages to whisk the cloth out from under thedishes without upsetting so much as a glass. Tosome this trick seems like true magic, or at leastsleight of hand; but under the right conditions, itcan be done. (This information, however, carrieswith it the warning, “Do not try this at home!”)

To make the trick work, several things mustalign. Most importantly, the person doing it hasto be skilled and practiced at performing the feat.On a physical level, it is best to minimize the fric-tion between the cloth and settings on the onehand, and the cloth and table on the other. It isalso important to maximize the mass (a property


WHEN A VEHICLE HITS A WALL, AS SHOWN HERE IN A CRASH TEST, ITS MOTION WILL BE STOPPED, AND QUITE ABRUPT-LY. BUT THOUGH ITS MOTION HAS STOPPED, IN THE SPLIT SECONDS AFTER THE CRASH IT IS STILL RESPONDING TO

INERTIA: RATHER THAN BOUNCING OFF THE BRICK WALL, IT WILL CONTINUE PLOWING INTO IT. (Photograph by Tim

Wright/Corbis. Reproduced by permission.)


Laws ofMotion

that will be discussed below) of the table settings,thus making them resistant to movement. Hence,inertia—which is measured by mass—plays a keyrole in making the tablecloth trick work.

You might question the value of the table-cloth stunt, but it is not hard to recognize theimportance of the inertial navigation system(INS) that guides planes across the sky. Prior tothe 1970s, when INS made its appearance, navi-gation techniques for boats and planes relied onreference to external points: the Sun, the stars,the magnetic North Pole, or even nearby areas ofland. This created all sorts of possibilities forerror: for instance, navigation by magnet (that is,a compass) became virtually useless in the polarregions of the Arctic and Antarctic.

By contrast, the INS uses no outside pointsof reference: it navigates purely by sensing theinertial force that results from changes in veloci-ty. Not only does it function as well near the polesas it does at the equator, it is difficult to tamperwith an INS, which uses accelerometers in asealed, shielded container. By contrast, radio sig-nals or radar can be “confused” by signals fromthe ground—as, for instance, from an enemyunit during wartime.

As the plane moves along, its INS measuresmovement along all three geometrical axes, andprovides a continuous stream of data regardingacceleration, velocity, and displacement. Thanksto this system, it is possible for a pilot leaving Cal-ifornia for Japan to enter the coordinates of a half-dozen points along the plane’s flight path, and letthe INS guide the autopilot the rest of the way.

Yet INS has its limitations, as illustrated bythe tragedy that occurred aboard Korean AirLines (KAL) Flight 007 on September 1, 1983.The plane, which contained 269 people and crewmembers, departed Anchorage, Alaska, on coursefor Seoul, South Korea. The route they would flywas an established one called “R-20,” and itappears that all the information regarding theirflight plan had been entered correctly in theplane’s INS.

This information included coordinates forinternationally recognized points of reference,actually just spots on the northern Pacific withnames such as NABIE, NUKKS, NEEVA, and soon, to NOKKA, thirty minutes east of Japan. Yet,just after passing the fishing village of Bethel,Alaska, on the Bering Sea, the plane started toveer off course, and ultimately wandered into

Soviet airspace over the Kamchatka Peninsulaand later Sakhalin Island. There a Soviet Su-15shot it down, killing all the plane’s passengers.

In the aftermath of the Flight 007 shoot-down, the Soviets accused the United States andSouth Korea of sending a spy plane into their air-space. (Among the passengers was Larry McDon-ald, a staunchly anti-Communist Congressmanfrom Georgia.) It is more likely, however, that thetragedy of 007 resulted from errors in navigationwhich probably had something to do with theINS. The fact is that the R-20 flight plan had beendesigned to keep aircraft well out of Soviet air-space, and at the time KAL 007 passed over Kam-chatka, it should have been 200 mi (320 km) tothe east—over the Sea of Japan.

Among the problems in navigating atranspacific flight is the curvature of the Earth,combined with the fact that the planet continuesto rotate as the aircraft moves. On such longflights, it is impossible to “pretend,” as on a shortflight, that Earth is flat: coordinates have to beadjusted for the rounded surface of the planet. Inaddition, the flight plan must take into accountthat (in the case of a flight from California toJapan), Earth is moving eastward even as theplane moves westward. The INS aboard KAL 007may simply have failed to correct for these fac-tors, and thus the error compounded as the planemoved further. In any case, INS will eventually berendered obsolete by another form of navigationtechnology: the global positioning satellite (GPS)system.

Understanding Inertia

From examples used above, it should be clearthat inertia is a more complex topic than youmight immediately guess. In fact, inertia as aprocess is rather straightforward, but confusionregarding its meaning has turned it into a com-plicated subject.

In everyday terminology, people typicallyuse the word inertia to describe the tendency of astationary object to remain in place. This is par-ticularly so when the word is used metaphorical-ly: as suggested earlier, the concept of inertia, likenumerous other aspects of the laws of motion, isoften applied to personal or emotional processesas much as the physical. Hence, you could say, forinstance, “He might have changed professionsand made more money, but inertia kept him athis old job.” Yet you could just as easily say, for



Laws ofMotion

example, “He might have taken a vacation, butinertia kept him busy.” Because of the misguidedway that most people use the term, it is easy toforget that “inertia” equally describes a tendencytoward movement or nonmovement: in terms ofNewtonian mechanics, it simply does not matter.

The significance of the clause “unless oruntil outside forces act upon it” in the first lawindicates that the object itself must be in equilib-rium—that is, the forces acting upon it must bebalanced. In order for an object to be in equilib-rium, its rate of movement in a given directionmust be constant. Since a rate of movementequal to 0 is certainly constant, an object at rest isin equilibrium, and therefore qualifies; but also,any object moving in a constant direction at aconstant speed is also in equilibrium.

The Second Law: Force,Mass, Acceleration

As noted earlier, the first law of motion deservesspecial attention because it is the key to unlock-ing the other two. Having established in the firstlaw the conditions under which an object inmotion will change velocity, the second law pro-vides a measure of the force necessary to causethat change.

Understanding the second law requiresdefining terms that, on the surface at least, seemlike a matter of mere common sense. Even iner-tia requires additional explanation in light ofterms related to the second law, because it wouldbe easy to confuse it with momentum.

The measure of inertia is mass, whichreflects the resistance of an object to a change inits motion. Weight, on the other hand, measuresthe gravitational force on an object. (The conceptof force itself will require further definitionshortly.) Hence a person’s mass is the same every-where in the universe, but their weight would dif-fer from planet to planet.

This can get somewhat confusing when youattempt to convert between English and metricunits, because the pound is a unit of weight orforce, whereas the kilogram is a unit of mass. Infact it would be more appropriate to set up kilo-grams against the English unit called the slug(equal to 14.59 kg), or to compare pounds to themetric unit of force, the newton (N), which isequal to the acceleration of one meter per secondper second on an object of 1 kg in mass.

Hence, though many tables of weights andmeasures show that 1 kg is equal to 2.21 lb, this isonly true at sea level on Earth. A person with amass of 100 kg on Earth would have the samemass on the Moon; but whereas he might weigh221 lb on Earth, he would be considerably lighteron the Moon. In other words, it would be mucheasier to lift a 221-lb man on the Moon than onEarth, but it would be no easier to push himaside.

To return to the subject of momentum,whereas inertia is measured by mass, momentumis equal to mass multiplied by velocity. Hencemomentum, which Newton called “quantity ofmotion,” is in effect inertia multiplied by veloci-ty. Momentum is a subject unto itself; what mat-ters here is the role that mass (and thus inertia)plays in the second law of motion.

According to the second law, the net forceacting upon an object is a product of its massmultiplied by its acceleration. The latter isdefined as a change in velocity over a given timeinterval: hence acceleration is usually presentedin terms of “feet (or meters) per second per sec-ond”—that is, feet or meters per second squared.The acceleration due to gravity is 32 ft (9.8 m)per second per second, meaning that as every sec-ond passes, the speed of a falling object isincreasing by 32 ft (9.8 m) per second.

The second law, as stated earlier, serves todevelop the first law by defining the force neces-sary to change the velocity of an object. The lawwas integral to the confirming of the Copernicanmodel, in which planets revolve around the Sun.Because velocity indicates movement in a single(straight) direction, when an object moves in acurve—as the planets do around the Sun—it isby definition changing velocity, or accelerating.The fact that the planets, which clearly possessedmass, underwent acceleration meant that someforce must be acting on them: a gravitational pullexerted by the Sun, most massive object in thesolar system.

Gravity is in fact one of four types of force atwork in the universe. The others are electromag-netic interactions, and “strong” and “weak”nuclear interactions. The other three wereunknown to Newton—yet his definition of forceis still applicable. Newton’s calculation of gravi-tational force (which, like momentum, is a sub-ject unto itself) made it possible for Halley todetermine that the comet he had observed in



Laws ofMotion


1682—the comet that today bears his name—would reappear in 1758, as indeed it has for every75–76 years since then. Today scientists use theunderstanding of gravitational force imparted byNewton to determine the exact altitude necessaryfor a satellite to remain stationary above the samepoint on Earth’s surface.

The second law is so fundamental to theoperation of the universe that you seldom noticeits application, and it is easiest to illustrate byexamples such as those above—of astronomersand physicists applying it to matters far beyondthe scope of daily life. Yet the second law alsomakes it possible, for instance, to calculate theamount of force needed to move an object, andthus people put it into use every day withoutknowing that they are doing so.

The Third Law: Action andReaction

As with the second law, the third law of motionbuilds on the first two. Having defined the forcenecessary to overcome inertia, the third law pre-dicts what will happen when one force comesinto contact with another force. As the third lawstates, when one object exerts a force on another,the second object exerts on the first a force equalin magnitude but opposite in direction.

Unlike the second law, this one is much eas-ier to illustrate in daily life. If a book is sitting ona table, that means that the book is exerting aforce on the table equal to its mass multiplied byits rate of acceleration. Though it is not moving,the book is subject to the rate of gravitationalacceleration, and in fact force and weight (whichis defined as mass multiplied by the rate of accel-eration due to gravity) are the same. At the sametime, the table pushes up on the book with anexactly equal amount of force—just enough tokeep it stationary. If the table exerted more forcethat the book—in other words, if instead ofbeing an ordinary table it were some sort ofpneumatic press pushing upward—then thebook would fly off the table.

There is no such thing as an unpaired forcein the universe. The table rests on the floor just asthe book rests on it, and the floor pushes up onthe table with a force equal in magnitude to thatwith which the table presses down on the floor.The same is true for the floor and the supportingbeams that hold it up, and for the supporting

beams and the foundation of the building, andthe building and the ground, and so on.

These pairs of forces exist everywhere. Whenyou walk, you move forward by pushing back-ward on the ground with a force equal to yourmass multiplied by your rate of downward grav-itational acceleration. (This force, in other words,is the same as weight.) At the same time, theground actually pushes back with an equal force.You do not perceive the fact that Earth is pushingyou upward, simply because its enormous massmakes this motion negligible—but it does push.

If you were stepping off of a smallunmoored boat and onto a dock, however, some-thing quite different would happen. The force ofyour leap to the dock would exert an equal forceagainst the boat, pushing it further out into thewater, and as a result, you would likely end up inthe water as well. Again, the reaction is equal andopposite; the problem is that the boat in thisillustration is not fixed in place like the groundbeneath your feet.

Differences in mass can result in apparentlydifferent reactions, though in fact the force is thesame. This can be illustrated by imagining amother and her six-year-old daughter skating onice, a relatively frictionless surface. Facing oneanother, they push against each other, and as aresult each moves backward. The child, of course,will move backward faster because her mass isless than that of her mother. Because the forcethey exerted is equal, the daughter’s accelerationis greater, and she moves farther.

Ice is not a perfectly frictionless surface, ofcourse: otherwise, skating would be impossible.Likewise friction is absolutely necessary for walk-ing, as you can illustrate by trying to walk on aperfectly slick surface—for instance, a skatingrink covered with oil. In this situation, there isstill an equally paired set of forces—your bodypresses down on the surface of the ice with asmuch force as the ice presses upward—but thelack of friction impedes the physical process ofpushing off against the floor.

It will only be possible to overcome inertiaby recourse to outside intervention, as forinstance if someone who is not on the ice tossedout a rope attached to a pole in the ground. Alter-natively, if the person on the ice were carrying aheavy load of rocks, it would be possible to moveby throwing the rocks backward. In this situa-tion, you are exerting force on the rock, and this


ACCELERATION: A change in velocity

over a given time period.

EQUILIBRIUM: A situation in which

the forces acting upon an object are in

balance.

FRICTION: Any force that resists the

motion of body in relation to another with

which it is in contact.






motion—including a change in velocity. A

kilogram is a unit of mass, whereas a

pound is a unit of weight. The mass of an

object remains the same throughout the

universe, whereas its weight is a function of

gravity on any given planet.


motion.

MOMENTUM: The product of mass

multiplied by velocity.


of an object changes over a given period

of time.



VISCOSITY: The internal friction in a

fluid that makes it resistant to flow.


al force on an object. A pound is a unit of

weight, whereas a kilogram is a unit of

mass. Weight thus would change from

planet to planet, whereas mass remains

constant throughout the universe.

KEY TERMSLaws ofMotion

backward force results in a force propelling the

thrower forward.

This final point about friction and move-

ment is an appropriate place to close the discus-

sion on the laws of motion. Where walking or

skating are concerned—and in the absence of a

bag of rocks or some other outside force—fric-

tion is necessary to the action of creating a back-

ward force and therefore moving forward. On the

other hand, the absence of friction would make it

possible for an object in movement to continue

moving indefinitely, in line with the first law of

motion. In either case, friction opposes inertia.

The fact is that friction itself is a force. Thus,

if you try to slide a block of wood across a floor,

friction will stop it. It is important to remember

this, lest you fall into the fallacy that bedeviled

Aristotle’s thinking and thus confused the world

for many centuries. The block did not stop mov-

ing because the force that pushed it was no

longer being applied; it stopped because an

opposing force, friction, was greater than theforce that was pushing it.

WHERE TO LEARN MORE

Ardley, Neil. The Science Book of Motion. San Diego:Harcourt Brace Jovanovich, 1992.


Chase, Sara B. Moving to Win: The Physics of Sports. NewYork: Messner, 1977.

Fleisher, Paul. Secrets of the Universe: Discovering the Uni-versal Laws of Science. Illustrated by Patricia A. Keel-er. New York: Atheneum, 1987.

“The Laws of Motion.” How It Flies (Web site).<http://www.monmouth.com/~jsd/how/htm/motion.html> (February 27, 2001).

Newton, Isaac (translated by Andrew Motte, 1729). ThePrincipia (Web site).<http://members.tripod.com/~gravitee/principia.html> (February 27, 2001).

Newton’s Laws of Motion (Web site). <http://www.glen-brook.k12.il.us/gbssci/phys/Class/newtlaws/newtloc.html> (February 27, 2001).



Laws ofMotion

“Newton’s Laws of Motion.” Dryden Flight Research Cen-

ter, National Aeronautics and Space Administration

(NASA) (Web site). <http://www.dfrc.nasa.gov/

trc/saic/newton.html> (February 27, 2001).

“Newton’s Laws of Motion: Movin’ On.” Beyond Books

(Web site). <http://www.beyondbooks.com/psc91/4.asp> (February 27, 2001).

Roberts, Jeremy. How Do We Know the Laws of Motion?New York: Rosen, 2001.





GR AV I T Y AND GR AV I TAT IONGravity and Gravitation

CONCEPTGravity is, quite simply, the force that holdstogether the universe. People are accustomed tothinking of it purely in terms of the gravitationalpull Earth exerts on smaller bodies—a stone, ahuman being, even the Moon—or perhaps interms of the Sun’s gravitational pull on Earth. Infact, everything exerts a gravitational attractiontoward everything else, an attraction commensu-rate with the two body’s relative mass, andinversely related to the distance between them.The earliest awareness of gravity emerged inresponse to a simple question: why do objects fallwhen released from any restraining force? Theanswers, which began taking shape in the six-teenth century, were far from obvious. In mod-ern times, understanding of gravitational forcehas expanded manyfold: gravity is clearly a lawthroughout the universe—yet some of the morecomplicated questions regarding gravitationalforce are far from settled.

HOW IT WORKS

Aristotle’s Model

Greek philosophers of the period from the sixthto the fourth century B.C. grappled with a varietyof questions concerning the fundamental natureof physical reality, and the forces that bind thatreality into a whole. Among the most advancedthinkers of that period was Democritus (c. 460-370 B.C.), who put forth a hypothesis many thou-sands of years ahead of its time: that all of matterinteracts at the atomic level.

Aristotle (384-322 B.C.), however, rejectedthe explanation offered by Democritus, an unfor-tunate circumstance given the fact that the great

philosopher exerted an incalculable influence onthe development of scientific thought. Aristotle’scontributions to the advancement of the scienceswere many and varied, yet his influence inphysics was at least as harmful as it was benefi-cial. Furthermore, the fact that intellectualprogress began slowing after several fruitful cen-turies of development in Greece only com-pounded the error. By the time civilization hadreached the Middle Ages (c. 500 A.D.) the Aris-totelian model of physical reality had been firm-ly established, and an entire millennium passedbefore it was successfully challenged.

Wrong though it was in virtually all particu-lars, the Aristotelian system offered a comfortingsymmetry amid the troubled centuries of theearly medieval period. It must have been reassur-ing indeed to believe that the physical universewas as simple as the world of human affairs wascomplex. According to this neat model, all mate-rials on Earth consisted of four elements: earth,water, air, and fire.

Each element had its natural place. Hence,earth was always the lowest, and in some places,earth was covered by water. Water must then behigher, but clearly air was higher still, since itcovered earth and water. Highest of all was fire,whose natural place was in the skies above theair. Reflecting these concentric circles were theorbits of the Sun, the Moon, and the five knownplanets. Their orbital paths, in the Aristotelianmodel of the universe—a model developed to agreat degree by the astronomer Ptolemy (c. 100-170)—were actually spheres that revolvedaround Earth with clockwork precision.

On Earth, according to the Aristotelianmodel, objects tended to fall toward the groundin accordance with the admixtures of differing


Gravity andGravitation


elements they contained. A rock, for instance,was mostly earth, and hence it sought its ownlevel, the lowest of all four elements. For the samereason, a burning fire rose, seeking the heightsthat were fire’s natural domain. It followed fromthis that an object falls faster or slower, depend-ing on the relative mixtures of elements in it: or,to use more modern terms, the heavier theobject, the faster it falls.

Galileo Takes Up the Coper-nican Challenge

Over the centuries, a small but significant bodyof scientists and philosophers—each workingindependent from the other but building on theideas of his predecessors—slowly began chippingaway at the Aristotelian framework. The pivotalchallenge came in the early part of the century,and the thinker who put it forward was not aphysicist but an astronomer: Nicolaus Coperni-cus (1473-1543.)

Based on his study of the planets, Coperni-cus offered an entirely new model of the uni-verse, one that placed the Sun and not Earth at itscenter. He was not the first to offer such an idea:half a century after Aristotle’s death, Aristarchus(fl. 270 B.C.) had a similar idea, but Ptolemy

rejected his heliocentric (Sun-centered) model infavor of the geocentric or Earth-centered one. Insubsequent centuries, no less a political authori-ty than the Catholic Church gave its approval tothe Ptolemaic system. This system seemed to fitwell with a literal interpretation of biblical pas-sages concerning God’s relationship with man,and man’s relationship to the cosmos; hence, theheliocentric model of Copernicus constituted anoffense to morality.

For this reason, Copernicus was hesitant todefend his ideas publicly, yet these conceptsfound their way into the consciousness of Euro-pean thinkers, causing a paradigm shift so funda-mental that it has been dubbed “the CopernicanRevolution.” Still, Copernicus offered no expla-nation as to why the planets behaved as they did:hence, the true leader of the Copernican Revolu-tion was not Copernicus himself but GalileoGalilei (1564-1642.)

Initially, Galileo set out to study and defendthe ideas of Copernicus through astronomy, butsoon the Church forced him to recant. It is saidthat after issuing a statement in which he refutedthe proposition that Earth moves—a directattack on the static harmony of the Aris-totelian/Ptolemaic model—he protested in pri-

BECAUSE OF EARTH’S GRAVITY, THE WOMAN BEING SHOT OUT OF THIS CANNON WILL EVENTUALLY FALL

TO THE GROUND RATHER THAN ASCEND INTO OUTER SPACE. (Underwood & Underwood/Corbis. Reproduced by

permission.)



vate: “E pur si muove!” (But it does move!) Placedunder house arrest by authorities from Rome, heturned his attention to an effort that, ironically,struck the fatal blow against the old model of thecosmos: a proof of the Copernican systemaccording to the laws of physics.

GRAVITATIONAL ACCELERA-

TION. In the process of defending Copernicus,Galileo actually inaugurated the modern historyof physics as a science (as opposed to what it hadbeen during the Middle Ages: a nest of supposi-tions masquerading as knowledge). Specifically,Galileo set out to test the hypothesis that objectsfall as they do, not because of their weight, but asa consequence of gravitational force. If this wereso, the acceleration of falling bodies would haveto be the same, regardless of weight. Of course, itwas clear that a stone fell faster than a feather, butGalileo reasoned that this was a result of factorsother than weight, and later investigations con-firmed that air resistance and friction, notweight, are responsible for this difference.

On the other hand, if one drops two objectsthat have similar air resistance but differingweight—say, a large stone and a smaller one—they fall at almost exactly the same rate. To testthis directly, however, would have been difficultfor Galileo: stones fall so fast that, even ifdropped from a great height, they would hit theground too soon for their rate of fall to be testedwith the instruments then available.

Instead, Galileo used the motion of a pendu-lum, and the behavior of objects rolling or slid-ing down inclined planes, as his models. On thebasis of his observations, he concluded that allbodies are subject to a uniform rate of gravita-tional acceleration, later calibrated at 32 ft (9.8m) per second. What this means is that for every32 ft an object falls, it is accelerating at a rate of32 ft per second as well; hence, after 2 seconds, itfalls at the rate of 64 ft (19.6 m) per second; after3 seconds, at 96 ft (29.4 m) per second, and so on.

Newton Discovers the Princi-ple of Gravity

Building on the work of his distinguished fore-bear, Sir Isaac Newton (1642-1727)—who, inci-dentally, was born the same year Galileo died—developed a paradigm for gravitation that, eventoday, explains the behavior of objects in virtual-ly all situations throughout the universe. Indeed,the Newtonian model reigned until the early


twentieth century, when Albert Einstein (1879-1955) challenged it on certain specifics.

Even so, Einstein’s relativity did not disprovethe Newtonian system as Copernicus and Galileodisproved Aristotle’s and Ptolemy’s theories;rather, it showed the limitations of Newtonianmechanics for describing the behavior of certainobjects and phenomena. However, in the ordi-nary world of day-to-day experience—the worldin which stones drop and heavy objects are hardto lift—the Newtonian system still offers the keyto how and why things work as they do. This isparticularly the case with regard to gravity andgravitation.

Like Galileo, Newton began in part with theaim of testing hypotheses put forth by anastronomer—in this case Johannes Kepler (1571-1630). In the early years of the seventeenth cen-tury, Kepler published his three laws of planetarymotion, which together identified the elliptical(oval-shaped) path of the planets around theSun. Kepler had discovered a mathematical rela-tionship that connected the distances of the plan-ets from the Sun to the period of their revolution

THIS PHOTO SHOWS AN APPLE AND A FEATHER BEING

DROPPED IN A VACUUM TUBE. BECAUSE OF THE

ABSENCE OF AIR RESISTANCE, THE TWO OBJECTS FALL

AT THE SAME RATE. (Photograph by James A. Sugar/Corbis. Repro-




around it. Like Galileo with Copernicus, Newtonsought to generalize these principles to explain,not only how the planets moved, but also whythey did.

Almost everyone has heard the story ofNewton and the apple—specifically, that while hewas sitting under an apple tree, a falling applestruck him on the head, spurring in him a greatintuitive leap that led him to form his theory ofgravitation. One contemporary biographer,William Stukely, wrote that he and Newton weresitting in a garden under some apple trees whenNewton told him that “...he was just in the samesituation, as when formerly, the notion of gravi-tation came into his mind. It was occasion’d bythe fall of an apple, as he sat in a contemplativemood. Why should that apple always descendperpendicularly to the ground, he thought tohimself. Why should it not go sideways orupwards, but constantly to the earth’s centre?”

The tale of Newton and the apple hasbecome a celebrated myth, rather like that ofGeorge Washington and the cherry tree. It is anembellishment of actual events: Newton neversaid that an apple hit him on the head, just thathe was thinking about the way that apples fell. Yetthe story has become symbolic of the creativeintellectual process that occurs when a thinkermakes a vast intuitive leap in a matter ofmoments. Of course, Newton had spent manyyears contemplating these ideas, and their devel-opment required great effort. What is importantis that he brought together the best work of hispredecessors, yet transcended all that had gonebefore—and in the process, forged a model thatexplained a great deal about how the universefunctions.

The result was his Philosophiae NaturalisPrincipia Mathematica, or “Mathematical Princi-ples of Natural Philosophy.” Published in 1687,the book—usually referred to simply as the Prin-cipia—was one of the most influential works everwritten. In it, Newton presented his three laws ofmotion, as well as his law of universal gravita-tion.

The latter stated that every object in the uni-verse attracts every other one with a force pro-portional to the masses of each, and inverselyproportional to the square of the distancebetween them. This statement requires someclarification with regard to its particulars, after

which it will be reintroduced as a mathematicalformula.

MASS AND FORCE. The three lawsof motion are a subject unto themselves, coveredelsewhere in this volume. However, in order tounderstand gravitation, it is necessary to under-stand at least a few rudimentary concepts relatingto them. The first law identifies inertia as the ten-dency of an object in motion to remain inmotion, and of an object at rest to remain at rest.Inertia is measured by mass, which—as the sec-ond law states—is a component of force.

Specifically, the second law of motion statesthat force is equal to mass multiplied by acceler-ation. This means that there is an inverse rela-tionship between mass and acceleration: if forceremains constant and one of these factorsincreases, the other must decrease—a situationthat will be discussed in some depth below.

Also, as a result of Newton’s second law, it ispossible to define weight scientifically. Peopletypically assume that mass and weight are thesame, and indeed they are on Earth—or at least,they are close enough to be treated as compara-ble factors. Thus, tables of weights and measuresshow that a kilogram, the metric unit of mass, isequal to 2.2 pounds, the latter being the principalunit of weight in the British system.

In fact, this is—if not a case of comparing toapples to oranges—certainly an instance of com-paring apples to apple pies. In this instance, thekilogram is the “apple” (a fitting Newtonianmetaphor!) and the pound the “apple pie.” Just asan apple pie contains apples, but other things aswell, the pound as a unit of force contains anadditional factor, acceleration, not included inthe kilo.

BRITISH VS. SI UNITS. Physi-cists universally prefer the metric system, whichis known in the scientific community as SI (anabbreviation of the French Système Internationald’Unités—that is, “International System ofUnits”). Not only is SI much more convenient touse, due to the fact that it is based on units of 10;but in discussing gravitation, the unequal rela-tionship between kilograms and pounds makesconversion to British units a tedious and ulti-mately useless task.

Though Americans prefer the British systemto SI, and are much more familiar with poundsthan with kilos, the British unit of mass—calledthe slug—is hardly a household word. By con-




trast, scientists make regular use of the SI unit offorce—named, appropriately enough, the new-ton. In the metric system, a newton (N) is theamount of force required to accelerate 1 kilo-gram of mass by 1 meter per second squared(m/s2) Due to the simplicity of using SI over theBritish system, certain aspects of the discussionbelow will be presented purely in terms of SI.Where appropriate, however, conversion toBritish units will be offered.

CALCULATING GRAVITATION-

AL FORCE. The law of universal gravitationcan be stated as a formula for calculating thegravitational attraction between two objects of acertain mass, m1 AND M2: Fgrav = G • (m1M2)/R2. Fgrav is gravitational force, and r2 the square ofthe distance between m1 and m2.

As for G, in Newton’s time the value of thisnumber was unknown. Newton was aware sim-ply that it represented a very small quantity:without it, (m1m2)/r2 could be quite sizeable forobjects of relatively great mass separated by a rel-atively small distance. When multiplied by thisvery small number, however, the gravitationalattraction would be revealed to be very small aswell. Only in 1798, more than a century afterNewton’s writing, did English physicist HenryCavendish (1731-1810) calculate the value of G.

As to how Cavendish derived the figure, thatis an exceedingly complex subject far beyond thescope of the present discussion. Even to identifyG as a number is a challenging task. First of all, itis a unit of force multiplied by squared area, thendivided by squared mass: in other words, it isexpressed in terms of (N • m2)/kg2, where Nstands for newtons, m for meters, and kg for kilo-grams. Nor is the coefficient, or numerical value,of G a whole number such as 1. A figure as largeas 1, in fact, is astronomically huge compared toG, whose coefficient is 6.67 • 10-11—in otherwords, 0.0000000000667.


Weight vs. Mass

Before discussing the significance of the gravita-tional constant, however, at this point it is appro-priate to address a few issues that were raised ear-lier—issues involving mass and weight. In manyways, understanding these properties from the

framework of physics requires setting asideeveryday notions.

First of all, why the distinction betweenweight and mass? People are so accustomed toconverting pounds to kilos on Earth that the dif-ference is difficult to comprehend, but if oneconsiders the relation of mass and weight inouter space, the distinction becomes much clear-er. Mass is the same throughout the universe,making it a much more fundamental characteris-tic—and hence, physicists typically speak interms of mass rather than weight.

Weight, on the other hand, differs accordingto the gravitational pull of the nearest large body.On Earth, a person weighs a certain amount, buton the Moon, this weight is much less, becausethe Moon possesses less mass than Earth. There-fore, in accordance with Newton’s formula foruniversal gravitation, it exerts less gravitationalpull. By contrast, if one were on Jupiter, it wouldbe almost impossible even to stand up, becausethe pull of gravity on that planet—with itsgreater mass—would be vastly greater than onEarth.

It should be noted that mass is not at all afunction of size: Jupiter does have a greater massthan Earth, but not because it is bigger. Mass, asnoted earlier, is purely a measure of inertia: themore resistant an object is to a change in itsvelocity, the greater its mass. This in itself yieldssome results that seem difficult to understand aslong as one remains wedded to the concept—true enough on Earth—that weight and mass areidentical.

A person might weigh less on the Moon, butit would be just as difficult to move that personfrom a resting position as it would be to do so onEarth. This is because the person’s mass, andhence his or her resistance to inertia, has notchanged. Again, this is a mentally challengingconcept: is not lifting a person, which impliesupward acceleration, not an attempt to counter-act their inertia when standing still? Does it notfollow that their mass has changed? Understand-ing the distinction requires a greater clarificationof the relationship between mass, gravity, andweight.

F = ma. Newton’s second law of motion,stated earlier, shows that force is equal to massmultiplied by acceleration, or in shorthand form,F = ma. To reiterate a point already made, if oneassumes that force is constant, then mass and




acceleration must have an inverse relationship.This can be illustrated by performing a simpleexperiment.

Suppose one were to apply a certain amountof force to an empty shopping cart. Assuming thefloor had just enough friction to allow move-ment, it would be easy for almost anyone toaccelerate the shopping cart. Now assume thatthe shopping cart were filled with heavy leadballs, so that it weighed, say, 1,102 lb (500 kg). Ifone applied the same force, it would not move.

What has changed, clearly, is the mass of theshopping cart. Because force remained constant,the rate of acceleration would become verysmall—in this case, almost infinitesimal. In thefirst case, with an empty shopping cart, the masswas relatively small, so acceleration was relativelyhigh.

Now to return to the subject of lifting some-one on the Moon. It is true that in order to liftthat person, one would have to overcome inertia,and, in that sense, it would be as difficult as it ison Earth. But the other component of force,acceleration, has diminished greatly.

Weight is, again, a unit of force, but in calcu-lating weight it is useful to make a slight changeto the formula F = ma. By definition, the acceler-ation factor in weight is the downward accelera-tion due to gravity, usually rendered as g. So one’sweight is equal to mg—but on the Moon, g ismuch smaller than it is on Earth, and hence, thesame amount of force yields much greaterresults.

These facts shed new light on a question thatbedeviled physicists at least from the time ofAristotle, until Galileo began clarifying the issuesome 2,000 years later: why shouldn’t an object ofgreater mass fall at a different rate than one ofsmaller mass? There are two answers to thatquestion, one general and one specific. The gen-eral answer—that Earth exerts more gravitation-al pull on an object of greater mass—requires adeeper examination of Newton’s gravitationalformula. But the more specific answer, relatingpurely to conditions on Earth, is easily addressedby considering the effect of air resistance.

Gravity and Air Resistance

One of Galileo’s many achievements lay in usingan idealized model of reality, one that does nottake into account the many complex factors thataffect the behavior of objects in the real world.

This permitted physicists to study processes thatapparently defy common sense. For instance, inthe real world, an apple does drop at a greaterrate of speed than does a feather. However, in avacuum, they will drop at the same rate. SinceGalileo’s time, it has become commonplace forphysicists to discuss specific processes such asgravity with the assumption that all non-perti-nent factors (in this case, air resistance or fric-tion) are nonexistent or irrelevant. This greatlysimplified the means of testing hypotheses.

Idealization of reality makes it possible to setaside the things people think they know aboutthe real world, where events are complicated dueto friction. The latter may be defined as a forcethat resists motion when the surface of oneobject comes into contact with the surface ofanother. If two balls are released in an environ-ment free from friction—one of them simplydropped while the other is rolled down a curvedsurface or inclined plane—they will reach thebottom at the same time. This seems to goagainst everything that is known, but that is onlybecause what people “know” is complicated byvariables that have nothing to do with gravity.

The same is true for the behavior of fallingobjects with regard to air resistance. If air resist-ance were not a factor, one could fire a cannon-ball over horizontal space and then, when the ballreached the highest point in its trajectory, releaseanother ball from the same height—and again,they would hit the ground at the same time. Thisis the case, even though the cannonball that wasfired from the cannon has to cover a great deal ofhorizontal space, whereas the dropped ball doesnot. The fact is that the rate of acceleration dueto gravity will be identical for the two balls, andthe fact that the ball fired from a cannon alsocovers a horizontal distance during that sameperiod is irrelevant.

TERMINAL VELOCITY. In the realworld, air resistance creates a powerful drag forceon falling objects. The faster the rate of fall, thegreater the drag force, until the air resistanceforces a leveling in the rate of fall. At this point,the object is said to have reached terminal veloc-ity, meaning that its rate of fall will not increasethereafter. Galileo’s idealized model, on the otherhand, treated objects as though they were fallingin a vacuum—space entirely devoid of matter,including air. In such a situation, the rate ofacceleration would continue to grow indefinitely.




By means of a graph, one can compare thebehavior of an object falling through air withthat of an object falling in a vacuum. If the x axismeasures time and the y axis downward speed,the rate of an object falling in a vacuum describesa 60°-angle. In other words, the speed of itsdescent is increasing at a much faster rate than isthe rate of time of its descent—as indeed shouldbe the case, in accordance with gravitationalacceleration. The behavior of an object fallingthrough air, on the other hand, describes a curve.Up to a point, the object falls at the same rate asit would in a vacuum, but soon velocity begins toincrease at a much slower rate than time. Eventu-ally, the curve levels off at the point where theobject experiences terminal velocity.

Air resistance and friction have been men-tioned separately as though they were two differ-ent forces, but in fact air resistance is simply aprominent form of friction. Hence air resistanceexerts an upward force to counter the downwardforce of mass multiplied by gravity—that is,weight. Since g is a constant (32 ft or 9.8 m/sec2),the greater the weight of the falling object, thelonger it takes for air resistance to bring it to ter-minal velocity.

A feather quickly reaches terminal velocity,whereas it takes much longer for a cannonball todo the same. As a result, a heavier object doestake less time to fall, even from a great height,than does a light one—but this is only because offriction, and not because of “elements” seekingtheir “natural level.” Incidentally, if raindrops(which of course fall from a very great height)did not reach terminal velocity, they would causeserious injury by the time they hit the ground.

Applying the GravitationalFormula

Using Newton’s gravitational formula, it is rela-tively easy to calculate the pull of gravity betweentwo objects. It is also easy to see why the attrac-tion is insignificant unless at least one of theobjects has enormous mass. In addition, applica-tion of the formula makes it clear why G (thegravitational constant, as opposed to g, the rate ofacceleration due to gravity) is such a tiny number.

If two people each have a mass of 45.5 kg(100 lb) and stand 1 m (3.28 ft) apart, m1m2 isequal to 2,070 kg (4,555 lb) and r2 is equal to 1m2. Applied to the gravitational formula, this fig-ure is rendered as 2,070 kg2/1 m2. This number is

then multiplied by gravitational constant, whichagain is equal to 6.67 • 10-11 (N • m2)/kg2. Theresult is a net gravitational force of 0.000000138N (0.00000003 lb)—about the weight of a single-cell organism!

EARTH, GRAVITY, AND WEIGHT.

Though it is certainly interesting to calculate thegravitational force between any two people, com-putations of gravity are only significant forobjects of truly great mass. For instance, there isthe Earth, which has a mass of 5.98 • 1024 kg—that is, 5.98 septillion (1 followed by 24 zeroes)kilograms. And, of course, Earth’s mass is rela-tively minor compared to that of several planets,not to mention the Sun. Yet Earth exerts enoughgravitational pull to keep everything on it—liv-ing creatures, manmade structures, mountainsand other natural features—stable and in place.

One can calculate Earth’s gravitational forceon any one person—if one wants to take the timeto do so using Newton’s formula. In fact, it ismuch simpler than that: gravitational force isequal to weight, or m • g. Thus if a woman weighs100 lb (445 N), this amount is also equal to thegravitational force exerted on her. By divid-ing 445 N by the acceleration of gravity—9.8m/sec2—it is easy to obtain her mass: 45.4 kg.

The use of the mg formula for gravitationhelps, once again, to explain why heavier objectsdo not fall faster than lighter ones. The figure forg is a constant, but for the sake of argument, letus assume that it actually becomes larger forobjects with a greater mass. This in turn wouldmean that the gravitational force, or weight,would be bigger than it is—thus creating anirreconcilable logic loop.

Furthermore, one can compare results oftwo gravitation equations, one measuring thegravitational force between Earth and a largestone, the other measuring the force betweenEarth and a small stone. (The distance betweenEarth and each stone is assumed to be the same.)The result will yield a higher quantity for theforce exerted on the larger stone—but onlybecause its mass is greater. Clearly, then, theincrease of force results only from an increase inmass, not acceleration.

Gravity and Curved Space

As should be clear from Newton’s gravitationalformula, the force of gravity works both ways:not only does a stone fall toward Earth, but Earth





actually falls toward it. The mass of Earth is sogreat compared to that of the stone that themovement of Earth is imperceptible—but it doeshappen. Furthermore, because Earth is round,when one hurls a projectile at a great distance,Earth curves away from the projectile; but even-tually gravity itself forces the projectile to theground.

However, if one were to fire a rocket at17,700 MPH (28,500 km/h), at every instant oftime the projectile is falling toward Earth withthe force of gravity—but the curved Earth wouldbe falling away from it at the same moment aswell. Hence, the projectile would remain in con-stant motion around the planet—that is, it wouldbe in orbit.

The same is true of an artificial satellite’sorbit around Earth: even as the satellite fallstoward Earth, Earth falls away from it. This samerelationship exists between Earth and its greatnatural satellite, the Moon. Likewise, with the

Sun and its many satellites, including Earth:Earth plunges toward the Sun with every instantof its movement, but at every instant, the Sunfalls away.

WHY IS EARTH ROUND? Notethat in the above discussion, it was assumed thatEarth and the Sun are round. Everyone knowsthat to be the case, but why? The answer is“Because they have to be”—that is, gravity willnot allow them to be otherwise. In fact, the larg-er the mass of an object, the greater its tendencytoward roundness: specifically, the gravitationalpull of its interior forces the surface to assume arelatively uniform shape. There is a relativelysmall vertical differential for Earth’s surface:between the lowest point and the highest point isjust 12.28 mi (19.6 km)—not a great distance,considering that Earth’s radius is about 4,000 mi(6,400 km).

It is true that Earth bulges near the equator,but this is only because it is spinning rapidly on






another.




INVERSE RELATIONSHIP: A situa-

tion involving two variables, in which one

of the two increases in direct proportion to

the decrease in the other.

LAW OF UNIVERSAL GRAVITATION:

A principle, put forth by Sir Isaac Newton

(1642-1727), which states that every object

in the universe attracts every other one

with a force proportional to the masses of

each, and inversely proportional to the

square of the distance between them.



motion.

TERMINAL VELOCITY: A term

describing the rate of fall for an object

experiencing the drag force of air resist-

ance. In a vacuum, the object would con-

tinue to accelerate with the force of gravity,

but in most real-world situations, air

resistance creates a powerful drag force

that causes a leveling in the object’s rate of

fall.



WEIGHT: A measure of the gravitational

force on an object; the product of mass mul-

tiplied by the acceleration due to gravity.

KEY TERMS



its axis, and thus responding to the centripetalforce of its motion, which produces a centrifugalcomponent. If Earth were standing still, it wouldbe much nearer to the shape of a sphere. On theother hand, an object of less mass is more likelyto retain a shape that is far less than spherical.This can be shown by reference to the Martianmoons Phobos and Deimos, both of which areoblong—and both of which are tiny, in terms ofsize and mass, compared to Earth’s Moon.

Mars itself has a radius half that of Earth, yetits mass is only about 10% of Earth’s. In light ofwhat has been said about mass, shape, and grav-ity, it should not surprising to learn that Mars isalso home to the tallest mountain in the solarsystem. Standing 15 mi (24 km) high, the volcanoOlympus Mons is not only much taller thanEarth’s tallest peak, Mount Everest (29,028 ft[8,848 m]); it is 22% taller than the distance fromthe top of Mount Everest to the lowest spot onEarth, the Mariana Trench in the Pacific Ocean (-35,797 ft [-10,911 m])

A spherical object behaves with regard togravitation as though its mass were concentratednear its center. And indeed, 33% of Earth’s massis at is core (as opposed to the crust or mantle),even though the core accounts for only about20% of the planet’s volume. Geologists believethat the composition of Earth’s core must bemolten iron, which creates the planet’s vast elec-tromagnetic field.

THE FRONTIERS OF GRAVITY.

The subject of curvature with regard to gravitycan be both a threshold or—as it is here—a pointof closure. Investigating questions over perceivedanomalies in Newton’s description of the behav-ior of large objects in space led Einstein to hisGeneral Theory of Relativity, which posited acurved four-dimensional space-time. This led toentirely new notions concerning gravity, mass,and light. But relativity, as well as its relation togravity, is another subject entirely. Einsteinoffered a new understanding of gravity, andindeed of physics itself, that has changed the way

thinkers both inside and outside the sciences per-ceive the universe. Here on Earth, however, grav-ity behaves much as Newton described it morethan three centuries ago.

Meanwhile, research in gravity continues toexpand, as a visit to the Web site <www.Gravi-ty.org> reveals. Spurred by studies in relativity, abranch of science called relativistic astrophysicshas developed as a synthesis of astronomy andphysics that incorporates ideas put forth by Ein-stein and others. The <www.Gravity.org> sitepresents studies—most of them too abstruse fora reader who is not a professional scientist—across a broad spectrum of disciplines. Amongthese is bioscience, a realm in which researchersare investigating the biological effects—such asmineral loss and motion sickness—of exposureto low gravity. The results of such studies willultimately protect the health of the astronautswho participate in future missions to outer space.

WHERE TO LEARN MORE

Ardley, Neil. The Science Book of Gravity. San Diego, CA:Harcourt Brace Jovanovich, 1992.


Bendick, Jeanne. Motion and Gravity. New York: F. Watts,1972.

Dalton, Cindy Devine. Gravity. Vero Beach, FL: Rourke,2001.

David, Leonard. “Artificial Gravity and Space Travel.” Bio-Science, March 1992, pp. 155-159.

Exploring Gravity—Curtin University, Australia (Website). <http://www.curtin.edu.au/curtin/dept/phys-sci/gravity/> (March 18, 2001).

The Gravity Society (Web site). <http://www.gravity.org>(March 18, 2001).

Nardo, Don. Gravity: The Universal Force. San Diego,CA: Lucent Books, 1990.


Stringer, John. The Science of Gravity. Austin, TX: Rain-tree Steck-Vaughn, 2000.




PROJECT I LE MOT IONProjectile Motion

CONCEPTA projectile is any object that has been thrown,shot, or launched, and ballistics is the study ofprojectile motion. Examples of projectiles rangefrom a golf ball in flight, to a curve ball thrownby a baseball pitcher to a rocket fired into space.The flight paths of all projectiles are affected bytwo factors: gravity and, on Earth at least, airresistance.

HOW IT WORKSThe effects of air resistance on the behavior ofprojectiles can be quite complex. Because effectsdue to gravity are much simpler and easier toanalyze, and since gravity applies in more situa-tions, we will discuss its role in projectile motionfirst. In most instances on Earth, of course, a pro-jectile will be subject to both forces, but theremay be specific cases in which an artificial vacu-um has been created, which means it will only besubjected to the force of gravity. Furthermore, inouter space, gravity—whether from Earth oranother body—is likely to be a factor, whereas airresistance (unless or until astronomers findanother planet with air) will not be.

The acceleration due to gravity is 32 ft (9.8 m)/sec2, usually expressed as “per secondsquared.” This means that as every second passes,the speed of a falling object is increasing by 32 ft/sec (9.8 m). Where there is no air resistance,a ball will drop at a velocity of 32 feet per secondafter one second, 64 ft (19.5 m) per second aftertwo seconds, 96 ft (29.4 m) per second after threeseconds, and so on. When an object experiencesthe ordinary acceleration due to gravity, this fig-ure is rendered in shorthand as g. Actually, thefigure of 32 ft (9.8 m) per second squared applies

at sea level, but since the value of g changes littlewith altitude—it only decreases by 5% at a heightof 10 mi (16 km)—it is safe to use this number.

When a plane goes into a high-speed turn, itexperiences much higher apparent g. This can beas high as 9 g, which is almost more than thehuman body can endure. Incidentally, people callthese “g-forces,” but in fact g is not a measure offorce but of a single component, acceleration. Onthe other hand, since force is the product of massmultiplied by acceleration, and since an aircraftsubject to a high g factor clearly experiences aheavy increase in net force, in that sense, theexpression “g-force” is not altogether inaccurate.

In a vacuum, where air resistance plays nopart, the effects of g are clearly demonstrated.Hence a cannonball and a feather, dropped into avacuum at the same moment, would fall at exact-ly the same rate and hit bottom at the same time.

The Cannonball or theFeather? Air Resistance vs.Mass

Naturally, air resistance changes the terms of theabove equation. As everyone knows, under ordi-nary conditions, a cannonball falls much fasterthan a feather, not simply because the feather islighter than the cannonball, but because the airresists it much better. The speed of descent is afunction of air resistance rather than mass, whichcan be proved with the following experiment.Using two identical pieces of paper—meaningthat their mass is exactly the same—wad one upwhile keeping the other flat. Then drop them.Which one lands first? The wadded piece will fallfaster and land first, precisely because it is lessair-resistant than the sail-like flat piece.


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Now to analyze the motion of a projectile ina situation without air resistance. Projectilemotion follows the flight path of a parabola, acurve generated by a point moving such that itsdistance from a fixed point on one axis is equal toits distance from a fixed line on the other axis. Inother words, there is a proportional relationshipbetween x and y throughout the trajectory orpath of a projectile in motion. Most often thisparabola can be visualized as a simple up-and-down curve like the shape of a domed roof. (TheGateway Arch in St. Louis, Missouri, is a steepparabola.)

Instead of referring to the more abstract val-ues of x and y, we will separate projectile motioninto horizontal and vertical components. Gravityplays a role only in vertical motion, whereasobviously, horizontal motion is not subject togravitational force. This means that in theabsence of air resistance, the horizontal velocityof a projectile does not change during flight; bycontrast, the force of gravity will ultimatelyreduce its vertical velocity to zero, and this will inturn bring a corresponding drop in its horizontalvelocity.

In the case of a cannonball fired at a 45°angle—the angle of maximum efficiency forheight and range together—gravity will eventu-

ally force the projectile downward, and once ithits the ground, it can no longer continue on itshorizontal trajectory. Not, at least, at the samevelocity: if you were to thrust a bowling ball for-ward, throwing it with both hands from the solarplexus, its horizontal velocity would be reducedgreatly once gravity forced it to the floor.Nonetheless, the force on the ball would proba-bly be enough (assuming the friction on the floorwas not enormous) to keep the ball moving in ahorizontal direction for at least a few more feet.

There are several interesting things aboutthe relationship between gravity and horizontalvelocity. Assuming, once again, that air resistanceis not a factor, the vertical acceleration of a pro-jectile is g. This means that when a cannonball isat the highest point of its trajectory, you couldsimply drop another cannonball from exactly thesame height, and they would land at the samemoment. This seems counterintuitive, or oppo-site to common sense: after all, the cannonballthat was fired from the cannon has to cover agreat deal of horizontal space, whereas thedropped ball does not. Nonetheless, the rate ofacceleration due to gravity will be identical forthe two balls, and the fact that the ball fired froma cannon also covers a horizontal distance duringthat same period is purely incidental.

BECAUSE OF THEIR DESIGN, THE BULLETS IN THIS .357 MAGNUM WILL COME OUT OF THE GUN SPINNING, WHICH

GREATLY INCREASES THEIR ACCURACY. (Photograph by Tim Wright/Corbis. Reproduced by permission.)


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ted to the barrel of the musket. When fired, theybounced erratically off the sides of the barrel,and this made their trajectories unpredictable.Compounding this was the unevenness of thelead balls themselves, and this irregularity ofshape could lead to even greater irregularities intrajectory.

Around 1500, however, the first true riflesappeared, and these greatly enhanced the accura-cy of firearms. The term rifle comes from the“rifling” of the musket barrels: that is, the barrelsthemselves were engraved with grooves, a processknown as rifling. Furthermore, ammunition-makers worked to improve the productionprocess where the musket balls were concerned,producing lead rounds that were more uniformin shape and size.

Despite these improvements, soldiers overthe next three centuries still faced many chal-lenges when firing lead balls from rifled barrels.The lead balls themselves, because they weremade of a soft material, tended to become mis-shapen during the loading process. Furthermore,the gunpowder that propelled the lead balls hada tendency to clog the rifle barrel. Most impor-tant of all was the fact that these rifles took timeto load—and in a situation of battle, this couldcost a man his life.

The first significant change came in the1840s, when in place of lead balls, armies beganusing bullets. The difference in shape greatlyimproved the response of rounds to aerodynam-ic factors. In 1847, Claude-Etienne Minié, a cap-tain in the French army, developed a bullet madeof lead, but with a base that was slightly hollow.Thus when fired, the lead in the round tended toexpand, filling the barrel’s diameter and grippingthe rifling.

As a result, the round came out of the barrelend spinning, and continued to spin throughoutits flight. Not only were soldiers able to fire theirrifles with much greater accuracy, but thanks tothe development of chambers and magazines,they could reload more quickly.

Curve Balls, Dimpled GolfBalls, and Other Tricks withSpin

In the case of a bullet, spin increases accuracy,ensuring that the trajectory will follow an expect-ed path. But sometimes spin can be used in more


Gravity, combined with the first law ofmotion, also makes it possible (in theory at least)for a projectile to keep moving indefinitely. Thisactually does take place at high altitudes, when asatellite is launched into orbit: Earth’s gravita-tional pull, combined with the absence of airresistance or other friction, ensures that the satel-lite will remain in constant circular motionaround the planet. The same is theoretically pos-sible with a cannonball at very low altitudes: ifone could fire a ball at 17,700 MPH (28,500k/mh), the horizontal velocity would be greatenough to put the ball into low orbit aroundEarth’s surface.

The addition of air resistance or airflow tothe analysis of projectile motion creates a num-ber of complications, including drag, or the forcethat opposes the forward motion of an object inairflow. Typically, air resistance can create a dragforce proportional to the squared value of a pro-jectile’s velocity, and this will cause it to fall farshort of its theoretical range.

Shape, as noted in the earlier illustrationconcerning two pieces of paper, also affects airresistance, as does spin. Due to a principle knownas the conservation of angular momentum, anobject that is spinning tends to keep spinning;moreover, the orientation of the spin axis (theimaginary “pole” around which the object isspinning) tends to remain constant. Thus spinensures a more stable flight.


Bullets on a Straight Spinning Flight

One of the first things people think of when theyhear the word “ballistics” is the study of gunfirepatterns for the purposes of crime-solving.Indeed, this application of ballistics is a signifi-cant part of police science, because it allows law-enforcement investigators to determine when,where, and how a firearm was used. In a largersense, however, the term as applied to firearmsrefers to efforts toward creating a more effective,predictable, and longer bullet trajectory.

From the advent of firearms in the West dur-ing the fourteenth century until about 1500,muskets were hopelessly unreliable. This wasbecause the lead balls they fired had not been fit-


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complex ways, as with a curveball thrown by abaseball pitcher.

The invention of the curveball is credited toArthur “Candy” Cummings, who as a pitcher forthe Brooklyn Excelsiors at the age of 18 in 1867—an era when baseball was still very young—intro-duced a new throw he had spent several yearsperfecting. Snapping as he released the ball, heand the spectators (not to mention the startledbatter for the opposing team) watched as thepitch arced, then sailed right past the batter for astrike.

The curveball bedeviled baseball players andfans alike for many years thereafter, and manydismissed it as a type of optical illusion. Thedebate became so heated that in 1941, both Lifeand Look magazines ran features using stop-action photography to show that a curveballtruly did curve. Even in 1982, a team ofresearchers from General Motors (GM) and theMassachusetts Institute of Technology (MIT),working at the behest of Science magazine, inves-tigated the curveball to determine if it was morethan a mere trick.

In fact, the curveball is a trick, but there isnothing fake about it. As the pitcher releases theball, he snaps his wrist. This puts a spin on theprojectile, and air resistance does the rest. As theball moves toward the plate, its spin movesagainst the air, which creates an airstream mov-ing against the trajectory of the ball itself. Theairstream splits into two lines, one curving overthe ball and one curving under, as the ball sailstoward home plate.

For the purposes of clarity, assume that youare viewing the throw from a position betweenthird base and home. Thus, the ball is movingfrom left to right, and therefore the direction ofairflow is from right to left. Meanwhile the ball,as it moves into the airflow, is spinning clock-wise. This means that the air flowing over the topof the ball is moving in a direction opposite tothe spin, whereas that flowing under it is movingin the same direction as the spin.

This creates an interesting situation, thanksto Bernoulli’s principle. The latter, formulated bySwiss mathematician and physicist DanielBernoulli (1700-1782), holds that where velocityis high, pressure is low—and vice versa. Bernoul-li’s principle is of the utmost importance to aero-dynamics, and likewise plays a significant role inthe operation of a curveball. At the top of the

ball, its clockwise spin is moving in a directionopposite to the airflow. This produces drag, slow-ing the ball, increasing pressure, and thus forcingit downward. At the bottom end of the ball, how-ever, the clockwise motion is flowing with the air,thus resulting in higher velocity and lower pres-sure. As per Bernoulli’s principle, this tends topull the ball downward.

In the 60-ft, 6-in (18.4-m) distance that sep-arates the pitcher’s mound from home plate on aregulation major-league baseball field, a curve-ball can move downward by a foot (0.3048 m) ormore. The interesting thing here is that thisdownward force is almost entirely due to airresistance rather than gravity, though of coursegravity eventually brings any pitch to the ground,assuming it has not already been hit, caught, orbounced off a fence.

A curveball represents a case in which spin isused to deceive the batter, but it is just as possiblethat a pitcher may create havoc at home plate bythrowing a ball with little or no spin. This iscalled a knuckleball, and it is based on the factthat spin in general—though certainly not thedeliberate spin of a curveball—tends to ensure a

GOLF BALLS ARE DIMPLED BECAUSE THEY TRAVEL MUCH

FARTHER THAN NONDIMPLED ONES. (Photograph by D.

Boone/Corbis. Reproduced by permission.)


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more regular trajectory. Because a knuckleballhas no spin, it follows an apparently randompath, and thus it can be every bit as tricky for thepitcher as for the batter.

Golf, by contrast, is a sport in which spin isexpected: from the moment a golfer hits the ball,it spins backward—and this in turn helps toexplain why golf balls are dimpled. Early golfballs, known as featheries, were merely smoothleather pouches containing goose feathers. Thesmooth surface seemed to produce relatively lowdrag, and golfers were impressed that a well-hitfeathery could travel 150-175 yd (137-160 m).

Then in the late nineteenth century, a pro-fessor at St. Andrews University in Scotland real-ized that a scored or marked ball would travelfarther than a smooth one. (The part about St.Andrews may simply be golfing legend, since thecourse there is regarded as the birthplace of golfin the fifteenth century.) Whatever the case, it istrue that a scored ball has a longer trajectory,again as a result of the effect of air resistance onprojectile motion.

Airflow produces two varieties of drag on asphere such as a golf ball: drag due to friction,which is only a small aspect of the total drag, andthe much more significant drag that results fromthe separation of airflow around the ball. As withthe curveball discussed earlier, air flows aboveand below the ball, but the issue here is morecomplicated than for the curved pitch.

Airflow comes in two basic varieties: lami-nar, meaning streamlined; or turbulent, indicat-ing an erratic, unpredictable flow. For a jet flyingthrough the air, it is most desirable to create alaminar flow passing over its airfoil, or thecurved front surface of the wing. In the case ofthe golf ball, however, turbulent flow is moredesirable.

In laminar flow, the airflow separates quick-ly, part of it passing over the ball and part passingunder. In turbulent flow, however, separationcomes later, further back on the ball. Each formof air separation produces a separation region, anarea of drag that the ball pulls behind it (so tospeak) as it flies through space. But because theseparation comes further back on the ball in tur-bulent flow, the separation region itself is nar-rower, thus producing less drag.

Clearly, scoring the ball produced turbulentflow, and for a few years in the early twentiethcentury, manufacturers experimented with

designs that included squares, rectangles, andhexagons. In time, they settled on the dimpleddesign known today. Golf balls made in Britainhave 330 dimples, and those in America 336; ineither case, the typical drive distance is much,much further than for an unscored ball—180-250 yd (165-229 m).

Powered Projectiles: Rock-ets and Missiles

The most complex form of projectile widelyknown in modern life is the rocket or missile.Missiles are unmanned vehicles, most often usedin warfare to direct some form of explosivetoward an enemy. Rockets, on the other hand,can be manned or unmanned, and may bepropulsion vehicles for missiles or for spacecraft.The term rocket can refer either to the engine orto the vehicle it propels.

The first rockets appeared in China duringthe late medieval period, and were used unsuc-cessfully by the Chinese against Mongol invadersin the early part of the thirteenth century. Euro-peans later adopted rocketry for battle, as forinstance when French forces under Joan of Arcused crude rockets in an effort to break the siegeon Orleans in 1429.

Within a century or so, however, rocketry asa form of military technology became obsolete,though projectile warfare itself remained aseffective a method as ever. From the catapults ofRoman times to the cannons that appeared in theearly Renaissance to the heavy artillery of today,armies have been shooting projectiles againsttheir enemies. The crucial difference betweenthese projectiles and rockets or missiles is that thelatter varieties are self-propelled.

Only around the end of World War II didrocketry and missile warfare begin to reappear innew, terrifying forms. Most notable among thesewas Hitler’s V-2 “rocket” (actually a missile),deployed against Great Britain in 1944, but for-tunately developed too late to make an impact.The 1950s saw the appearance of nuclear war-heads such as the ICBM (intercontinental ballis-tic missile). These were guided missiles, asopposed to the V-2, which was essentially a hugeself-propelled bullet fired toward London.

More effective than the ballistic missile,however, was the cruise missile, which appearedin later decades and which included aerodynam-ic structures that assisted in guidance and



maneuvering. In addition to guided or unguided,ballistic or aerodynamic, missiles can be classi-fied in terms of source and target: surface-to-sur-face, air-to-air, and so on. By the 1970s, the Unit-ed States had developed an extraordinarilysophisticated surface-to-air missile, the Stinger.Stingers proved a decisive factor in the Afghan-Soviet War (1979-89), when U.S.-suppliedAfghan guerrillas used them against Soviet air-craft.

In the period from the late 1940s to the late1980s, the United States, the Soviet Union, andother smaller nuclear powers stockpiled thesewarheads, which were most effective precisely

because they were never used. Thus, U.S. Presi-dent Ronald Reagan played an important role inending the Cold War, because his weaponsbuildup forced the Soviets to spend money theydid not have on building their own arsenal. Dur-ing the aftermath of the Cold War, America andthe newly democratized Russian Federationworked to reduce their nuclear stockpiles. Ironi-cally, this was also the period when sophisticatedmissiles such as the Patriot began gaining wide-spread use in the Persian Gulf War and later conflicts.

Certain properties unite the many varietiesof rocket that have existed across time and


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IN THE CASE OF A ROCKET, LIKE THIS PATRIOT MISSILE BEING LAUNCHED DURING A TEST, PROPULSION COMES BY

EXPELLING FLUID—WHICH IN SCIENTIFIC TERMS CAN MEAN A GAS AS WELL AS A LIQUID—FROM ITS REAR END. MOST

OFTEN THIS FLUID IS A MASS OF HOT GASES PRODUCED BY A CHEMICAL REACTION INSIDE THE ROCKET’S BODY, AND

THIS BACKWARD MOTION CREATES AN EQUAL AND OPPOSITE REACTION FROM THE ATMOSPHERE, PROPELLING THE

ROCKET FORWARD. (Corbis. Reproduced by permission.)


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ACCELERATION: A change in velocity

over a given time period.

AERODYNAMIC: Relating to airflow.

BALLISTICS: The study of projectile

motion.

DRAG: The force that opposes the for-

ward motion of an object in airflow. In

most cases, its opposite is lift.

FIRST LAW OF MOTION: A principle,

formulated by Sir Isaac Newton (1642-

1727), which states that an object at rest

will remain at rest, and an object in motion

will remain in motion, at a constant veloci-

ty unless or until outside forces act upon it.

FRICTION: Any force that resists the

motion of body in relation to another with

which it is in contact.




LAMINAR: A term describing a stream-

lined flow, in which all particles move at

the same speed and in the same direction.

Its opposite is turbulent flow.

LIFT: An aerodynamic force perpendi-

cular to the direction of the wind. In most

cases, its opposite is drag.




PARABOLA: A curve generated by a

point moving such that its distance from a

fixed point on one axis is equal to its dis-

tance from a fixed line on the other axis. As

a result, between any two points on the

parabola there is a proportional relation-

ship between x and y values.

PROJECTILE: Any object that has

been thrown, shot, or launched.

SPECIFIC IMPULSE: A measure of

rocket fuel efficiency—specifically, the

mass that can be lifted by a particular type

of fuel for each pound of fuel consumer

(that is, the rocket and its contents) per

second of operation time. Figures for spe-

cific impulse are rendered in seconds.



time. Unlike velocity, direction is not a

component of speed.

THIRD LAW OF MOTION: A princi-

ple, which like the first law of motion was

formulated by Sir Isaac Newton. The third

law states that when one object exerts a

force on another, the second object exerts

on the first a force equal in magnitude but

opposite in direction.

TRAJECTORY: The path of a projectile

in motion, a parabola upward and across

space.

TURBULENT: A term describing a

highly irregular form of flow, in which a

fluid is subject to continual changes in

speed and direction. Its opposite is laminar

flow.





KEY TERMS


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space—including the relatively harmless fire-works used in Fourth of July and New Year’s Evecelebrations around the country. One of the keyprinciples that makes rocket propulsion possibleis the third law of motion. Sometimes colloquial-ly put as “For every action, there is an equal andopposite reaction,” a more scientifically accurateversion of this law would be: “When one objectexerts a force on another, the second object exertson the first a force equal in magnitude but oppo-site in direction.”

In the case of a rocket, propulsion comes byexpelling fluid—which in scientific terms canmean a gas as well as a liquid—from its rear.Most often this fluid is a mass of hot gases pro-duced by a chemical reaction inside the rocket’sbody, and this backward motion creates an equaland opposite reaction from the rocket, propellingit forward.

Before it undergoes a chemical reaction,rocket fuel may be either in solid or liquid forminside the rocket’s fuel chamber, though it endsup as a gas when expelled. Both solid and liquidvarieties have their advantages and disadvantagesin terms of safety, convenience, and efficiency inlifting the craft. Scientists calculate efficiency by anumber of standards, among them specificimpulse, a measure of the mass that can be liftedby a particular type of fuel for each pound of fuelconsumed (that is, the rocket and its contents)per second of operation time. Figures for specif-ic impulse are rendered in seconds.

A spacecraft may be divided into segmentsor stages, which can be released as specific points

along the flight in part to increase specific

impulse. This was the case with the Saturn 5

rockets that carried astronauts to the Moon in

the period 1969-72, but not with the varieties of

space shuttle that have flown regular missions

since 1981.

The space shuttle is essentially a hybrid of an

airplane and rocket, with a physical structure

more like that of an aircraft but with rocket

power. In fact, the shuttle uses many rockets to

maximize efficiency, utilizing no less than 67

rockets—49 of which run on liquid fuel and the

rest on solid fuel—at different stages of its flight.

WHERE TO LEARN MORE

“Aerodynamics in Sports Equipment.” K8AIT Principles ofAeronautics—Advanced (Web site).<http://muttley.ucdavis.edu/Book/Sports/advanced/index.html> (March 2, 2001).

Asimov, Isaac. Exploring Outer Space: Rockets, Probes, andSatellites. Revisions and updates by Francis Reddy.Milwaukee, WI: G. Stevens, 1995.

How in the World? Pleasantville, N.Y.: Reader’s Digest,1990.

“Interesting Properties of Projectile of Motion” (Web site).<http://www.phy.ntnu.edu.tw/~hwang/projectile3/projectile3.html> (March 2, 2001).

JBM Small Arms Ballistics (Web site). <http://roadrun-ner.com/~jbm/index_rgt.html> (March 2, 2001).

The Physics of Projectile Motion (Web site).<http://library.thinkquest.org/2779/> (March 2,2001).

Richardson, Hazel. How to Build a Rocket. Illustrated byScoular Anderson. New York: F. Watts, 2001.




TORQUETorque

CONCEPTTorque is the application of force where there isrotational motion. The most obvious example oftorque in action is the operation of a crescentwrench loosening a lug nut, and a close second isa playground seesaw. But torque is also crucial tothe operation of gyroscopes for navigation, andof various motors, both internal-combustionand electrical.

HOW IT WORKSForce, which may be defined as anything thatcauses an object to move or stop moving, is thelinchpin of the three laws of motion formulatedby Sir Isaac Newton (1642-1727.) The first lawstates that an object at rest will remain at rest,and an object in motion will remain in motion,unless or until outside forces act upon it. The sec-ond law defines force as the product of massmultiplied by acceleration. According to the thirdlaw, when one object exerts a force on another,the second object exerts on the first a force equalin magnitude but opposite in direction.

One way to envision the third law is in termsof an active event—for instance, two balls strik-ing one another. As a result of the impact, eachflies backward. Given the fact that the force oneach is equal, and that force is the product ofmass and acceleration (this is usually renderedwith the formula F = ma), it is possible to makesome predictions regarding the properties ofmass and acceleration in this interchange. Forinstance, if the mass of one ball is relatively smallcompared to that of the other, its accelerationwill be correspondingly greater, and it will thusbe thrown backward faster.

On the other hand, the third law can bedemonstrated when there is no apparent move-ment, as for instance, when a person is sitting ona chair, and the chair exerts an equal and oppo-site force upward. In such a situation, when allthe forces acting on an object are in balance, thatobject is said to be in a state of equilibrium.

Physicists often discuss torque within thecontext of equilibrium, even though an objectexperiencing net torque is definitely not in equi-librium. In fact, torque provides a convenientmeans for testing and measuring the degree ofrotational or circular acceleration experienced byan object, just as other means can be used to cal-culate the amount of linear acceleration. In equi-librium, the net sum of all forces acting on anobject should be zero; thus in order to meet thestandards of equilibrium, the sum of all torqueson the object should also be zero.


Seesaws and Wrenches

As for what torque is and how it works, it is bestdiscuss it in relationship to actual objects in thephysical world. Two in particular are favoritesamong physicists discussing torque: a seesaw anda wrench turning a lug nut. Both provide an easymeans of illustrating the two ingredients oftorque, force and moment arm.

In any object experiencing torque, there is apivot point, which on the seesaw is the balance-point, and which in the wrench-and-lug nutcombination is the lug nut itself. This is the areaaround which all the forces are directed. In each


Torque


case, there is also a place where force is beingapplied. On the seesaw, it is the seats, each hold-ing a child of differing weight. In the realm ofphysics, weight is actually a variety of force.

Whereas force is equal to mass multiplied byacceleration, weight is equal to mass multipliedby the acceleration due to gravity. The latter isequal to 32 ft (9.8 m)/sec2. This means that forevery second that an object experiencing gravita-tional force continues to fall, its velocity increas-es at the rate of 32 ft or 9.8 m per second. Thus,the formula for weight is essentially the same asthat for force, with a more specific variety ofacceleration substituted for the generalized termin the equation for force.

As for moment arm, this is the distance fromthe pivot point to the vector on which force isbeing applied. Moment arm is always perpendi-cular to the direction of force. Consider a wrenchoperating on a lug nut. The nut, as noted earlier,is the pivot point, and the moment arm is the dis-tance from the lug nut to the place where the per-son operating the wrench has applied force. Thetorque that the lug nut experiences is the productof moment arm multiplied by force.

In English units, torque is measured inpound-feet, whereas the metric unit is Newton-meters, or N•m. (One newton is the amount of

force that, when applied to 1 kg of mass, will giveit an acceleration of 1 m/sec2). Hence if a personwere to a grip a wrench 9 in (23 cm) from thepivot point, the moment arm would be 0.75 ft(0.23 m.) If the person then applied 50 lb (11.24N) of force, the lug nut would be experiencing37.5 pound-feet (2.59 N•m) of torque.

The greater the amount of torque, thegreater the tendency of the object to be put intorotation. In the case of a seesaw, its overall design,in particular the fact that it sits on the ground,means that its board can never undergo anythingclose to 360° rotation; nonetheless, the boarddoes rotate within relatively narrow parameters.The effects of torque can be illustrated by imag-ining the clockwise rotational behavior of a see-saw viewed from the side, with a child sitting onthe left and a teenager on the right.

Suppose the child weighs 50 lb (11.24 N)and sits 3 ft (0.91 m) from the pivot point, givingher side of the seesaw a torque of 150 pound-feet(10.28 N•m). On the other side, her teenage sisterweighs 100 lb (22.48 N) and sits 6 ft (1.82 m)from the center, creating a torque of 600 pound-feet (40.91 N•m). As a result of the torque imbal-ance, the side holding the teenager will rotateclockwise, toward the ground, causing the child’sside to also rotate clockwise—off the ground.

A SEESAW ROTATES ON AND OFF THE GROUND DUE TO TORQUE IMBALANCE. (Photograph by Dean Conger/Corbis. Reproduced

by permission.)


Torque


In order for the two to balance one another

perfectly, the torque on each side has to be

adjusted. One way would be by changing weight,

but a more likely remedy is a change in position,

and therefore, of moment arm. Since the teenag-

er weighs exactly twice as much as the child, the

moment arm on the child’s side must be exactly

twice as long as that on the teenager’s.

TORQUE, ALONG WITH ANGULAR MOMENTUM, IS THE LEADING FACTOR DICTATING THE MOTION OF A GYROSCOPE.HERE, A WOMAN RIDES INSIDE A GIANT GYROSCOPE AT AN AMUSEMENT PARK. (Photograph by Richard Cummins/Corbis. Repro-



TorqueHence, a remedy would be for the two toswitch positions with regard to the pivot point.The child would then move out an additional 3 ft(.91 m), to a distance of 6 ft (1.83 m) from thepivot, and the teenager would cut her distancefrom the pivot point in half, to just 3 ft (.91 m). Infact, however, any solution that gave the child amoment arm twice as long as that of the teenagerwould work: hence, if the teenager sat 1 ft (.3 m)from the pivot point, the child should be at 2 ft (.61m) in order to maintain the balance, and so on.

On the other hand, there are many situationsin which you may be unable to increase force, butcan increase moment arm. Suppose you were try-ing to disengage a particularly stubborn lug nut,and after applying all your force, it still would notcome loose. The solution would be to increasemoment arm, either by grasping the wrench fur-ther from the pivot point, or by using a longerwrench.

For the same reason, on a door, the knob isplaced as far as possible from the hinges. Here thehinge is the pivot point, and the door itself is themoment arm. In some situations of torque, how-ever, moment arm may extend over “emptyspace,” and for this reason, the handle of awrench is not exactly the same as its momentarm. If one applies force on the wrench at a 90°-angle to the handle, then indeed handle andmoment arm are identical; however, if that forcewere at a 45° angle, then the moment arm wouldbe outside the handle, because moment arm andforce are always perpendicular. And if one wereto pull the wrench away from the lug nut, thenthere would be 0° difference between the direc-tion of force and the pivot point—meaning thatmoment arm (and hence torque) would also beequal to zero.

Gyroscopes

A gyroscope consists of a wheel-like disk, called aflywheel, mounted on an axle, which in turn ismounted on a larger ring perpendicular to theplane of the wheel itself. An outer circle on thesame plane as the flywheel provides structuralstability, and indeed, the gyroscope may includeseveral such concentric rings. Its focal point,however, is the flywheel and the axle. One end ofthe axle is typically attached to some outsideobject, while the other end is left free to float.

Once the flywheel is set spinning, gravity hasa tendency to pull the unattached end of the axle

downward, rotating it on an axis perpendicular tothat of the flywheel. This should cause the gyro-scope to fall over, but instead it begins to spin athird axis, a horizontal axis perpendicular both tothe plane of the flywheel and to the direction ofgravity. Thus, it is spinning on three axes, and as aresult becomes very stable—that is, very resistanttoward outside attempts to upset its balance.

This in turn makes the gyroscope a valuedinstrument for navigation: due to its high degreeof gyroscopic inertia, it resists changes in orienta-tion, and thus can guide a ship toward its destina-tion. Gyroscopes, rather than magnets, are oftenthe key element in a compass. A magnet will pointto magnetic north, some distance from “truenorth” (that is, the North Pole.) But with a gyro-scope whose axle has been aligned with true northbefore the flywheel is set spinning, it is possible topossess a much more accurate directional indica-tor. For this reason, gyroscopes are used on air-planes—particularly those flying over the poles—as well as submarines and even the Space Shuttle.

Torque, along with angular momentum, isthe leading factor dictating the motion of a gyro-scope. Think of angular momentum as themomentum (mass multiplied by velocity) that aturning object acquires. Due to a principleknown as the conservation of angular momen-tum, a spinning object has a tendency to reach aconstant level of angular momentum, and inorder to do this, the sum of the external torquesacting on the system must be reduced to zero.Thus angular momentum “wants” or “needs” tocancel out torque.

The “right-hand rule” can help you tounderstand the torque in a system such as thegyroscope. If you extend your right hand, palmdownward, your fingers are analogous to themoment arm. Now if you curl your fingersdownward, toward the ground, then your finger-tips point in the direction of g—that is, gravita-tional force. At that point, your thumb (involun-tarily, due to the bone structure of the hand)points in the direction of the torque vector.

When the gyroscope starts to spin, the vec-tors of angular momentum and torque are atodds with one another. Were this situation topersist, it would destabilize the gyroscope;instead, however, the two come into alignment.Using the right-hand rule, the torque vector on agyroscope is horizontal in direction, and the vec-tor of angular momentum eventually aligns with



Torque


it. To achieve this, the gyroscope experienceswhat is known as gyroscopic precession, pivotingalong its support post in an effort to bring angu-lar momentum into alignment with torque. Oncethis happens, there is no net torque on the sys-tem, and the conservation of angular momen-tum is in effect.

Torque in Complex Machines

Torque is a factor in several complex machinessuch as the electric motor that—with varia-tions—runs most household appliances. It isespecially important to the operation of automo-biles, playing a significant role in the engine andtransmission.

An automobile engine produces energy,which the pistons or rotor convert into torque fortransmission to the wheels. Though torque isgreatest at high speeds, the amount of torqueneeded to operate a car does not always vary pro-portionately with speed. At moderate speeds andon level roads, the engine does not need to pro-vide a great deal of torque. But when the car isstarting, or climbing a steep hill, it is important

that the engine supply enough torque to keep thecar running; otherwise it will stall. To allocatetorque and speed appropriately, the engine maydecrease or increase the number of revolutionsper minute to which the rotors are subjected.

Torque comes from the engine, but it has tobe supplied to the transmission. In an automatictransmission, there are two principal compo-nents: the automatic gearbox and the torque con-verter. It is the job of the torque converter totransmit power from the flywheel of the engineto the gearbox, and it has to do so as smoothly aspossible. The torque converter consists of threeelements: an impeller, which is turned by theengine flywheel; a reactor that passes this motionon to a turbine; and the turbine itself, whichturns the input shaft on the automatic gearbox.An infusion of oil to the converter assists theimpeller and turbine in synchronizing move-ment, and this alignment of elements in thetorque converter creates a smooth relationshipbetween engine and gearbox. This also leads toan increase in the car’s overall torque—that is, itsturning force.

ACCELERATION: A change in veloci-ty over a given time period.

EQUILIBRIUM: A situation in which

the forces acting upon an object are in

balance.









MOMENT ARM: For an object experi-

encing torque, moment arm is the distance

from the pivot or balance point to the vec-

tor on which force is being applied.

Moment arm is always perpendicular to

the direction of force.



time.

TORQUE: The product of moment

arm multiplied by force.


both magnitude and direction. By contrast,

a scalar quantity is one that possesses only

magnitude, with no specific direction.





multiplied by the acceleration due to

gravity.

KEY TERMS


TorqueTorque is also important in the operation ofelectric motors, found in everything from vacu-um cleaners and dishwashers to computer print-ers and videocassette recorders to subway sys-tems and water-pumping stations. Torque in thecontext of electricity involves reference to a num-ber of concepts beyond the scope of this discus-sion: current, conduction, magnetic field, andother topics relevant to electromagnetic force.

WHERE TO LEARN MORE



“Rotational Motion.” Physics Department, University ofGuelph (Web site).<http://www.physics.uoguelph.ca/tutorials/torque/>(March 4, 2001).

“Rotational Motion—Torque.” Lee College (Web site).<http://www.lee.edu/mathscience/physics/physics/Courses/LabManual/2b/2b.html> (March 4, 2001).

Schweiger, Peggy E. “Torque” (Web site).<http://www.cyberclassrooms.net/~pschweiger/rot-mot.html> (March 4, 2001).

“Torque and Rotational Motion” (Web site).<http://online.cctt.org/curriculumguide/units/torque.asp> (March 4, 2001).



93


FLU ID MECHAN ICS

AERODYNAM ICS

BERNOULL I ’ S PR INC IPLE

BUOYANCY

FLU ID MECHAN ICSFLU ID MECHAN ICS



F LU ID MECHAN ICSFluid Mechanics

CONCEPTThe term “fluid” in everyday language typicallyrefers only to liquids, but in the realm of physics,fluid describes any gas or liquid that conforms tothe shape of its container. Fluid mechanics is thestudy of gases and liquids at rest and in motion.This area of physics is divided into fluid statics,the study of the behavior of stationary fluids, andfluid dynamics, the study of the behavior of mov-ing, or flowing, fluids. Fluid dynamics is furtherdivided into hydrodynamics, or the study ofwater flow, and aerodynamics, the study of air-flow. Applications of fluid mechanics include avariety of machines, ranging from the water-wheel to the airplane. In addition, the study offluids provides an understanding of a number ofeveryday phenomena, such as why an open win-dow and door together create a draft in a room.

HOW IT WORKS

The Contrast Between Fluidsand Solids

To understand fluids, it is best to begin by con-trasting their behavior with that of solids.Whereas solids possess a definite volume and adefinite shape, these physical characteristics arenot so clearly defined for fluids. Liquids, thoughthey possess a definite volume, have no definiteshape—a factor noted above as one of the defin-ing characteristics of fluids. As for gases, theyhave neither a definite shape nor a definite vol-ume.

One of several factors that distinguishes flu-ids from solids is their response to compression,or the application of pressure in such a way as to

reduce the size or volume of an object. A solid ishighly noncompressible, meaning that it resistscompression, and if compressed with a sufficientforce, its mechanical properties alter significant-ly. For example, if one places a drinking glass in avise, it will resist a small amount of pressure, buta slight increase will cause the glass to break.

Fluids vary with regard to compressibility,depending on whether the fluid in question is aliquid or a gas. Most gases tend to be highly com-pressible—though air, at low speeds at least, isnot among them. Thus, gases such as propanefuel can be placed under high pressure. Liquidstend to be noncompressible: unlike a gas, a liquidcan be compressed significantly, yet its responseto compression is quite different from that of asolid—a fact illustrated below in the discussionof hydraulic presses.

One way to describe a fluid is “anything thatflows”—a behavior explained in large part by theinteraction of molecules in fluids. If the surfaceof a solid is disturbed, it will resist, and if theforce of the disturbance is sufficiently strong, itwill deform—as for instance, when a steel platebegins to bend under pressure. This deformationwill be permanent if the force is powerfulenough, as was the case in the above example ofthe glass in a vise. By contrast, when the surfaceof a liquid is disturbed, it tends to flow.

MOLECULAR BEHAVIOR OF

FLUIDS AND SOLIDS. At the molecu-lar level, particles of solids tend to be definite intheir arrangement and close to one another. Inthe case of liquids, molecules are close in prox-imity, though not as much so as solid molecules,and the arrangement is random. Thus, with aglass of water, the molecules of glass (which at


FluidMechanics


relatively low temperatures is a solid) in the con-tainer are fixed in place while the molecules ofwater contained by the glass are not. If one por-tion of the glass were moved to another place onthe glass, this would change its structure. On theother hand, no significant alteration occurs inthe character of the water if one portion of it ismoved to another place within the entire volumeof water in the glass.

As for gas molecules, these are both randomin arrangement and far removed in proximity.Whereas solid particles are slow-moving andhave a strong attraction to one another, liquidmolecules move at moderate speeds and exert amoderate attraction on each other. Gas mole-cules are extremely fast-moving and exert little orno attraction.

Thus, if a solid is released from a containerpointed downward, so that the force of gravitymoves it, it will fall as one piece. Upon hitting afloor or other surface, it will either rebound,come to a stop, or deform permanently. A liquid,on the other hand, will disperse in response toimpact, its force determining the area over whichthe total volume of liquid is distributed. But for agas, assuming it is lighter than air, the downwardpull of gravity is not even required to disperse it:

once the top on a container of gas is released, themolecules begin to float outward.

Fluids Under Pressure

As suggested earlier, the response of fluids topressure is one of the most significant aspects offluid behavior and plays an important role with-in both the statics and dynamics subdisciplinesof fluid mechanics. A number of interesting prin-ciples describe the response to pressure, on thepart of both fluids at rest inside a container, andfluids which are in a state of flow.

Within the realm of hydrostatics, among themost important of all statements describing thebehavior of fluids is Pascal’s principle. This law isnamed after Blaise Pascal (1623-1662), a Frenchmathematician and physicist who discovered thatthe external pressure applied on a fluid is trans-mitted uniformly throughout its entire body. Theunderstanding offered by Pascal’s principle laterbecame the basis for one of the most importantmachines ever developed, the hydraulic press.

HYDROSTATIC PRESSURE AND

BUOYANCY. Some nineteen centuries beforePascal, the Greek mathematician, physicist, andinventor Archimedes (c. 287-212 B.C.) discovereda precept of fluid statics that had implications at

IN A WIDE, UNCONSTRICTED REGION, A RIVER FLOWS SLOWLY. HOWEVER, IF ITS FLOW IS NARROWED BY CANYON

WALLS, AS WITH WYOMING’S BIGHORN RIVER, THEN IT SPEEDS UP DRAMATICALLY. (Photograph by Kevin R. Morris/Corbis.



FluidMechanics

least as great as those of Pascal’s principle. Thiswas Archimedes’s principle, which explains thebuoyancy of an object immersed in fluid.According to Archimedes’s principle, the buoyantforce exerted on the object is equal to the weightof the fluid it displaces.

Buoyancy explains both how a ship floats onwater, and how a balloon floats in the air. Thepressures of water at the bottom of the ocean,and of air at the surface of Earth, are both exam-ples of hydrostatic pressure—the pressure thatexists at any place in a body of fluid due to theweight of the fluid above. In the case of air pres-sure, air is pulled downward by the force ofEarth’s gravitation, and air along the planet’s sur-face has greater pressure due to the weight of theair above it. At great heights above Earth’s sur-face, however, the gravitational force is dimin-ished, and thus the air pressure is much smaller.

Water, too, is pulled downward by gravity,and as with air, the fluid at the bottom of theocean has much greater pressure due to theweight of the fluid above it. Of course, water ismuch heavier than air, and therefore, water ateven a moderate depth in the ocean has enor-mous pressure. This pressure, in turn, creates abuoyant force that pushes upward.

If an object immersed in fluid—a balloon inthe air, or a ship on the ocean—weighs less thatthe fluid it displaces, it will float. If it weighsmore, it will sink or fall. The balloon itself may be“heavier than air,” but it is not as heavy as the airit has displaced. Similarly, an aircraft carrier con-tains a vast weight in steel and other material, yetit floats, because its weight is not as great as thatof the displaced water.

BERNOULLI’S PRINCIPLE. Ar-chimedes and Pascal contributed greatly to whatbecame known as fluid statics, but the father offluid mechanics, as a larger realm of study, wasthe Swiss mathematician and physicist DanielBernoulli (1700-1782). While conducting exper-iments with liquids, Bernoulli observed thatwhen the diameter of a pipe is reduced, the waterflows faster. This suggested to him that someforce must be acting upon the water, a force thathe reasoned must arise from differences in pres-sure.

Specifically, the slower-moving fluid in thewider area of pipe had a greater pressure than theportion of the fluid moving through the narrow-er part of the pipe. As a result, he concluded that


pressure and velocity are inversely related—inother words, as one increases, the other decreas-es. Hence, he formulated Bernoulli’s principle,which states that for all changes in movement,the sum of static and dynamic pressure in a fluidremains the same.

A fluid at rest exerts pressure—whatBernoulli called “static pressure”—on its con-tainer. As the fluid begins to move, however, aportion of the static pressure—proportional tothe speed of the fluid—is converted to whatBernoulli called dynamic pressure, or the pres-sure of movement. In a cylindrical pipe, staticpressure is exerted perpendicular to the surfaceof the container, whereas dynamic pressure isparallel to it.

According to Bernoulli’s principle, thegreater the velocity of flow in a fluid, the greaterthe dynamic pressure and the less the static pres-sure. In other words, slower-moving fluid exertsgreater pressure than faster-moving fluid. Thediscovery of this principle ultimately made pos-sible the development of the airplane.


Bernoulli’s Principle inAction

As fluid moves from a wider pipe to a narrowerone, the volume of the fluid that moves a givendistance in a given time period does not change.But since the width of the narrower pipe is small-er, the fluid must move faster (that is, withgreater dynamic pressure) in order to move thesame amount of fluid the same distance in thesame amount of time. Observe the behavior of ariver: in a wide, unconstricted region, it flowsslowly, but if its flow is narrowed by canyon walls,it speeds up dramatically.

Bernoulli’s principle ultimately became thebasis for the airfoil, the design of an airplane’swing when seen from the end. An airfoil isshaped like an asymmetrical teardrop laid on itsside, with the “fat” end toward the airflow. As airhits the front of the airfoil, the airstream divides,part of it passing over the wing and part passingunder. The upper surface of the airfoil is curved,however, whereas the lower surface is muchstraighter.


FluidMechanics

As a result, the air flowing over the top has agreater distance to cover than the air flowingunder the wing. Since fluids have a tendency tocompensate for all objects with which they comeinto contact, the air at the top will flow faster tomeet the other portion of the airstream, the airflowing past the bottom of the wing, when bothreach the rear end of the airfoil. Faster airflow, asdemonstrated by Bernoulli, indicates lower pres-sure, meaning that the pressure on the bottom ofthe wing keeps the airplane aloft.

CREATING A DRAFT. Among themost famous applications of Bernoulli’s princi-ple is its use in aerodynamics, and this is dis-cussed in the context of aerodynamics itself else-where in this book. Likewise, a number of otherapplications of Bernoulli’s principle are exam-ined in an essay devoted to that topic. Bernoulli’sprinciple, for instance, explains why a showercurtain tends to billow inward when the water isturned on; in addition, it shows why an openwindow and door together create a draft.

Suppose one is in a hotel room where theheat is on too high, and there is no way to adjustthe thermostat. Outside, however, the air is cold,and thus, by opening a window, one can presum-ably cool down the room. But if one opens thewindow without opening the front door of theroom, there will be little temperature change.The only way to cool off will be by standing nextto the window: elsewhere in the room, the air willbe every bit as stuffy as before. But if the doorleading to the hotel hallway is opened, a nice coolbreeze will blow through the room. Why?

With the door closed, the room constitutesan area of relatively high pressure compared tothe pressure of the air outside the window.Because air is a fluid, it will tend to flow into theroom, but once the pressure inside reaches a cer-tain point, it will prevent additional air fromentering. The tendency of fluids is to move fromhigh-pressure to low-pressure areas, not theother way around. As soon as the door is opened,the relatively high-pressure air of the room flowsinto the relatively low-pressure area of the hall-way. As a result, the air pressure in the room isreduced, and the air from outside can now enter.Soon a wind will begin to blow through theroom.

A WIND TUNNEL. The above sce-nario of wind flowing through a room describesa rudimentary wind tunnel. A wind tunnel is a

chamber built for the purpose of examining thecharacteristics of airflow in contact with solidobjects, such as aircraft and automobiles. Thewind tunnel represents a safe and judicious useof the properties of fluid mechanics. Its purposeis to test the interaction of airflow and solids inrelative motion: in other words, either the air-craft has to be moving against the airflow, as itdoes in flight, or the airflow can be movingagainst a stationary aircraft. The first of thesechoices, of course, poses a number of dangers; onthe other hand, there is little danger in exposinga stationary craft to winds at speeds simulatingthat of the aircraft in flight.

The first wind tunnel was built in England in1871, and years later, aircraft pioneers Orville(1871-1948) and Wilbur (1867-1912) Wrightused a wind tunnel to improve their planes. Bythe late 1930s, the U.S. National Advisory Com-mittee for Aeronautics (NACA) was buildingwind tunnels capable of creating speeds equal to300 MPH (480 km/h); but wind tunnels builtafter World War II made these look primitive.With the development of jet-powered flight, itbecame necessary to build wind tunnels capableof simulating winds at the speed of sound—760MPH (340 m/s). By the 1950s, wind tunnels werebeing used to simulate hypersonic speeds—thatis, speeds of Mach 5 (five times the speed ofsound) and above. Researchers today use heliumto create wind blasts at speeds up to Mach 50.

Fluid Mechanics for Per-forming Work

HYDRAULIC PRESSES. Thoughapplications of Bernoulli’s principle are amongthe most dramatic examples of fluid mechanicsin operation, the everyday world is filled withinstances of other ideas at work. Pascal’s princi-ple, for instance, can be seen in the operation ofany number of machines that represent varia-tions on the idea of a hydraulic press. Amongthese is the hydraulic jack used to raise a car offthe floor of an auto mechanic’s shop.

Beneath the floor of the shop is a chambercontaining a quantity of fluid, and at either endof the chamber are two large cylinders side byside. Each cylinder holds a piston, and valvescontrol flow between the two cylinders throughthe channel of fluid that connects them. In accor-dance with Pascal’s principle, when one appliesforce by pressing down the piston in one cylinder



FluidMechanics

(the input cylinder), this yields a uniform pres-sure that causes output in the second cylinder,pushing up a piston that raises the car.

Another example of a hydraulic press is thehydraulic ram, which can be found in machinesranging from bulldozers to the hydraulic liftsused by firefighters and utility workers to reachheights. In a hydraulic ram, however, the charac-teristics of the input and output cylinders arereversed from those of a car jack. For the car jack,the input cylinder is long and narrow, while theoutput cylinder is wide and short. This is becausethe purpose of a car jack is to raise a heavy objectthrough a relatively short vertical range of move-ment—just high enough so that the mechaniccan stand comfortably underneath the car.

In the hydraulic ram, the input or mastercylinder is short and squat, while the output orslave cylinder is tall and narrow. This is becausethe hydraulic ram, in contrast to the car jack, car-ries a much lighter cargo (usually just one per-son) through a much greater vertical range—forinstance, to the top of a tree or building.

PUMPS. A pump is a device made formoving fluid, and it does so by utilizing a pres-sure difference, causing the fluid to move froman area of higher pressure to one of lower pres-sure. Its operation is based on aspects both ofPascal’s and Bernoulli’s principles—though, ofcourse, humans were using pumps thousands ofyears before either man was born.

A siphon hose used to draw gas from a car’sfuel tank is a very simple pump. Sucking on oneend of the hose creates an area of low pressurecompared to the relatively high-pressure area ofthe gas tank. Eventually, the gasoline will comeout of the low-pressure end of the hose.

The piston pump, slightly more complex,consists of a vertical cylinder along which a pis-ton rises and falls. Near the bottom of the cylin-der are two valves, an inlet valve through whichfluid flows into the cylinder, and an outlet valvethrough which fluid flows out. As the pistonmoves upward, the inlet valve opens and allowsfluid to enter the cylinder. On the downstroke,the inlet valve closes while the outlet valve opens,and the pressure provided by the piston forcesthe fluid through the outlet valve.

One of the most obvious applications of thepiston pump is in the engine of an automobile.In this case, of course, the fluid being pumped isgasoline, which pushes the pistons up and down

by providing a series of controlled explosionscreated by the spark plug’s ignition of the gas. Inanother variety of piston pump—the kind usedto inflate a basketball or a bicycle tire—air is thefluid being pumped. Then there is a pump forwater. Pumps for drawing usable water from theground are undoubtedly the oldest known vari-ety, but there are also pumps designed to removewater from areas where it is undesirable; forexample, a bilge pump, for removing water froma boat, or the sump pump used to pump floodwater out of a basement.

FLUID POWER. For several thousandyears, humans have used fluids—in particularwater—to power a number of devices. One of thegreat engineering achievements of ancient timeswas the development of the waterwheel, whichincluded a series of buckets along the rim thatmade it possible to raise water from the riverbelow and disperse it to other points. By about 70B.C., Roman engineers recognized that they coulduse the power of water itself to turn wheels andgrind grain. Thus, the waterwheel became one ofthe first mechanisms in which an inanimate


PUMPS FOR DRAWING USABLE WATER FROM THE

GROUND ARE UNDOUBTEDLY THE OLDEST PUMPS

KNOWN. (Photograph by Richard Cummins/Corbis. Reproduced by

permission.)


FluidMechanics


source (as opposed to the effort of humans or

animals) created power.

The water clock, too, was another ingenious

use of water developed by the ancients. It did not

use water for power; rather, it relied on gravity—

a concept only dimly understood by ancient peo-

ples—to move water from one chamber of the

clock to another, thus, marking a specific interval

of time. The earliest clocks were sundials, which

were effective for measuring time, provided the

Sun was shining, but which were less useful for

measuring periods shorter than an hour. Hence,

AERODYNAMICS: An area of fluid

dynamics devoted to studying the proper-

ties and characteristics of airflow.


of physics stating that the buoyant force of

an object immersed in fluid is equal to the

weight of the fluid displaced by the object.

It is named after the Greek mathematician,

physicist, and inventor, Archimedes (c.

287-212 B.C.), who first identified it.

BERNOULLI’S PRINCIPLE: A prop-

osition, credited to Swiss mathematician

and physicist Daniel Bernoulli (1700-

1782), which maintains that slower-mov-

ing fluid exerts greater pressure than faster-

moving fluid.




COMPRESSION: To reduce in size or

volume by applying pressure.

FLUID: Any substance, whether gas or

liquid, that conforms to the shape of its

container.

FLUID DYNAMICS: An area of fluid

mechanics devoted to studying of the

behavior of moving, or flowing, fluids.

Fluid dynamics is further divided into

hydrodynamics and aerodynamics.

FLUID MECHANICS: The study of

the behavior of gases and liquids at rest

and in motion. The major divisions of

fluid mechanics are fluid statics and fluid

dynamics.

FLUID STATICS: An area of fluid

mechanics devoted to studying the behav-

ior of stationary fluids.

HYDRODYNAMICS: An area of fluid

dynamics devoted to studying the proper-

ties and characteristics of water flow.

HYDROSTATIC PRESSURE: The

pressure that exists at any place in a body of

fluid due to the weight of the fluid above.

PASCAL’S PRINCIPLE: A statement,

formulated by French mathematician and

physicist Blaise Pascal (1623-1662), which

holds that the external pressure applied on

a fluid is transmitted uniformly through-

out the entire body of that fluid.

PRESSURE: The ratio of force to sur-

face area, when force is applied in a direc-

tion perpendicular to that surface.

TURBINE: A machine that converts the

kinetic energy (the energy of movement)

in fluids to useable mechanical energy by

passing the stream of fluid through a series

of fixed and moving fans or blades.

WIND TUNNEL: A chamber built for

the purpose of examining the characteris-

tics of airflow in relative motion against

solid objects such as aircraft and auto-

mobiles.

KEY TERMS


FluidMechanics

the development of the hourglass, which usedsand, a solid that in larger quantities exhibits thebehavior of a fluid. Then, in about 270 B.C., Cte-sibius of Alexandria (fl. c. 270-250 B.C.) usedgearwheel technology to devise a constant-flowwater clock called a “clepsydra.” Use of waterclocks prevailed for more than a thousand years,until the advent of the first mechanical clocks.

During the medieval period, fluids providedpower to windmills and water mills, and at thedawn of the Industrial Age, engineers beganapplying fluid principles to a number of sophis-ticated machines. Among these was the turbine, amachine that converts the kinetic energy (theenergy of movement) in fluids to useablemechanical energy by passing the stream of fluidthrough a series of fixed and moving fans orblades. A common house fan is an example of aturbine in reverse: the fan adds energy to thepassing fluid (air), whereas a turbine extractsenergy from fluids such as air and water.

The turbine was developed in the mid-eigh-teenth century, and later it was applied to theextraction of power from hydroelectric dams, thefirst of which was constructed in 1894. Today,hydroelectric dams provide electric power tomillions of homes around the world. Among themost dramatic examples of fluid mechanics inaction, hydroelectric dams are vast in size andequally impressive in the power they can generateusing a completely renewable resource: water.

A hydroelectric dam forms a huge steel-and-concrete curtain that holds back millions of tonsof water from a river or other body. The water

nearest the top—the “head” of the dam—hasenormous potential energy, or the energy that anobject possesses by virtue of its position. Hydro-electric power is created by allowing controlledstreams of this water to flow downward, gather-ing kinetic energy that is then transferred topowering turbines, which in turn generate elec-tric power.

WHERE TO LEARN MORE

Aerodynamics for Students (Web site).<http://www.ae.su.oz.au/aero/contents.html> (April8, 2001).


Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Sciencefor Curious Minds. Illustrated by Ann HumphreyWilliams. Hauppauge, N.Y.: Barron’s, 2000.

“Educational Fluid Mechanics Sites.” Virginia Institute ofTechnology (Web site). <http://www.eng.vt.edu/flu-ids/links/edulinks.htm> (April 8, 2001).

Fleisher, Paul. Liquids and Gases: Principles of FluidMechanics. Minneapolis, MN: Lerner Publications,2002.

Institute of Fluid Mechanics (Web site).<http://www.ts.go.dlr.de> (April 8, 2001).

K8AIT Principles of Aeronautics Advanced Text (web site).<http://wings.ucdavis.edu/Book/advanced.html>(February 19, 2001).


Sobey, Edwin J. C. Wacky Water Fun with Science: ScienceYou Can Float, Sink, Squirt, and Sail. Illustrated byBill Burg. New York: McGraw-Hill, 2000.

Wood, Robert W. Mechanics Fundamentals. Illustrated byBill Wright. Philadelphia: Chelsea House, 1997.




A ERODYNAM ICSAerodynamics

CONCEPTThough the term “aerodynamics” is most com-monly associated with airplanes and the overallscience of flight, in fact, its application is muchbroader. Simply put, aerodynamics is the study ofairflow and its principles, and applied aerody-namics is the science of improving manmadeobjects such as airplanes and automobiles in lightof those principles. Aside from the obvious appli-cation to these heavy forms of transportation,aerodynamic concepts are also reflected in thesimplest of manmade flying objects—and in thenatural model for all studies of flight, a bird’swings.

HOW IT WORKSAll physical objects on Earth are subject to grav-ity, but gravity is not the only force that tends tokeep them pressed to the ground. The air itself,though it is invisible, operates in such a way as toprevent lift, much as a stone dropped into thewater will eventually fall to the bottom. In fact,air behaves much like water, though the down-ward force is not as great due to the fact that air’spressure is much less than that of water. Yet bothare media through which bodies travel, and airand water have much more in common with oneanother than either does with a vacuum.

Liquids such as water and gasses such as airare both subject to the principles of fluid dynam-ics, a set of laws that govern the motion of liquidsand vapors when they come in contact with solidsurfaces. In fact, there are few significant differ-ences—for the purposes of the present discus-sion—between water and air with regard to theirbehavior in contact with solid surfaces.

When a person gets into a bathtub, the waterlevel rises uniformly in response to the fact that asolid object is taking up space. Similarly, air cur-rents blow over the wings of a flying aircraft insuch a way that they meet again more or lesssimultaneously at the trailing edge of the wing.In both cases, the medium adjusts for the intru-sion of a solid object. Hence within the parame-ters of fluid dynamics, scientists typically use theterm “fluid” uniformly, even when describing themovement of air.

The study of fluid dynamics in general, andof air flow in particular, brings with it an entirevocabulary. One of the first concepts of impor-tance is viscosity, the internal friction in a fluidthat makes it resistant to flow and resistant toobjects flowing through it. As one might suspect,viscosity is a far greater factor with water thanwith air, the viscosity of which is less than twopercent that of water. Nonetheless, near a solidsurface—for example, the wing of an airplane—viscosity becomes a factor because air tends tostick to that surface.

Also significant are the related aspects ofdensity and compressibility. At speeds below 220MPH (354 km/h), the compressibility of air isnot a significant factor in aerodynamic design.However, as air flow approaches the speed ofsound—660 MPH (1,622 km/h)—compressibil-ity becomes a significant factor. Likewise temper-ature increases greatly when airflow is superson-ic, or faster than the speed of sound.

All objects in the air are subject to two typesof airflow, laminar and turbulent. Laminar flowis smooth and regular, always moving at the samespeed and in the same direction. This type of air-flow is also known as streamlined flow, andunder these conditions every particle of fluid that


Aero-dynamics

passes a particular point follows a path identicalto all particles that passed that point earlier. Thismay be illustrated by imagining a stream flowingaround a twig.

By contrast, in turbulent flow the air is sub-ject to continual changes in speed and direc-tion—as for instance when a stream flows overshoals of rocks. Whereas the mathematical modelof laminar airflow is rather straightforward, con-ditions are much more complex in turbulentflow, which typically occurs in the presenceeither of obstacles or of high speeds.

Absent the presence of viscosity, and thus inconditions of perfect laminar flow, an objectbehaves according to Bernoulli’s principle, some-times known as Bernoulli’s equation. Named afterthe Swiss mathematician and physicist DanielBernoulli (1700-1782), this proposition goes tothe heart of that which makes an airplane fly.

While conducting experiments concerningthe conservation of energy in liquids, Bernoulliobserved that when the diameter of a pipe isreduced, the water flows faster. This suggested tohim that some force must be acting upon thewater, a force that he reasoned must arise fromdifferences in pressure. Specifically, the slower-moving fluid had a greater pressure than the por-tion of the fluid moving through the narrowerpart of the pipe. As a result, he concluded thatpressure and velocity are inversely related.

Bernoulli’s principle states that for allchanges in movement, the sum of static anddynamic pressure in a fluid remain the same. Afluid at rest exerts static pressure, which is thesame as what people commonly mean when theysay “pressure,” as in “water pressure.” As the fluidbegins to move, however, a portion of the staticpressure—proportional to the speed of thefluid—is converted to what scientists call dynam-ic pressure, or the pressure of movement. Thegreater the speed, the greater the dynamic pres-sure and the less the static pressure. Bernoulli’sfindings would prove crucial to the design of air-craft in the twentieth century, as engineerslearned how to use currents of faster and slowerair for keeping an airplane aloft.

Very close to the surface of an object experi-encing airflow, however, the presence of viscosityplays havoc with the neat proportions of theBernoulli’s principle. Here the air sticks to theobject’s surface, slowing the flow of nearby airand creating a “boundary layer” of slow-moving


air. At the beginning of the flow—for instance, atthe leading edge of an airplane’s wing—thisboundary layer describes a laminar flow; but thewidth of the layer increases as the air movesalong the surface, and at some point it becomesturbulent.

These and a number of other factors con-tribute to the coefficients of drag and lift. Simplyput, drag is the force that opposes the forwardmotion of an object in airflow, whereas lift is aforce perpendicular to the direction of the wind,which keeps the object aloft. Clearly these con-cepts can be readily applied to the operation ofan airplane, but they also apply in the case of anautomobile, as will be shown later.


How a Bird Flies—and Why aHuman Being Cannot

Birds are exquisitely designed (or adapted) forflight, and not simply because of the obvious fact

A TYPICAL PAPER AIRPLANE HAS LOW ASPECT RATIO

WINGS, A TERM THAT REFERS TO THE SIZE OF THE

WINGSPAN COMPARED TO THE CHORD. IN SUBSONIC

FLIGHT, HIGHER ASPECT RATIOS ARE USUALLY PRE-FERRED. (Photograph by Bruce Burkhardt/Corbis. Reproduced by per-

mission.)


BIRDS LIKE THESE FAIRY TERNS ARE SUPREME EXAMPLES OF AERODYNAMIC PRINCIPLES, FROM THEIR LOW BODY

WEIGHT AND LARGE STERNUM AND PECTORALIS MUSCLES TO THEIR LIGHTWEIGHT FEATHERS. (Corbis. Reproduced by per-

mission.)

Aero-dynamics

When a bird beats its wings, its downstrokespropel it, and as it rises above the ground, theforce of aerodynamic lift helps push its wingsupward in preparation for the next downstroke.However, to reduce aerodynamic drag during theupstroke, the bird folds its wings, thus decreasingits wingspan. Another trick that birds executeinstinctively is the moving of their wings forwardand backward in order to provide balance. Theyalso “know” how to flap their wings in a directionalmost parallel to the ground when they need tofly slowly or hover.

Witnessing the astonishing aerodynamicfeats of birds, humans sought the elusive goal offlight from the earliest of times. This was sym-bolized by the Greek myth of Icarus andDaedalus, who escaped from a prison in Crete byconstructing a set of bird-like wings and flyingaway. In the world of physical reality, however,the goal would turn out to be unattainable aslong as humans attempted to achieve flight byimitating birds.

As noted earlier, a bird’s physiology is quitedifferent from that of a human being. There issimply no way that a human can fly by flappinghis arms—nor will there ever be a man strongenough to do so, no matter how apparently well-


that they have wings. Thanks to light, hollow

bones, their body weight is relatively low, giving

them the advantage in overcoming gravity and

remaining aloft. Furthermore, a bird’s sternum

or breast bone, as well as its pectoralis muscles

(those around the chest) are enormous in pro-

portion to its body size, thus helping it to achieve

the thrust necessary for flight. And finally, the

bird’s lightweight feathers help to provide opti-

mal lift and minimal drag.

A bird’s wing is curved along the top, a cru-

cial aspect of its construction. As air passes over

the leading edge of the wing, it divides, and

because of the curve, the air on top must travel a

greater distance before meeting the air that

flowed across the bottom. The tendency of air-

flow, as noted earlier, is to correct for the presence

of solid objects. Therefore, in the absence of out-

side factors such as viscosity, the air on top “tries”

to travel over the wing in the same amount of

time that it takes the air below to travel under the

wing. As shown by Bernoulli, the fast-moving air

above the wing exerts less pressure than the slow-

moving air below it; hence there is a difference in

pressure between the air below and the air above,

and this keeps the wing aloft.


Aero-dynamics


designed his mechanical wings are. Indeed, to becapable of flying like a bird, a man would have tohave a chest so enormous in proportion to hisbody that he would be hideous in appearance.

Not realizing this, humans for centuriesattempted to fly like birds—with disastrousresults. An English monk named Eilmer (b. 980)attempted to fly off the tower of MalmesburyAbbey with a set of wings attached to his armsand feet. Apparently Eilmer panicked after glid-ing some 600 ft (about 200 m) and suddenlyplummeted to earth, breaking both of his legs. Atleast he lived; more tragic was the case of AbulQasim Ibn Firnas (d. 873), an inventor from Cor-doba in Arab Spain who devised and demon-strated a glider. Much of Cordoba’s populationcame out to see him demonstrate his flyingmachine, but after covering just a short distance,the craft fell to earth. Severely wounded, Ibn Fir-nas died shortly afterward.

The first real progress in the development offlying machines came when designers stoppedtrying to imitate birds and instead used the prin-ciple of buoyancy. Hence in 1783, the Frenchbrothers Jacques-Etienne and Joseph-MichelMontgolfier constructed the first practical bal-loon.

Balloons and their twentieth-centurydescendant, the dirigible, had a number of obvi-ous drawbacks, however. Without a motor, a bal-loon could not be guided, and even with a motor,dirigibles proved highly dangerous. At that stage,most dirigibles used hydrogen, a gas that is cheapand plentiful, but extremely flammable. After theHindenburg exploded in 1937, the age of passen-ger travel aboard airships was over.

However, the German military continued touse dirigibles for observation purposes, as did theUnited States forces in World War II. Today air-ships, the most famous example being theGoodyear Blimp, are used not only for observa-tion but for advertising. Scientists working inrain forests, for instance, use dirigibles to glideabove the forest canopy; as for the GoodyearBlimp, it provides television networks with “eyein the sky” views of large sporting events.

The first man to make a serious attempt atcreating a heavier-than-air flying machine (asopposed to a balloon, which uses gases that arelighter than air) was Sir George Cayley (1773-1857), who in 1853 constructed a glider. It isinteresting to note that in creating this, the fore-

runner of the modern airplane, Cayley went backto an old model: the bird. After studying thephysics of birds’ flight for many years, heequipped his glider with an extremely widewingspan, used the lightest possible materials inits construction, and designed it with exception-ally smooth surfaces to reduce drag.

The only thing that in principle differentiat-ed Cayley’s craft from a modern airplane was itslack of an engine. In those days, the only possiblesource of power was a steam engine, whichwould have added far too much weight to his air-craft. However, the development of the internal-combustion engine in the nineteenth centuryovercame that obstacle, and in 1903 Orville andWilbur Wright achieved the dream of flight thathad intrigued and eluded human beings for cen-turies.

Airplanes: Getting Aloft,Staying Aloft, and RemainingStable

Once engineers and pilots took to the air, theyencountered a number of factors that affectflight. In getting aloft and staying aloft, an air-craft is subject to weight, lift, drag, and thrust.

As noted earlier, the design of an airplanewing takes advantage of Bernoulli’s principle togive it lift. Seen from the end, the wing has theshape of a long teardrop lying on its side, withthe large end forward, in the direction of airflow,and the narrow tip pointing toward the rear.(Unlike a teardrop, however, an airplane’s wing isasymmetrical, and the bottom side is flat.) Thiscross-section is known as an airfoil, and thegreater curvature of its upper surface in compar-ison to the lower side is referred to as the air-plane’s camber. The front end of the airfoil is alsocurved, and the chord line is an imaginarystraight line connecting the spot where the airhits the front—known as the stagnation point—to the rear, or trailing edge, of the wing.

Again in accordance with Bernoulli’s princi-ple, the shape of the airflow facilitates the spreadof laminar flow around it. The slower-movingcurrents beneath the airfoil exert greater pressurethan the faster currents above it, giving lift to theaircraft.

Another parameter influencing the lift coef-ficient (that is, the degree to which the aircraftexperiences lift) is the size of the wing: the longerthe wing, the greater the total force exerted


Aero-dynamics

beneath it, and the greater the ratio of this pres-sure to that of the air above. The size of a mod-ern aircraft’s wing is actually somewhat variable,due to the presence of flaps at the trailing edge.

With regard to the flaps, however, it shouldbe noted that they have different properties atdifferent stages of flight: in takeoff, they providelift, but in stable flight they increase drag, and forthat reason the pilot retracts them. In preparingfor landing, as the aircraft slows and descends,the extended flaps then provide stability andassist in the decrease of speed.

Speed, too, encourages lift: the faster thecraft, the faster the air moves over the wing. Thepilot affects this by increasing or decreasing thepower of the engine, thus regulating the speedwith which the plane’s propellers turn. Anotherhighly significant component of lift is the airfoil’sangle of attack—the orientation of the airfoilwith regard to the air flow, or the angle that thechord line forms with the direction of the airstream.

Up to a point, increasing the angle of attackprovides the aircraft with extra lift because itmoves the stagnation point from the leadingedge down along the lower surface; this increasesthe low-pressure area of the upper surface. How-ever, if the pilot increases the angle of attack toomuch, this affects the boundary layer of slow-moving air, causing the aircraft to go into a stall.

Together the engine provides the propellerswith power, and this gives the aircraft thrust, orpropulsive force. In fact, the propeller bladesconstitute miniature wings, pivoted at the centerand powered by the engine to provide rotationalmotion. As with the wings of the aircraft, theblades have a convex forward surface and a nar-row trailing edge. Also like the aircraft wings,their angle of attack (or pitch) is adjusted at dif-ferent points for differing effects. In stable flight,the pilot increases the angle of attack for the pro-peller blades sharply as against airflow, whereasat takeoff and landing the pitch is dramaticallyreduced. During landing, in fact, the pilot actual-ly reverses the direction of the propeller blades,turning them into a brake on the aircraft’s for-ward motion—and producing that lurching sen-sation that a passenger experiences as the aircraftslows after touching down.

By this point there have been several exam-ples regarding the use of the same techniquealternately to provide lift or—when slowing or

preparing to land—drag. This apparent inconsis-tency results from the fact that the characteristicsof air flow change drastically from situation tosituation, and in fact, air never behaves as per-fectly as it does in a textbook illustration ofBernoulli’s principle.

Not only is the aircraft subject to air viscosi-ty—the air’s own friction with itself—it alsoexperiences friction drag, which results from thefact that no solid can move through a fluid with-out experiencing a retarding force. An evengreater drag factor, accounting for one-third ofthat which an aircraft experiences, is induceddrag. The latter results because air does not flowin perfect laminar streams over the airfoil; rather,it forms turbulent eddies and currents that actagainst the forward movement of the plane.

In the air, an aircraft experiences forces thattend to destabilize flight in each of three dimen-sions. Pitch is the tendency to rotate forward orbackward; yaw, the tendency to rotate on a hori-zontal plane; and roll, the tendency to rotate ver-tically on the axis of its fuselage. Obviously, eachof these is a terrifying prospect, but fortunately,pilots have a solution for each. To prevent pitch-ing, they adjust the angle of attack of the hori-zontal tail at the rear of the craft. The vertical reartail plays a part in preventing yawing, and to pre-vent rolling, the pilot raises the tips of the mainwings so that the craft assumes a V-shape whenseen from the front or back.

The above factors of lift, drag, thrust, andweight, as well as the three types of possibledestabilization, affect all forms of heavier-than-air flying machines. But since the 1944 advent ofjet engines, which travel much faster than piston-driven engines, planes have flown faster andfaster, and today some craft such as the Concordeare capable of supersonic flight. In these situa-tions, air compressibility becomes a significantissue.

Sound is transmitted by the successive com-pression and expansion of air. But when a planeis traveling at above Mach 1.2—the Mach num-ber indicates the speed of an aircraft in relationto the speed of sound—there is a significant dis-crepancy between the speed at which sound istraveling away from the craft, and the speed atwhich the craft is moving away from the sound.Eventually the compressed sound waves build up,resulting in a shock wave.



Aero-dynamics

Down on the ground, the shock wave mani-fests as a “sonic boom”; meanwhile, for the air-craft, it can cause sudden changes in pressure,density, and temperature, as well as an increase indrag and a loss of stability. To counteract thiseffect, designers of supersonic and hypersonic(Mach 5 and above) aircraft are altering wingdesign, using a much narrower airfoil and swept-back wings.

One of the pioneers in this area is RichardWhitcomb of the National Aeronautics andSpace Administration (NASA). Whitcomb hasdesigned a supercritical airfoil for a proposedhypersonic plane, which would ascend into outerspace in the course of a two-hour flight—all thetime needed for it to travel from Washington,D.C., to Tokyo, Japan. Before the craft canbecome operational, however, researchers willhave to figure out ways to control temperaturesand keep the plane from bursting into flame as itreenters the atmosphere.

Much of the research for improving theaerodynamic qualities of such aircraft takes placein wind tunnels. First developed in 1871, theseuse powerful fans to create strong air currents,and over the years the top speed in wind tunnelshas been increased to accommodate testing onsupersonic and hypersonic aircraft. Researcherstoday use helium to create wind blasts at speedsup to Mach 50.

Thrown and Flown: The Aero-dynamics of Small Objects

Long before engineers began to dream of sendingplanes into space for transoceanic flight—about14,000 years ago, in fact—many of the featuresthat make an airplane fly were already present inthe boomerang. It might seem backward to movefrom a hypersonic jet to a boomerang, but infact, it is easier to appreciate the aerodynamics ofsmall objects, including the kite and even thepaper airplane, once one comprehends the largerpicture.

There is a certain delicious irony in the factthat the first manmade object to take flight wasconstructed by people who never advancedbeyond the Stone Age until the nineteenth centu-ry, when the Europeans arrived in Australia. Asthe ethnobotanist Jared Diamond showed in hisgroundbreaking work Guns, Germs, and Steel:The Fates of Human Societies (1997), this was notbecause the Aborigines of Australia were less

intelligent than Europeans. In fact, as Diamondshowed, an individual would actually have to besmarter to figure out how to survive on the lim-ited range of plants and animals available in Aus-tralia prior to the introduction of Eurasian floraand fauna. Hence the wonder of the boomerang,one of the most ingenious inventions ever fash-ioned by humans in a “primitive” state.

Thousands of years before Bernoulli, theboomerang’s designers created an airfoil consis-tent with Bernoulli’s principle. The air belowexerts more pressure than the air above, and this,combined with the factors of gyroscopic stabilityand gyroscopic precession, gives the boomerangflight.

Gyroscopic stability can be illustrated byspinning a top: the action of spinning itself keepsthe top stable. Gyroscopic precession is a muchmore complex process: simply put, the leadingwing of the boomerang—the forward or upwardedge as it spins through the air—creates more liftthan the other wing. At this point it should benoted that, contrary to the popular image, aboomerang travels on a plane perpendicular tothat of the ground, not parallel. Hence anythrower who knows what he or she is doing toss-es the boomerang not with a side-arm throw, butoverhand.

And of course a boomerang does not justsail through the air; a skilled thrower can make itcome back as if by magic. This is because theforce of the increased lift that it experiences inflight, combined with gyroscopic precession,turns it around. As noted earlier, in different sit-uations the same force that creates lift can createdrag, and as the boomerang spins downward theincreasing drag slows it. Certainly it takes greatskill for a thrower to make a boomerang comeback, and for this reason, participants inboomerang competitions often attach devicessuch as flaps to increase drag on the return cycle.

Another very early example of an aerody-namically sophisticated humanmade device—though it is quite recent compared to theboomerang—is the kite, which first appeared inChina in about 1000 B.C. The kite’s design bor-rows from avian anatomy, particularly the bird’slight, hollow bones. Hence a kite, in its simplestform, consists of two crossed strips of very lightwood such as balsa, with a lightweight fabricstretched over them.



Aero-dynamics

Kites can come in a variety of shapes, thoughfor many years the well-known diamond shapehas been the most popular, in part because itsaerodynamic qualities make it easiest for thenovice kite-flyer to handle. Like birds andboomerangs, kites can “fly” because of the physi-cal laws embodied in Bernoulli’s principle: at thebest possible angle of attack, the kite experiencesa maximal ratio of pressure from the slower-moving air below as against the faster-moving airabove.

For centuries, when the kite represented theonly way to put a humanmade object many hun-dreds of feet into the air, scientists and engineersused them for a variety of experiments. Ofcourse, the most famous example of this wasBenjamin Franklin’s 1752 experiment with elec-tricity. More significant to the future of aerody-namics were investigations made half a centurylater by Cayley, who recognized that the kite,rather than the balloon, was an appropriatemodel for the type of heavier-than-air flight heintended.

In later years, engineers built larger kitescapable of lifting men into the air, but the adventof the airplane rendered kites obsolete for thispurpose. However, in the 1950s an Americanengineer named Francis Rogallo invented theflexible kite, which in turn spawned the deltawing kite used by hang gliders. During the 1960s,Domina Jolbert created the parafoil, an evenmore efficient device, which took nonmecha-nized human flight perhaps as far as it can go.

Akin to the kite, glider, and hang glider isthat creation of childhood fancy, the paper air-plane. In its most basic form—and paper air-plane enthusiasts are capable of fairly complexdesigns—a paper airplane is little more than a setof wings. There are a number or reasons for this,not least the fact that in most cases, a person fly-ing a paper airplane is not as concerned aboutpitch, yaw, and roll as a pilot flying with severalhundred passengers on board would be.

However, when fashioning a paper airplaneit is possible to add a number of design features,for instance by folding flaps upward at the tail.These become the equivalent of the elevator, acontrol surface along the horizontal edge of a realaircraft’s tail, which the pilot rotates upward toprovide stability. But as noted by Ken Blackburn,author of several books on paper airplanes, it isnot necessarily the case that an airplane must

have a tail; indeed, some of the most sophisticat-ed craft in the sky today—including the fearsomeB-2 “Stealth” bomber—do not have tails.

A typical paper airplane has low aspect ratiowings, a term that refers to the size of thewingspan compared to the chord line. In subson-ic flight, higher aspect ratios are usually pre-ferred, and this is certainly the case with most“real” gliders; hence their wings are longer, andtheir chord lines shorter. But there are severalreasons why this is not the case with a paper air-plane.

First of all, as Blackburn noted wryly on hisWeb site, “Paper is a lousy building material.There is a reason why real airplanes are not madeof paper.” He stated the other factors governingpaper airplanes’ low aspect ratio in similarlywhimsical terms. First, “Low aspect ratio wingsare easier to fold....”; second, “Paper airplanegliding performance is not usually very impor-tant....”; and third, “Low-aspect ratio wings lookfaster, especially if they are swept back.”

The reason why low-aspect ratio wings lookfaster, Blackburn suggested, is that people seethem on jet fighters and the Concorde, andassume that a relatively narrow wing span with along chord line yields the fastest speeds. Andindeed they do—but only at supersonic speeds.Below the speed of sound, high-aspect ratiowings are best for preventing drag. Furthermore,as Blackburn went on to note, low-aspect ratiowings help the paper airplane to withstand therelatively high launch speeds necessary to sendthem into longer glides.

In fact, a paper airplane is not subject to any-thing like the sort of design constraints affectinga real craft. All real planes look somewhat similar,because the established combinations, ratios, anddimensions of wings, tails, and fuselage workbest. Certainly there is a difference in basicappearance between subsonic and supersonicaircraft—but again, all supersonic jets have moreor less the same low-aspect, swept wing. “Withpaper airplanes,” Blackburn wrote, “it’s easy tomake airplanes that don’t look like real airplanes”since “The mission of a paper airplane is [simply]to provide a good time for the pilot.”

Aerodynamics on the Ground

The preceding discussions of aerodynamics inaction have concerned the behavior of objects offthe ground. But aerodynamics is also a factor in



Aero-dynamics


wheeled transport on Earth’s surface, whether bybicycle, automobile, or some other variation.

On a bicycle, the rider accounts for 65-80%of the drag, and therefore his or her position withregard to airflow is highly important. Thus, fromas early as the 1890s, designers of racing bikeshave favored drop handlebars, as well as a seatand frame that allow a crouched position. Sincethe 1980s, bicycle designers have worked to elim-inate all possible extra lines and barriers to air-flow, including the crossbar and chainstays.

A typical bicycle’s wheel contains 32 or 36cylindrical spokes, and these can affect aerody-namics adversely. As the wheel rotates, the air-flow behind the spoke separates, creating turbu-lence and hence drag. For this reason, some ofthe most advanced bicycles today use either aero-dynamic rims, which reduce the length of thespokes, three-spoke aerodynamic wheels, or evensolid wheels.

The rider’s gear can also serve to impede orenhance his velocity, and thus modern racinghelmets have a streamlined shape—rather likethat of an airfoil. The best riders, such as thosewho compete in the Olympics or the Tour deFrance, have bikes custom-designed to fit theirown body shape.

One interesting aspect of aerodynamicswhere it concerns bicycle racing is the phenome-non of “drafting.” Riders at the front of a pack,like riders pedaling alone, consume 30-40%more energy than do riders in the middle of apack. The latter are benefiting from the efforts ofbicyclists in front of them, who put up most of the wind resistance. The same is true for bicyclists who ride behind automobiles ormotorcycles.

The use of machine-powered pace vehiclesto help in achieving extraordinary speeds is farfrom new. Drafting off of a railroad car with spe-cially designed aerodynamic shields, a rider in1896 was able to exceed 60 MPH (96 km/h), athen unheard-of speed. Today the record is justunder 167 MPH (267 km/h). Clearly one must bea highly skilled, powerful rider to approach any-thing like this speed; but design factors also comeinto play, and not just in the case of the pacevehicle. Just as supersonic jets are quite differentfrom ordinary planes, super high-speed bicyclesare not like the average bike; they are designed insuch a way that they must be moving faster than60 MPH before the rider can even pedal.

With regard to automobiles, as noted earlier,aerodynamics has a strong impact on bodydesign. For this reason, cars over the years havebecome steadily more streamlined and aerody-namic in appearance, a factor that designers bal-ance with aesthetic appeal. Today’s Chrysler PTCruiser, which debuted in 2000, may share out-ward features with 1930s and 1940s cars, but thePT Cruiser’s design is much more sound aerody-namically—not least because a modern vehiclecan travel much, much faster than the cars driv-en by previous generations.

Nowhere does the connection between aero-dynamics and automobiles become more crucialthan in the sport of auto racing. For race-cardrivers, drag is always a factor to be avoided andcounteracted by means ranging from drafting toaltering the body design to reduce the airflowunder the vehicle. However, as strange as it mayseem, a car—like an airplane—is also subject tolift.

It was noted earlier that in some cases liftcan be undesirable in an airplane (for instance,when trying to land), but it is virtually alwaysundesirable in an automobile. The greater thespeed, the greater the lift force, which increases

A PROFESSIONAL BICYCLE RACER’S STREAMLINED HEL-MET AND CROUCHED POSITION HELP TO IMPROVE AIR-FLOW, THUS INCREASING SPEED. (Photograph by Ronnen

Eshel/Corbis. Reproduced by permission.)


Aero-dynamics


the threat of instability. For this reason, buildersof race cars design their vehicles for negative lift:hence a typical family car has a lift coefficient ofabout 0.03, whereas a race car is likely to have acoefficient of -3.00.

Among the design features most often usedto reduce drag while achieving negative lift is arear-deck spoiler. The latter has an airfoil shape,but its purpose is different: to raise the rear stag-nation point and direct air flow so that it does

not wrap around the vehicle’s rear end. Instead,the spoiler creates a downward force to stabilizethe rear, and it may help to decrease drag byreducing the separation of airflow (and hence thecreation of turbulence) at the rear window.

Similar in concept to a spoiler, though some-what different in purpose, is the aerodynamicallycurved shield that sits atop the cab of most mod-ern eighteen-wheel transport trucks. The pur-pose of the shield becomes apparent when the

AERODYNAMICS: The study of air

flow and its principles. Applied aerody-

namics is the science of improving man-

made objects in light of those principles.

AIRFOIL: The design of an airplane’s

wing when seen from the end, a shape

intended to maximize the aircraft’s

response to airflow.

ANGLE OF ATTACK: The orientation of

the airfoil with regard to the airflow, or the

angle that the chord line forms with the

direction of the air stream.

BERNOULLI’S PRINCIPLE: A proposi-

tion, credited to Swiss mathematician and

physicist Daniel Bernoulli (1700-1782),

which maintains that slower-moving fluid

exerts greater pressure than faster-moving

fluid.

CAMBER: The enhanced curvature on the

upper surface of an airfoil.

CHORD LINE: The distance, along an

imaginary straight line, from the stagna-

tion point of an airfoil to the rear, or trail-

ing edge.

DRAG: The force that opposes the forward

motion of an object in airflow.





LIFT: An aerodynamic force perpendicu-

lar to the direction of the wind. For an air-

craft, lift is the force that raises it off the

ground and keeps it aloft.

PITCH: The tendency of an aircraft in

flight to rotate forward or backward; see

also yaw and roll.

ROLL: The tendency of an aircraft in

flight to rotate vertically on the axis of its

fuselage; see also pitch and yaw.

STAGNATION POINT: The spot where

airflow hits the leading edge of an airfoil.

SUPERSONIC: Faster than Mach 1, or

the speed of sound—660 MPH (1,622

km/h). Speeds above Mach 5 are referred to

as hypersonic.

TURBULENT: A term describing a highly

irregular form of flow, in which a fluid is

subject to continual changes in speed and

direction. Its opposite is laminar flow.



YAW: The tendency of an aircraft in flight

to rotate on a horizontal plane; see also

Pitch and Roll.

KEY TERMS


Aero-dynamics

truck is moving at high speeds: wind resistancebecomes strong, and if the wind were to hit thetruck’s trailer head-on, it would be as though theair were pounding a brick wall. Instead, the shieldscoops air upward, toward the rear of the truck.At the rear may be another panel, patented bytwo young engineers in 1994, that creates a drag-reducing vortex between panel and truck.

WHERE TO LEARN MORE

Cockpit Physics (Department of Physics, United StatesAir Force Academy web site.).<http://www.usafa.af.mil/dfp/cockpit-phys/> (Febru-ary 19, 2001).

K8AIT Principles of Aeronautics Advanced Text. (website). <http://wings.ucdavis.edu/Book/advanced.html> (February 19, 2001).

Macaulay, David. The New Way Things Work. Boston:

Houghton Mifflin, 1998.

Blackburn, Ken. Paper Airplane Aerodynamics. (web site).

<http://www.geocities.com/CapeCanaveral/1817/

paero.html> (February 19, 2001).

Schrier, Eric and William F. Allman. Newton at the Bat:

The Science in Sports. New York: Charles Scribner’s

Sons, 1984.

Smith, H. C. The Illustrated Guide to Aerodynamics. Blue

Ridge Summit, PA: Tab Books, 1992.

Stever, H. Guyford, James J. Haggerty, and the Editors of

Time-Life Books. Flight. New York: Time-Life Books,

1965.






BERNOULLI ’S PR INCIPLEBernoulli’s Principle

CONCEPTBernoulli’s principle, sometimes known asBernoulli’s equation, holds that for fluids in anideal state, pressure and density are inverselyrelated: in other words, a slow-moving fluidexerts more pressure than a fast-moving fluid.Since “fluid” in this context applies equally to liq-uids and gases, the principle has as many appli-cations with regard to airflow as to the flow ofliquids. One of the most dramatic everydayexamples of Bernoulli’s principle can be found inthe airplane, which stays aloft due to pressure dif-ferences on the surface of its wing; but the truthof the principle is also illustrated in something asmundane as a shower curtain that billowsinward.

HOW IT WORKSThe Swiss mathematician and physicist DanielBernoulli (1700-1782) discovered the principlethat bears his name while conducting experi-ments concerning an even more fundamentalconcept: the conservation of energy. This is a lawof physics that holds that a system isolated fromall outside factors maintains the same totalamount of energy, though energy transforma-tions from one form to another take place.

For instance, if you were standing at the topof a building holding a baseball over the side, theball would have a certain quantity of potentialenergy—the energy that an object possesses byvirtue of its position. Once the ball is dropped, itimmediately begins losing potential energy andgaining kinetic energy—the energy that an objectpossesses by virtue of its motion. Since the totalenergy must remain constant, potential and

kinetic energy have an inverse relationship: as thevalue of one variable decreases, that of the otherincreases in exact proportion.

The ball cannot keep falling forever, losingpotential energy and gaining kinetic energy. Infact, it can never gain an amount of kinetic ener-gy greater than the potential energy it possessedin the first place. At the moment before the ballhits the ground, its kinetic energy is equal to thepotential energy it possessed at the top of thebuilding. Correspondingly, its potential energy iszero—the same amount of kinetic energy it pos-sessed before it was dropped.

Then, as the ball hits the ground, the energyis dispersed. Most of it goes into the ground, anddepending on the rigidity of the ball and theground, this energy may cause the ball to bounce.Some of the energy may appear in the form ofsound, produced as the ball hits bottom, andsome will manifest as heat. The total energy,however, will not be lost: it will simply havechanged form.

Bernoulli was one of the first scientists topropose what is known as the kinetic theory ofgases: that gas, like all matter, is composed of tinymolecules in constant motion. In the 1730s, heconducted experiments in the conservation ofenergy using liquids, observing how water flowsthrough pipes of varying diameter. In a segmentof pipe with a relatively large diameter, heobserved, water flowed slowly, but as it entered asegment of smaller diameter, its speed increased.

It was clear that some force had to be actingon the water to increase its speed. Earlier, RobertBoyle (1627-1691) had demonstrated that pres-sure and volume have an inverse relationship,


Bernoulli’sPrinciple


and Bernoulli seems to have applied Boyle’s find-ings to the present situation. Clearly the volumeof water flowing through the narrower pipe atany given moment was less than that flowingthrough the wider one. This suggested, accordingto Boyle’s law, that the pressure in the wider pipemust be greater.

As fluid moves from a wider pipe to a nar-rower one, the volume of that fluid that moves agiven distance in a given time period does notchange. But since the width of the narrower pipeis smaller, the fluid must move faster in order toachieve that result. One way to illustrate this is toobserve the behavior of a river: in a wide, uncon-stricted region, it flows slowly, but if its flow isnarrowed by canyon walls (for instance), then itspeeds up dramatically.

The above is a result of the fact that water isa fluid, and having the characteristics of a fluid, itadjusts its shape to fit that of its container orother solid objects it encounters on its path.Since the volume passing through a given lengthof pipe during a given period of time will be thesame, there must be a decrease in pressure. HenceBernoulli’s conclusion: the slower the rate offlow, the higher the pressure, and the faster therate of flow, the lower the pressure.

Bernoulli published the results of his workin Hydrodynamica (1738), but did not present hisideas or their implications clearly. Later, hisfriend the German mathematician LeonhardEuler (1707-1783) generalized his findings in the statement known today as Bernoulli’sprinciple.

The Venturi Tube

Also significant was the work of the Italian physi-cist Giovanni Venturi (1746-1822), who is credit-ed with developing the Venturi tube, an instru-ment for measuring the drop in pressure thattakes place as the velocity of a fluid increases. Itconsists of a glass tube with an inward-slopingarea in the middle, and manometers, devices formeasuring pressure, at three places: the entrance,the point of constriction, and the exit. The Ven-turi meter provided a consistent means ofdemonstrating Bernoulli’s principle.

Like many propositions in physics,Bernoulli’s principle describes an ideal situationin the absence of other forces. One such force is

viscosity, the internal friction in a fluid thatmakes it resistant to flow. In 1904, the Germanphysicist Ludwig Prandtl (1875-1953) was con-ducting experiments in liquid flow, the firsteffort in well over a century to advance the find-ings of Bernoulli and others. Observing the flowof liquid in a tube, Prandtl found that a tinyportion of the liquid adheres to the surface ofthe tube in the form of a thin film, and does notcontinue to move. This he called the viscousboundary layer.

Like Bernoulli’s principle itself, Prandtl’sfindings would play a significant part in aerody-namics, or the study of airflow and its principles.They are also significant in hydrodynamics, orthe study of water flow and its principles, a disci-pline Bernoulli founded.

Laminar vs. Turbulent Flow

Air and water are both examples of fluids, sub-stances which—whether gas or liquid—conformto the shape of their container. The flow patternsof all fluids may be described in terms either oflaminar flow, or of its opposite, turbulent flow.

Laminar flow is smooth and regular, alwaysmoving at the same speed and in the same direc-tion. Also known as streamlined flow, it is char-acterized by a situation in which every particle offluid that passes a particular point follows a pathidentical to all particles that passed that pointearlier. A good illustration of laminar flow iswhat occurs when a stream flows around a twig.

By contrast, in turbulent flow, the fluid issubject to continual changes in speed and direc-tion—as, for instance, when a stream flows overshoals of rocks. Whereas the mathematical modelof laminar flow is rather straightforward, condi-tions are much more complex in turbulent flow,which typically occurs in the presence of obsta-cles or high speeds.

Turbulent flow makes it more difficult fortwo streams of air, separated after hitting a barri-er, to rejoin on the other side of the barrier; yetthat is their natural tendency. In fact, if a singleair current hits an airfoil—the design of an air-plane’s wing when seen from the end, a stream-lined shape intended to maximize the aircraft’sresponse to airflow—the air that flows over thetop will “try” to reach the back end of the airfoilat the same time as the air that flows over the




bottom. In order to do so, it will need to speedup—and this, as will be shown below, is the basisfor what makes an airplane fly.

When viscosity is absent, conditions of per-fect laminar flow exist: an object behaves in com-plete alignment with Bernoulli’s principle. Of

A KITE’S DESIGN, PARTICULARLY ITS USE OF LIGHTWEIGHT FABRIC STRETCHED OVER TWO CROSSED STRIPS OF VERY

LIGHT WOOD, MAKES IT WELL-SUITED FOR FLIGHT, BUT WHAT KEEPS IT IN THE AIR IS A DIFFERENCE IN AIR PRESSURE.AT THE BEST POSSIBLE ANGLE OF ATTACK, THE KITE EXPERIENCES AN IDEAL RATIO OF PRESSURE FROM THE SLOW-ER-MOVING AIR BELOW VERSUS THE FASTER-MOVING AIR ABOVE, AND THIS GIVES IT LIFT. (Roger Ressmeyer/Corbis. Repro-




course, though ideal conditions seldom occur inthe real world, Bernoulli’s principle provides aguide for the behavior of planes in flight, as wellas a host of everyday things.


Flying Machines

For thousands of years, human beings vainlysought to fly “like a bird,” not realizing that this isliterally impossible, due to differences in phys-iognomy between birds and homo sapiens. Noman has ever been born (or ever will be) whopossesses enough strength in his chest that hecould flap a set of attached wings and lift hisbody off the ground. Yet the bird’s physical struc-ture proved highly useful to designers of practi-cal flying machines.

A bird’s wing is curved along the top, so thatwhen air passes over the wing and divides, thecurve forces the air on top to travel a greater dis-tance than the air on the bottom. The tendencyof airflow, as noted earlier, is to correct for thepresence of solid objects and to return to its orig-inal pattern as quickly as possible. Hence, when

the air hits the front of the wing, the rate of flowat the top increases to compensate for the greaterdistance it has to travel than the air below thewing. And as shown by Bernoulli, fast-movingfluid exerts less pressure than slow-moving fluid;therefore, there is a difference in pressurebetween the air below and the air above, and thiskeeps the wing aloft.

Only in 1853 did Sir George Cayley (1773-1857) incorporate the avian airfoil to create his-tory’s first workable (though engine-less) flyingmachine, a glider. Much, much older than Cay-ley’s glider, however, was the first manmade fly-ing machine built “according to Bernoulli’s prin-ciple”—only it first appeared in about 12,000B.C., and the people who created it had had littlecontact with the outside world until the late eigh-teenth century A.D. This was the boomerang, oneof the most ingenious devices ever created by astone-age society—in this case, the Aborigines ofAustralia.

Contrary to the popular image, aboomerang flies through the air on a plane per-pendicular to the ground, rather than parallel.Hence, any thrower who properly knows howtosses the boomerang not with a side-arm throw,but overhand. As it flies, the boomerang becomes


THE BOOMERANG, DEVELOPED BY AUSTRALIA’S ABORIGINAL PEOPLE, FLIES THROUGH THE AIR ON A PLANE PER-PENDICULAR TO THE GROUND, RATHER THAN PARALLEL. AS IT FLIES, THE BOOMERANG BECOMES BOTH A GYROSCOPE

AND AN AIRFOIL, AND THIS DUAL ROLE GIVES IT AERODYNAMIC LIFT. (Bettmann/Corbis. Reproduced by permission.)



both a gyroscope and an airfoil, and this dual rolegives it aerodynamic lift.

Like the gyroscope, the boomerang imitatesa top; spinning keeps it stable. It spins throughthe air, its leading wing (the forward or upwardwing) creating more lift than the other wing. Asan airfoil, the boomerang is designed so that theair below exerts more pressure than the air above,which keeps it airborne.

Another very early example of a flyingmachine using Bernoulli’s principles is the kite,which first appeared in China in about 1000 B.C.The kite’s design, particularly its use of light-weight fabric stretched over two crossed strips ofvery light wood, makes it well-suited for flight,but what keeps it in the air is a difference in airpressure. At the best possible angle of attack, thekite experiences an ideal ratio of pressure fromthe slower-moving air below versus the faster-moving air above, and this gives it lift.

Later Cayley studied the operation of thekite, and recognized that it—rather than the bal-loon, which at first seemed the most promisingapparatus for flight—was an appropriate modelfor the type of heavier-than-air flying machinehe intended to build. Due to the lack of a motor,however, Cayley’s prototypical airplane couldnever be more than a glider: a steam engine, thenstate-of-the-art technology, would have beenmuch too heavy.

Hence, it was only with the invention of theinternal-combustion engine that the modern air-plane came into being. On December 17, 1903, atKitty Hawk, North Carolina, Orville (1871-1948)and Wilbur (1867-1912) Wright tested a craftthat used a 25-horsepower engine they haddeveloped at their bicycle shop in Ohio. By max-imizing the ratio of power to weight, the enginehelped them overcome the obstacles that haddogged recent attempts at flight, and by the timethe day was over, they had achieved a dream thathad eluded men for more than four millennia.

Within fifty years, airplanes would increas-ingly obtain their power from jet rather thaninternal-combustion engines. But the principlethat gave them flight, and the principle that keptthem aloft once they were airborne, reflectedback to Bernoulli’s findings of more than 160years before their time. This is the concept of theairfoil.

As noted earlier, an airfoil has a streamlineddesign. Its shape is rather like that of an elongat-

ed, asymmetrical teardrop lying on its side, withthe large end toward the direction of airflow, andthe narrow tip pointing toward the rear. Thegreater curvature of its upper surface in compar-ison to the lower side is referred to as the air-plane’s camber. The front end of the airfoil is alsocurved, and the chord line is an imaginarystraight line connecting the spot where the airhits the front—known as the stagnation point—to the rear, or trailing edge, of the wing.

Again, in accordance with Bernoulli’s princi-ple, the shape of the airflow facilitates the spreadof laminar flow around it. The slower-movingcurrents beneath the airfoil exert greater pressurethan the faster currents above it, giving lift to theaircraft. Of course, the aircraft has to be movingat speeds sufficient to gain momentum for itsleap from the ground into the air, and here again,Bernoulli’s principle plays a part.

Thrust comes from the engines, which runthe propellers—whose blades in turn aredesigned as miniature airfoils to maximize theirpower by harnessing airflow. Like the aircraftwings, the blades’ angle of attack—the angle atwhich airflow hits it. In stable flight, the pilotgreatly increases the angle of attack (also calledpitched), whereas at takeoff and landing, thepitch is dramatically reduced.

Drawing Fluids Upward:Atomizers and Chimneys

A number of everyday objects use Bernoulli’sprinciple to draw fluids upward, and though interms of their purposes, they might seem verydifferent—for instance, a perfume atomizer vs. achimney—they are closely related in their appli-cation of pressure differences. In fact, the ideabehind an atomizer for a perfume spray bottlecan also be found in certain garden-hose attach-ments, such as those used to provide a high-pres-sure car wash.

The air inside the perfume bottle is movingrelatively slowly; therefore, according to Bernoul-li’s principle, its pressure is relatively high, and itexerts a strong downward force on the perfumeitself. In an atomizer there is a narrow tube run-ning from near the bottom of the bottle to thetop. At the top of the perfume bottle, it opensinside another tube, this one perpendicular tothe first tube. At one end of the horizontal tube isa simple squeeze-pump which causes air to flowquickly through it. As a result, the pressure




toward the top of the bottle is reduced, and theperfume flows upward along the vertical tube,drawn from the area of higher pressure at thebottom. Once it is in the upper tube, the squeeze-pump helps to eject it from the spray nozzle.

A carburetor works on a similar principle,though in that case the lower pressure at the topdraws air rather than liquid. Likewise a chimneydraws air upward, and this explains why a windyday outside makes for a better fire inside. Withwind blowing over the top of the chimney, the airpressure at the top is reduced, and tends to drawhigher-pressure air from down below.

The upward pull of air according to theBernoulli principle can also be illustrated bywhat is sometimes called the “Hoover bugle”—aname perhaps dating from the Great Depression,when anything cheap or contrived bore theappellation “Hoover” as a reflection of populardissatisfaction with President Herbert Hoover. Inany case, the Hoover bugle is simply a long cor-rugated tube that, when swung overhead, pro-duces musical notes.

You can create a Hoover bugle using any sortof corrugated tube, such as vacuum-cleaner hoseor swimming-pool drain hose, about 1.8 in (4cm) in diameter and 6 ft (1.8 m) in length. Tooperate it, you should simply hold the tube inboth hands, with extra length in the leadinghand—that is, the right hand, for most people.This is the hand with which to swing the tubeover your head, first slowly and then faster,observing the changes in tone that occur as youchange the pace.

The vacuum hose of a Hoover tube can alsobe returned to a version of its original purpose inan illustration of Bernoulli’s principle. If a pieceof paper is torn into pieces and placed on a table,with one end of the tube just above the paper andthe other end spinning in the air, the paper tendsto rise. It is drawn upward as though by a vacu-um cleaner—but in fact, what makes it happen isthe pressure difference created by the movementof air.

In both cases, reduced pressure draws airfrom the slow-moving region at the bottom ofthe tube. In the case of the Hoover bugle, the cor-rugations produce oscillations of a certain fre-quency. Slower speeds result in slower oscilla-tions and hence lower frequency, which producesa lower tone. At higher speeds, the opposite is

true. There is little variation in tones on a Hooverbugle: increasing the velocity results in a fre-quency twice that of the original, but it is difficultto create enough speed to generate a third tone.

Spin, Curve, and Pull: TheCounterintuitive Principle

There are several other interesting illustrations—sometimes fun and in one case potentially trag-ic—of Bernoulli’s principle. For instance, there isthe reason why a shower curtain billows inwardonce the shower is turned on. It would seem log-ical at first that the pressure created by the waterwould push the curtain outward, securing it tothe side of the bathtub.

Instead, of course, the fast-moving air gener-ated by the flow of water from the shower createsa center of lower pressure, and this causes thecurtain to move away from the slower-movingair outside. This is just one example of the waysin which Bernoulli’s principle creates results that,on first glance at least, seem counterintuitive—that is, the opposite of what common sensewould dictate.

Another fascinating illustration involvesplacing two empty soft drink cans parallel to oneanother on a table, with a couple of inches or afew centimeters between them. At that point, theair on all sides has the same slow speed. If youwere to blow directly between the cans, however,this would create an area of low pressure betweenthem. As a result, the cans push together. Forships in a harbor, this can be a frighteningprospect: hence, if two crafts are parallel to oneanother and a strong wind blows between them,there is a possibility that they may behave like thecans.

Then there is one of the most illusory uses ofBernoulli’s principle, that infamous baseballpitcher’s trick called the curve ball. As the ballmoves through the air toward the plate, its veloc-ity creates an air stream moving against the tra-jectory of the ball itself. Imagine it as two lines,one curving over the ball and one curving under,as the ball moves in the opposite direction.

In an ordinary throw, the effects of the air-flow would not be particularly intriguing, but inthis case, the pitcher has deliberately placed a“spin” on the ball by the manner in which he hasthrown it. How pitchers actually produce spin isa complex subject unto itself, involving grip,





wrist movement, and other factors, and in anycase, the fact of the spin is more important thanthe way in which it was achieved.

If the direction of airflow is from right toleft, the ball, as it moves into the airflow, is spin-ning clockwise. This means that the air flowing

AERODYNAMICS: The study of air-

flow and its principles. Applied aerody-

namics is the science of improving man-

made objects in light of those principles.

AIRFOIL: The design of an airplane’s

wing when seen from the end, a shape

intended to maximize the aircraft’s

response to airflow.

ANGLE OF ATTACK: The orientation of

the airfoil with regard to the airflow, or the

angle that the chord line forms with the

direction of the air stream.

BERNOULLI’S PRINCIPLE: A proposi-

tion, credited to Swiss mathematician and

physicist Daniel Bernoulli (1700-1782),

which maintains that slower-moving fluid

exerts greater pressure than faster-moving

fluid.

CAMBER: The enhanced curvature on the

upper surface of an airfoil.

CHORD LINE: The distance, along an

imaginary straight line, from the stagna-

tion point of an airfoil to the rear, or trail-

ing edge.


law of physics which holds that within a

system isolated from all other outside fac-

tors, the total amount of energy remains

the same, though transformations of ener-

gy from one form to another take place.



container.

HYDRODYNAMICS: The study of

water flow and its principles.





KINETIC ENERGY: The energy that

an object possesses by virtue of its motion.





LIFT: An aerodynamic force perpendicu-

lar to the direction of the wind. For an air-

craft, lift is the force that raises it off the

ground and keeps it aloft.

MANOMETERS: Devices for measur-

ing pressure in conjunction with a Venturi

tube.

POTENTIAL ENERGY: The energy

that an object possesses by virtue of its

position.STAGNATION POINT: The spot

where airflow hits the leading edge of an

airfoil.

TURBULENT: A term describing a highly

irregular form of flow, in which a fluid is

subject to continual changes in speed and

direction. Its opposite is laminar flow.

VENTURI TUBE: An instrument, con-

sisting of a glass tube with an inward-slop-

ing area in the middle, for measuring the

drop in pressure that takes place as the

velocity of a fluid increases.



KEY TERMS



over the ball is moving in a direction opposite tothe spin, whereas that flowing under it is movingin the same direction. The opposite forces pro-duce a drag on the top of the ball, and this cutsdown on the velocity at the top compared to thatat the bottom of the ball, where spin and airfloware moving in the same direction.

Thus the air pressure is higher at the top ofthe ball, and as per Bernoulli’s principle, thistends to pull the ball downward. The curve ball—of which there are numerous variations, such asthe fade and the slider—creates an unpredictablesituation for the batter, who sees the ball leave thepitcher’s hand at one altitude, but finds to his dis-may that it has dropped dramatically by the timeit crosses the plate.

A final illustration of Bernoulli’s often coun-terintuitive principle neatly sums up its effects onthe behavior of objects. To perform the experi-ment, you need only an index card and a flat sur-face. The index card should be folded at the endsso that when the card is parallel to the surface,the ends are perpendicular to it. These foldsshould be placed about half an inch (about onecentimeter) from the ends.

At this point, it would be handy to have anunsuspecting person—someone who has notstudied Bernoulli’s principle—on the scene, andchallenge him or her to raise the card by blowingunder it. Nothing could seem easier, of course: by


blowing under the card, any person would natu-rally assume, the air will lift it. But of course thisis completely wrong according to Bernoulli’sprinciple. Blowing under the card, as illustrated,will create an area of high velocity and low pres-sure. This will do nothing to lift the card: in fact,it only pushes the card more firmly down on thetable.

WHERE TO LEARN MORE


“Bernoulli’s Principle: Explanations and Demos.” (Website). <http://207.10.97.102/physicszone/lesson/02forces/bernoull/bernoul l.html> (February 22,2001).

Cockpit Physics (Department of Physics, United StatesAir Force Academy. Web site.).<http://www.usafa.af.mil/dfp/cockpit-phys/> (Febru-ary 19, 2001).

K8AIT Principles of Aeronautics Advanced Text. (Website). <http://wings.ucdavis.edu/Book/advanced.html> (February 19, 2001).

Schrier, Eric and William F. Allman. Newton at the Bat:The Science in Sports. New York: Charles Scribner’sSons, 1984.

Smith, H. C. The Illustrated Guide to Aerodynamics. BlueRidge Summit, PA: Tab Books, 1992.

Stever, H. Guyford, James J. Haggerty, and the Editors ofTime-Life Books. Flight. New York: Time-Life Books,1965.



BUOYANC YBuoyancy

CONCEPTThe principle of buoyancy holds that the buoy-ant or lifting force of an object submerged in afluid is equal to the weight of the fluid it has dis-placed. The concept is also known asArchimedes’s principle, after the Greek mathe-matician, physicist, and inventor Archimedes (c.287-212 B.C.), who discovered it. Applications ofArchimedes’s principle can be seen across a widevertical spectrum: from objects deep beneath theoceans to those floating on its surface, and fromthe surface to the upper limits of the stratosphereand beyond.

HOW IT WORKS

Archimedes Discovers Buoy-ancy

There is a famous story that Sir Isaac Newton(1642-1727) discovered the principle of gravitywhen an apple fell on his head. The tale, an exag-gerated version of real events, has become somuch a part of popular culture that it has beenparodied in television commercials. Almostequally well known is the legend of howArchimedes discovered the concept of buoyancy.

A native of Syracuse, a Greek colony in Sici-ly, Archimedes was related to one of that city’skings, Hiero II (308?-216 B.C.). After studying inAlexandria, Egypt, he returned to his hometown,where he spent the remainder of his life. At somepoint, the royal court hired (or compelled) himto set about determining the weight of the goldin the king’s crown. Archimedes was in his bathpondering this challenge when suddenly itoccurred to him that the buoyant force of a sub-

merged object is equal to the weight of the fluiddisplaced by it.

He was so excited, the legend goes, that hejumped out of his bath and ran naked throughthe streets of Syracuse shouting “Eureka!” (I havefound it). Archimedes had recognized a principleof enormous value—as will be shown—to ship-builders in his time, and indeed to shipbuildersof the present.

Concerning the history of science, it was aparticularly significant discovery; few useful andenduring principles of physics date to the periodbefore Galileo Galilei (1564-1642.) Even amongthose few ancient physicists and inventors whocontributed work of lasting value—Archimedes,Hero of Alexandria (c. 65-125 A.D.), and a fewothers—there was a tendency to miss the largerimplications of their work. For example, Hero,who discovered steam power, considered it usefulonly as a toy, and as a result, this enormously sig-nificant discovery was ignored for seventeen cen-turies.

In the case of Archimedes and buoyancy,however, the practical implications of the discov-ery were more obvious. Whereas steam powermust indeed have seemed like a fanciful notion tothe ancients, there was nothing farfetched aboutoceangoing vessels. Shipbuilders had long beenconfronted with the problem of how to keep avessel afloat by controlling the size of its load onthe one hand, and on the other hand, its tenden-cy to bob above the water. Here, Archimedesoffered an answer.

Buoyancy and Weight

Why does an object seem to weigh less underwa-ter than above the surface? How is it that a ship


Buoyancymade of steel, which is obviously heavier thanwater, can float? How can we determine whethera balloon will ascend in the air, or a submarinewill descend in the water? These and other ques-tions are addressed by the principle of buoyancy,which can be explained in terms of properties—most notably, gravity—unknown to Archimedes.

To understand the factors at work, it is use-ful to begin with a thought experiment. Imaginea certain quantity of fluid submerged within alarger body of the same fluid. Note that the terms“liquid” or “water” have not been used: not onlyis “fluid” a much more general term, but also, ingeneral physical terms and for the purposes ofthe present discussion, there is no significant dif-ference between gases and liquids. Both conformto the shape of the container in which they areplaced, and thus both are fluids.

To return to the thought experiment, whathas been posited is in effect a “bag” of fluid—thatis, a “bag” made out of fluid and containing fluidno different from the substance outside the“bag.” This “bag” is subjected to a number offorces. First of all, there is its weight, which tendsto pull it to the bottom of the container. There isalso the pressure of the fluid all around it, whichvaries with depth: the deeper within the contain-er, the greater the pressure.

Pressure is simply the exertion of force overa two-dimensional area. Thus it is as though thefluid is composed of a huge number of two-dimensional “sheets” of fluid, each on top of theother, like pages in a newspaper. The deeper intothe larger body of fluid one goes, the greater thepressure; yet it is precisely this increased force atthe bottom of the fluid that tends to push the“bag” upward, against the force of gravity.

Now consider the weight of this “bag.”Weight is a force—the product of mass multi-plied by acceleration—that is, the downwardacceleration due to Earth’s gravitational pull. Foran object suspended in fluid, it is useful to sub-stitute another term for mass. Mass is equal tovolume, or the amount of three-dimensionalspace occupied by an object, multiplied by densi-ty. Since density is equal to mass divided by vol-ume, this means that volume multiplied by den-sity is the same as mass.

We have established that the weight of thefluid “bag” is Vdg, where V is volume, d is densi-ty, and g is the acceleration due to gravity. Nowimagine that the “bag” has been replaced by a


solid object of exactly the same size. The solidobject will experience exactly the same degree ofpressure as the imaginary “bag” did—and hence,it will also experience the same buoyant forcepushing it up from the bottom. This means thatbuoyant force is equal to the weight—Vdg—ofdisplaced fluid.

Buoyancy is always a double-edged proposi-tion. If the buoyant force on an object is greaterthan the weight of that object—in other words, ifthe object weighs less than the amount of waterit has displaced—it will float. But if the buoyantforce is less than the object’s weight, the objectwill sink. Buoyant force is not the same as netforce: if the object weighs more than the water itdisplaces, the force of its weight cancels out andin fact “overrules” that of the buoyant force.

At the heart of the issue is density. Often, thedensity of an object in relation to water isreferred to as its specific gravity: most metals,which are heavier than water, are said to have ahigh specific gravity. Conversely, petroleum-based products typically float on the surface ofwater, because their specific gravity is low. Notethe close relationship between density andweight where buoyancy is concerned: in fact, themost buoyant objects are those with a relativelyhigh volume and a relatively low density.

This can be shown mathematically by meansof the formula noted earlier, whereby density isequal to mass divided by volume. If Vd =V(m/V), an increase in density can only mean anincrease in mass. Since weight is the product ofmass multiplied by g (which is assumed to be aconstant figure), then an increase in densitymeans an increase in mass and hence, an increasein weight—not a good thing if one wants anobject to float.


Staying Afloat

In the early 1800s, a young Mississippi River flat-boat operator submitted a patent applicationdescribing a device for “buoying vessels overshoals.” The invention proposed to prevent aproblem he had often witnessed on the river—boats grounded on sandbars—by equipping theboats with adjustable buoyant air chambers. Theyoung man even whittled a model of his inven-


Buoyancy


tion, but he was not destined for fame as aninventor; instead, Abraham Lincoln (1809-1865)was famous for much else. In fact Lincoln had asound idea with his proposal to use buoyantforce in protecting boats from running aground.

Buoyancy on the surface of water has a num-ber of easily noticeable effects in the real world.(Having established the definition of fluid, fromthis point onward, the fluids discussed will beprimarily those most commonly experienced:water and air.) It is due to buoyancy that fish,human swimmers, icebergs, and ships stay afloat.Fish offer an interesting application of volumechange as a means of altering buoyancy: a fishhas an internal swim bladder, which is filled withgas. When it needs to rise or descend, it changesthe volume in its swim bladder, which thenchanges its density. The examples of swimmersand icebergs directly illustrate the principle ofdensity—on the part of the water in the firstinstance, and on the part of the object itself in thesecond.

To a swimmer, the difference between swim-ming in fresh water and salt water shows thatbuoyant force depends as much on the density ofthe fluid as on the volume displaced. Fresh waterhas a density of 62.4 lb/ft3 (9,925 N/m3), whereasthat of salt water is 64 lb/ft3 (10,167 N/m3). Forthis reason, salt water provides more buoyantforce than fresh water; in Israel’s Dead Sea, thesaltiest body of water on Earth, bathers experi-ence an enormous amount of buoyant force.

Water is an unusual substance in a numberof regards, not least its behavior as it freezes.Close to the freezing point, water thickens up,but once it turns to ice, it becomes less dense.This is why ice cubes and icebergs float. Howev-er, their low density in comparison to the wateraround them means that only part of an icebergstays atop the surface. The submerged percentageof an iceberg is the same as the ratio of the den-sity of ice to that of water: 89%.

Ships at Sea

Because water itself is relatively dense, a high-volume, low-density object is likely to displace aquantity of water more dense—and heavier—than the object itself. By contrast, a steel balldropped into the water will sink straight to thebottom, because it is a low-volume, high-densityobject that outweighs the water it displaced.

This brings back the earlier question: howcan a ship made out of steel, with a density of 487lb/ft3 (77,363 N/m3), float on a salt-water oceanwith an average density of only about one-eighththat amount? The answer lies in the design of theship’s hull. If the ship were flat like a raft, or if allthe steel in it were compressed into a ball, itwould indeed sink. Instead, however, the hollowhull displaces a volume of water heavier than theship’s own weight: once again, volume has beenmaximized, and density minimized.

For a ship to be seaworthy, it must maintaina delicate balance between buoyancy and stabili-ty. A vessel that is too light—that is, too muchvolume and too little density—will bob on thetop of the water. Therefore, it needs to carry acertain amount of cargo, and if not cargo, thenwater or some other form of ballast. Ballast is aheavy substance that increases the weight of anobject experiencing buoyancy, and therebyimproves its stability.

Ideally, the ship’s center of gravity should bevertically aligned with its center of buoyancy. Thecenter of gravity is the geometric center of theship’s weight—the point at which weight above isequal to weight below, weight fore is equal toweight aft, and starboard (right-side) weight isequal to weight on the port (left) side. The centerof buoyancy is the geometric center of its sub-merged volume, and in a stable ship, it is somedistance directly below center of gravity.

Displacement, or the weight of the fluid thatis moved out of position when an object isimmersed, gives some idea of a ship’s stability. Ifa ship set down in the ocean causes 1,000 tons(8.896 • 106 N) of water to be displaced, it is saidto possess a displacement of 1,000 tons. Obvi-ously, a high degree of displacement is desirable.The principle of displacement helps to explainhow an aircraft carrier can remain afloat, eventhough it weighs many thousands of tons.

Down to the Depths

A submarine uses ballast as a means of descend-ing and ascending underwater: when the subma-rine captain orders the crew to take the craftdown, the craft is allowed to take water into itsballast tanks. If, on the other hand, the commandis given to rise toward the surface, a valve will beopened to release compressed air into the tanks.The air pushes out the water, and causes the craftto ascend.


Buoyancy


A submarine is an underwater ship; itsstreamlined shape is designed to ease its move-ment. On the other hand, there are certain kindsof underwater vessels, known as submersibles,that are designed to sink—in order to observe orcollect data from the ocean floor. Originally, theidea of a submersible was closely linked to that ofdiving itself. An early submersible was the divingbell, a device created by the noted Englishastronomer Edmund Halley (1656-1742.)

Though his diving bell made it possible forHalley to set up a company in which hired diverssalvaged wrecks, it did not permit divers to gobeyond relatively shallow depths. First of all, thediving bell received air from the surface: in Hal-ley’s time, no technology existed for taking anoxygen supply below. Nor did it provide substan-tial protection from the effects of increased pres-sure at great depths.

PERILS OF THE DEEP. The mostimmediate of those effects is, of course, the ten-dency of an object experiencing such pressure tosimply implode like a tin can in a vise. Further-more, the human body experiences several severereactions to great depth: under water, nitrogengas accumulates in a diver’s bodily tissues, pro-

ducing two different—but equally frightening—effects.

Nitrogen is an inert gas under normal con-ditions, yet in the high pressure of the oceandepths it turns into a powerful narcotic, causingnitrogen narcosis—often known by the poetic-sounding name “rapture of the deep.” Under theinfluence of this deadly euphoria, divers begin tothink themselves invincible, and their alteredjudgment can put them into potentially fatal sit-uations.

Nitrogen narcosis can occur at depths asshallow as 60 ft (18.29 m), and it can be over-come simply by returning to the surface. Howev-er, one should not return to the surface tooquickly, particularly after having gone down to asignificant depth for a substantial period of time.In such an instance, on returning to the surfacenitrogen gas will bubble within the body, pro-ducing decompression sickness—known collo-quially as “the bends.” This condition may mani-fest as itching and other skin problems, jointpain, choking, blindness, seizures, unconscious-ness, and even permanent neurological defectssuch as paraplegia.

Ic

0°

4°

THE MOLECULAR STRUCTURE OF WATER BEGINS TO EXPAND ONCE IT COOLS BEYOND 39.4°F (4°C) AND CONTINUES

TO EXPAND UNTIL IT BECOMES ICE. FOR THIS REASON, ICE IS LESS DENSE THAN WATER, FLOATS ON THE SURFACE,AND RETARDS FURTHER COOLING OF DEEPER WATER, WHICH ACCOUNTS FOR THE SURVIVAL OF FRESHWATER PLANT

AND ANIMAL LIFE THROUGH THE WINTER. FOR THEIR PART, FISH CHANGE THE VOLUME OF THEIR INTERNAL SWIM BLAD-DER IN ORDER TO ALTER THEIR BUOYANCY.


Buoyancy French physiologist Paul Bert (1833-1886)first identified the bends in 1878, and in 1907,John Scott Haldane (1860-1936) developed amethod for counteracting decompression sick-ness. He calculated a set of decompression tablesthat advised limits for the amount of time atgiven depths. He recommended what he calledstage decompression, which means that theascending diver stops every few feet duringascension and waits for a few minutes at eachlevel, allowing the body tissues time to adjust tothe new pressure. Modern divers use a decom-pression chamber, a sealed container that simu-lates the stages of decompression.

BATHYSPHERE, SCUBA, AND

BATHYSCAPHE. In 1930, the Americannaturalist William Beebe (1877-1962) and Amer-ican engineer Otis Barton created the bathy-sphere. This was the first submersible that pro-vided the divers inside with adequate protectionfrom external pressure. Made of steel and spher-ical in shape, the bathysphere had thick quartzwindows and was capable of maintaining ordi-nary atmosphere pressure even when lowered bya cable to relatively great depths. In 1934, a bath-ysphere descended to what was then an extreme-ly impressive depth: 3,028 ft (923 m). However,the bathysphere was difficult to operate andmaneuver, and in time it was be replaced by amore workable vessel, the bathyscaphe.

Before the bathyscaphe appeared, however,in 1943, two Frenchmen created a means fordivers to descend without the need for any sort ofexternal chamber. Certainly a diver with this newapparatus could not go to anywhere near thesame depths as those approached by the bathy-sphere; nonetheless, the new aqualung made itpossible to spend an extended time under thesurface without need for air. It was now theoret-ically feasible for a diver to go below without anyneed for help or supplies from above, because hecarried his entire oxygen supply on his back. Thename of one of inventors, Emile Gagnan, is hard-ly a household word; but that of the other—Jacques Cousteau (1910-1997)—certainly is. So,too, is the name of their invention: the self-con-tained underwater breathing apparatus, betterknown as scuba.

The most important feature of the scubagear was the demand regulator, which made itpossible for the divers to breathe air at the samepressure as their underwater surroundings. This

in turn facilitated breathing in a more normal,comfortable manner. Another important featureof a modern diver’s equipment is a buoyancycompensation device. Like a ship atop the water,a diver wants to have only so much buoyancy—not so much that it causes him to surface.

As for the bathyscaphe—a term whose twoGreek roots mean “deep” and “boat”—it made itsdebut five years after scuba gear. Built by theSwiss physicist and adventurer Auguste Piccard(1884-1962), the bathyscaphe consisted of twocompartments: a heavy steel crew cabin that wasresistant to sea pressure, and above it, a larger,light container called a float. The float was filledwith gasoline, which in this case was not used asfuel, but to provide extra buoyancy, because ofthe gasoline’s low specific gravity.

When descending, the occupants of thebathyscaphe—there could only be two, since thepressurized chamber was just 79 in (2.01 m) indiameter—released part of the gasoline todecrease buoyancy. They also carried iron ballastpellets on board, and these they released whenpreparing to ascend. Thanks to battery-drivenscrew propellers, the bathyscaphe was muchmore maneuverable than the bathysphere hadever been; furthermore, it was designed to reachdepths that Beebe and Barton could hardly haveconceived.

REACHING NEW DEPTHS. Ittook several years of unsuccessful dives, but in1953 a bathyscaphe set the first of many depthrecords. This first craft was the Trieste, mannedby Piccard and his son Jacques, which descended10,335 ft (3,150 m) below the Mediterranean, offCapri, Italy. A year later, in the Atlantic Ocean offDakar, French West Africa (now Senegal), Frenchdivers Georges Houot and Pierre-Henri Willmreached 13,287 ft (4,063 m) in the FNRS 3.

Then in 1960, Jacques Piccard and UnitedStates Navy Lieutenant Don Walsh set a recordthat still stands: 35,797 ft (10,911 m)—23%greater than the height of Mt. Everest, the world’stallest peak. This they did in the Trieste some 250mi (402 km) southeast of Guam at the MarianaTrench, the deepest spot in the Pacific Ocean andindeed the deepest spot on Earth. Piccard andWalsh went all the way to the bottom, a descentthat took them 4 hours, 48 minutes. Coming uptook 3 hours, 17 minutes.

Thirty-five years later, in 1995, the Japanesecraft Kaiko also made the Mariana descent and



Buoyancyconfirmed the measurements of Piccard andWalsh. But the achievement of the Kaiko was notnearly as impressive of that of the Trieste’s two-man crew: the Kaiko, in fact, had no crew. By the1990s, sophisticated remote-sensing technologyhad made it possible to send down unmannedocean expeditions, and it became less necessaryto expose human beings to the incredible risksencountered by the Piccards, Walsh, and others.

FILMING TITANIC. An example ofsuch an unmanned vessel is the one featured inthe opening minutes of the Academy Award-win-ning motion picture Titanic (1997). The vesselitself, whose sinking in 1912 claimed more than1,000 lives, rests at such a great depth in theNorth Atlantic that it is impractical either to raiseit, or to send manned expeditions to explore theinterior of the wreck. The best solution, then, is aremotely operated vessel of the kind also used forpurposes such as mapping the ocean floor,exploring for petroleum and other deposits, andgathering underwater plate technology data.

The craft used in the film, which has “arms”for grasping objects, is of a variety speciallydesigned for recovering items from shipwrecks.For the scenes that showed what was supposed tobe the Titanic as an active vessel, director JamesCameron used a 90% scale model that depictedthe ship’s starboard side—the side hit by the ice-berg. Therefore, when showing its port side, aswhen it was leaving the Southampton, England,dock on April 15, 1912, all shots had to bereversed: the actual signs on the dock were inreverse lettering in order to appear correct whenseen in the final version. But for scenes of thewrecked vessel lying at the bottom of the ocean,Cameron used the real Titanic.

To do this, he had to use a submersible; buthe did not want to shoot only from inside thesubmersible, as had been done in the 1992 IMAXfilm Titanica. Therefore, his brother MikeCameron, in cooperation with Panavision, built aspecial camera that could withstand 400 atm(3.923 • 107 Pa)—that is, 400 times the air pres-sure at sea level. The camera was attached to theoutside of the submersible, which for these exter-nal shots was manned by Russian submarineoperators.

Because the special camera only held twelveminutes’ worth of film, it was necessary to makea total of twelve dives. On the last two, a remote-ly operated submersible entered the wreck, which

would have been too dangerous for the humansin the manned craft. Cameron had intended theremotely operated submersible as a mere prop,but in the end its view inside the ruined Titanicadded one of the most poignant touches in theentire film. To these he later added scenes involv-ing objects specific to the film’s plot, such as thesafe. These he shot in a controlled underwaterenvironment designed to look like the interior ofthe Titanic.

Into the Skies

In the earlier description of Piccard’s bathy-scaphe design, it was noted that the craft consist-ed of two compartments: a heavy steel crew cabinresistant to sea pressure, and above it a larger,light container called a float. If this sounds ratherlike the structure of a hot-air balloon, there is noaccident in that.

In 1931, nearly two decades before thebathyscaphe made its debut, Piccard and anotherSwiss scientist, Paul Kipfer, set a record of a dif-ferent kind with a balloon. Instead of going lower


THE DIVERS PICTURED HERE HAVE ASCENDED FROM A

SUNKEN SHIP AND HAVE STOPPED AT THE 10-FT (3-M)DECOMPRESSION LEVEL TO AVOID GETTING DECOMPRES-SION SICKNESS, BETTER KNOWN AS THE “BENDS.” (Pho-

tograph, copyright Jonathan Blair/Corbis. Reproduced by permission.)


Buoyancy than anyone ever had, as Piccard and his sonJacques did in 1953—and as Jacques and Walshdid in an even greater way in 1960—Piccard andKipfer went higher than ever, ascending to 55,563ft (16,940 m). This made them the first two mento penetrate the stratosphere, which is the nextatmospheric layer above the troposphere, a layerapproximately 10 mi (16.1 km) high that coversthe surface of Earth.

Piccard, without a doubt, experienced thegreatest terrestrial altitude range of any humanbeing over a lifetime: almost 12.5 mi (20.1 km)from his highest high to his lowest low, 84% of itabove sea level and the rest below. His career,then, was a tribute to the power of buoyantforce—and to the power of overcoming buoyantforce for the purpose of descending to the oceandepths. Indeed, the same can be said of the Pic-card family as a whole: not only did Jacques setthe world’s depth record, but years later, Jacques’sson Bertrand took to the skies for anotherrecord-setting balloon flight.

In 1999, Bertrand Piccard and British bal-loon instructor Brian Wilson became the firstmen to circumnavigate the globe in a balloon, theBreitling Orbiter 3. The craft extended 180 ft(54.86) from the top of the envelope—the part ofthe balloon holding buoyant gases—to the bot-tom of the gondola, the part holding riders. Thepressurized cabin had one bunk in which onepilot could sleep while the other flew, and upfront was a computerized control panel whichallowed the pilot to operate the burners, switchpropane tanks, and release empty ones. It tookPiccard and Wilson just 20 days to circle theEarth—a far cry from the first days of ballooningtwo centuries earlier.

THE FIRST BALLOONS. The Pic-card family, though Swiss, are francophone; thatis, they come from the French-speaking part ofSwitzerland. This is interesting, because the his-tory of human encounters with buoyancy—below the ocean and even more so in the air—has been heavily dominated by French names. Infact, it was the French brothers, Joseph-Michel(1740-1810) and Jacques-Etienne (1745-1799)Montgolfier, who launched the first balloon in1783. These two became to balloon flight whattwo other brothers, the Americans Orville andWilbur Wright, became with regard to the inven-tion that superseded the balloon twelve decadeslater: the airplane.

On that first flight, the Montgolfiers sent upa model 30 ft (9.15 m) in diameter, made oflinen-lined paper. It reached a height of 6,000 ft(1,828 m), and stayed in the air for 10 minutesbefore coming back down. Later that year, theMontgolfiers sent up the first balloon flight withliving creatures—a sheep, a rooster, and a duck—and still later in 1783, Jean-François Pilatre deRozier (1756-1785) became the first humanbeing to ascend in a balloon.

Rozier only went up 84 ft (26 m), which wasthe length of the rope that tethered him to theground. As the makers and users of balloonslearned how to use ballast properly, however,flight times were extended, and balloon flightbecame ever more practical. In fact, the world’sfirst military use of flight dates not to the twenti-eth century but to the eighteenth—1794, specifi-cally, when France created a balloon corps.

HOW A BALLOON FLOATS.

There are only three gases practical for lifting aballoon: hydrogen, helium, and hot air. Each ismuch less than dense than ordinary air, and thisgives them their buoyancy. In fact, hydrogen isthe lightest gas known, and because it is cheap toproduce, it would be ideal—except for the factthat it is extremely flammable. After the 1937crash of the airship Hindenburg, the era ofhydrogen use for lighter-than-air transport effec-tively ended.

Helium, on the other hand, is perfectly safeand only slightly less buoyant than hydrogen.This makes it ideal for balloons of the sort thatchildren enjoy at parties; but helium is expensive,and therefore impractical for large balloons.Hence, hot air—specifically, air heated to a tem-perature of about 570°F (299°C), is the only trulyviable option.

Charles’s law, one of the laws regarding thebehavior of gases, states that heating a gas willincrease its volume. Gas molecules, unlike theirliquid or solid counterparts, are highly non-attractive—that is, they tend to spread towardrelatively great distances from one another. Thereis already a great deal of empty space between gasmolecules, and the increase in volume onlyincreases the amount of empty space. Hence,density is lowered, and the balloon floats.

AIRSHIPS. Around the same time theMontgolfier brothers launched their first bal-loons, another French designer, Jean-Baptiste-Marie Meusnier, began experimenting with a



Buoyancy

more streamlined, maneuverable model. Earlyballoons, after all, could only be maneuveredalong one axis, up and down: when it came tomoving sideways or forward and backward, theywere largely at the mercy of the elements.

It was more than a century beforeMeusnier’s idea—the prototype for an airship—became a reality. In 1898, Alberto Santos-Dumont of Brazil combined a balloon with apropeller powered by an internal-combustioninstrument, creating a machine that improved onthe balloon, much as the bathyscaphe laterimproved on the bathysphere. Santos-Dumont’sairship was non-rigid, like a balloon. It also usedhydrogen, which is apt to contract during descentand collapse the envelope. To counter this prob-lem, Santos-Dumont created the ballonet, aninternal airbag designed to provide buoyancyand stabilize flight.

One of the greatest figures in the history oflighter-than-air flight—a man whose name,along with blimp and dirigible, became a syn-onym for the airship—was Count Ferdinand vonZeppelin (1838-1917). It was he who created alightweight structure of aluminum girders andrings that made it possible for an airship toremain rigid under varying atmospheric condi-

tions. Yet Zeppelin’s earliest launches, in thedecade that followed 1898, were fraught with anumber of problems—not least of which weredisasters caused by the flammability of hydrogen.

Zeppelin was finally successful in launchingairships for public transport in 1911, and thequarter-century that followed marked the goldenage of airship travel. Not that all was “golden”about this age: in World War I, Germany usedairships as bombers, launching the first Londonblitz in May 1915. By the time Nazi Germany ini-tiated the more famous World War II Londonblitz 25 years later, ground-based anti-aircrafttechnology would have made quick work of anyzeppelin; but by then, airplanes had long sincereplaced airships.

During the 1920s, though, airships such asthe Graf Zeppelin competed with airplanes as amode of civilian transport. It is a hallmark of theperceived safety of airships over airplanes at thetime that in 1928, the Graf Zeppelin made its firsttransatlantic flight carrying a load of passengers.Just a year earlier, Charles Lindbergh had madethe first-ever solo, nonstop transatlantic flight inan airplane. Today this would be the equivalentof someone flying to the Moon, or perhaps evenMars, and there was no question of carrying pas-


ONCE CONSIDERED OBSOLETE, BLIMPS ARE ENJOYING A RENAISSANCE AMONG SCIENTISTS AND GOVERNMENT AGEN-CIES. THE BLIMP PICTURED HERE, THE AEROSTAT BLIMP, IS EQUIPPED WITH RADAR FOR DRUG ENFORCEMENT AND

INSTRUMENTS FOR WEATHER OBSERVATION. (Corbis. Reproduced by permission.)


Buoyancy


sengers. Furthermore, Lindbergh was celebratedas a hero for the rest of his life, whereas the pas-sengers aboard the Graf Zeppelin earned no moredistinction for bravery than would pleasure-seekers aboard a cruise.

THE LIMITATIONS OF LIGHT-

ER-THAN-AIR TRANSPORT. For afew years, airships constituted the luxury liners ofthe skies; but the Hindenburg crash signaled theend of relatively widespread airship transport. Inany case, by the time of the 1937 Hindenburgcrash, lighter-than-air transport was no longer

the leading contender in the realm of flight tech-nology.

Ironically enough, by 1937 the airplane hadlong since proved itself more viable—eventhough it was actually heavier than air. The prin-ciples that make an airplane fly have little to dowith buoyancy as such, and involve differences inpressure rather than differences in density. Yetthe replacement of lighter-than-air craft on thecutting edge of flight did not mean that balloonsand airships were relegated to the museum;instead, their purposes changed.


of physics which holds that the buoyant

force of an object immersed in fluid is

equal to the weight of the fluid displaced

by the object. It is named after the Greek

mathematician, physicist, and inventor

Archimedes (c. 287-212 B.C.), who first

identified it.

BALLAST: A heavy substance that, by

increasing the weight of an object experi-

encing buoyancy, improves its stability.




DENSITY: Mass divided by volume.

DISPLACEMENT: A measure of the

weight of the fluid that has had to be

moved out of position so that an object can

be immersed. If a ship set down in the

ocean causes 1,000 tons of water to be dis-

placed, it is said to possess a displacement

of 1,000 tons.



container.





motion. For an object immerse in fluid,

mass is equal to volume multiplied by

density.

PRESSURE: The exertion of force

over a two-dimensional area; hence the

formula for pressure is force divided by

area. The British system of measures typi-

cally reckons pressure in pounds per

square inch. In metric terms, this is meas-

ured in terms of newtons (N) per square

meter, a figure known as a pascal (Pa.)

SPECIFIC GRAVITY: The density of

an object or substance relative to the densi-

ty of water; or more generally, the ratio

between the densities of two objects or

substances.

VOLUME: The amount of three-

dimensional space occupied by an object.

Volume is usually measured in cubic units.

WEIGHT: A force equal to mass multi-

plied by the acceleration due to gravity (32

ft/9.8 m/sec2). For an object immersed in

fluid, weight is the same as volume multi-

plied by density multiplied by gravitation-

al acceleration.

KEY TERMS


BuoyancyThe airship enjoyed a brief resurgence ofinterest during World War II, though purely as asurveillance craft for the United States military.In the period after the war, the U.S. Navy hiredthe Goodyear Tire and Rubber Company to pro-duce airships, and as a result of this relationshipGoodyear created the most visible airship sincethe Graf Zeppelin and the Hindenburg: theGoodyear Blimp.

BLIMPS AND BALLOONS: ON

THE CUTTING EDGE?. The blimp,known to viewers of countless sporting events, ismuch better-suited than a plane or helicopter toproviding TV cameras with an aerial view of astadium—and advertisers with a prominent bill-board. Military forces and science communitieshave also found airships useful for unexpectedpurposes. Their virtual invisibility with regard toradar has reinvigorated interest in blimps on thepart of the U.S. Department of Defense, whichhas discussed plans to use airships as radar plat-forms in a larger Strategic Air Initiative. In addi-tion, French scientists have used airships forstudying rain forest treetops or canopies.

Balloons have played a role in aiding spaceexploration, which is emblematic of the relation-ship between lighter-than-air transport andmore advanced means of flight. In 1961, Mal-colm D. Ross and Victor A. Prother of the U.S.Navy set the balloon altitude record with a heightof 113,740 ft (34,668 m.) The technology thatenabled their survival at more than 21 mi (33.8km) in the air was later used in creating life-sup-port systems for astronauts.

Balloon astronomy provides some of theclearest images of the cosmos: telescopes mount-ed on huge, unmanned balloons at elevations ashigh as 120,000 ft (35,000 m)—far above the dust

and smoke of Earth—offer high-resolutionimages. Balloons have even been used on otherplanets: for 46 hours in 1985, two balloonslaunched by the unmanned Soviet expedition toVenus collected data from the atmosphere of thatplanet.

American scientists have also considered acombination of a large hot-air balloon and asmaller helium-filled balloon for gathering dataon the surface and atmosphere of Mars duringexpeditions to that planet. As the air balloon isheated by the Sun’s warmth during the day, itwould ascend to collect information on theatmosphere. (In fact the “air” heated would befrom the atmosphere of Mars, which is com-posed primarily of carbon dioxide.) Then atnight when Mars cools, the air balloon wouldlose its buoyancy and descend, but the heliumballoon would keep it upright while it collecteddata from the ground.

WHERE TO LEARN MORE

“Buoyancy” (Web site). <http://www.aquaholic.com/gasses/laws.htm> (March 12, 2001).

“Buoyancy” (Web site). <http://www.uncwil.edu/nurc/aquarius/lessons/buoyancy.htm> (March 12, 2001).

“Buoyancy Basics” Nova/PBS (Web site).<http://www.pbs.org/wgbh/nova/lasalle/buoybasics.html> (March 12, 2001).

Challoner, Jack. Floating and Sinking. Austin, TX: Rain-tree Steck-Vaughn, 1997.

Cobb, Allan B. Super Science Projects About Oceans. NewYork: Rosen, 2000.

Gibson, Gary. Making Things Float and Sink. Illustratedby Tony Kenyon. Brookfield, CT: Copper BeeckBrooks, 1995.

Taylor, Barbara. Liquid and Buoyancy. New York: War-wick Press, 1990.



131


S TAT I C SS TAT I C S

STAT ICS AND EQU I L IBR IUM

PRESSURE

ELAST IC I T Y



S TAT I CS AND EQU I L IBR IUMStatics and Equilibrium

CONCEPTStatics, as its name suggests, is the study of bod-ies at rest. Those bodies may be acted upon by avariety of forces, but as long as the lines of forcemeet at a common point and their vector sum isequal to zero, the body itself is said to be in a stateof equilibrium. Among the topics of significancein the realm of statics is center of gravity, whichis relatively easy to calculate for simple bodies,but much more of a challenge where aircraft orships are concerned. Statics is also applied inanalysis of stress on materials—from a pictureframe to a skyscraper.

HOW IT WORKS

Equilibrium and Vectors

Essential to calculations in statics is the use ofvectors, or quantities that have both magnitudeand direction. By contrast, a scalar has only mag-nitude. If one says that a certain piece of proper-ty has an area of one acre, there is no directionalcomponent. Nor is there a directional compo-nent involved in the act of moving the distance of1 mi (1.6 km), since no statement has been madeas to the direction of that mile. On the otherhand, if someone or something experiences a dis-placement, or change in position, of 1 mi to thenortheast, then what was a scalar description hasbeen placed in the language of vectors.

Not only are mass and speed (as opposed tovelocity) considered scalars; so too is time. Thismight seem odd at first glance, but—on Earth atleast, and outside any special circumstancesposed by quantum mechanics—time can onlymove forward. Hence, direction is not a factor. By

contrast, force, equal to mass multiplied by acceleration, is a vector. So too is weight, a spe-cific type of force equal to mass multiplied by the acceleration due to gravity (32 ft or [9.8 m] /sec2). Force may be in any direction, but thedirection of weight is always downward along avertical plane.

VECTOR SUMS. Adding scalars issimple, since it involves mere arithmetic. Theaddition of vectors is more challenging, and usu-ally requires drawing a diagram, for instance, iftrying to obtain a vector sum for the velocity of acar that has maintained a uniform speed, but haschanged direction several times.

One would begin by representing each vec-tor as an arrow on a graph, with the tail of eachvector at the head of the previous one. It wouldthen be possible to draw a vector from the tail ofthe first to the head of the last. This is the sum ofthe vectors, known as a resultant, which meas-ures the net change.

Suppose, for instance, that a car travelsnorth 5 mi (8 km), east 2 mi (3.2 km), north 3 mi(4.8 km), east 3 mi, and finally south 3 mi. Onemust calculate its net displacement—in otherwords, not the sum of all the miles it has traveled,but the distance and direction between its start-ing point and its end point. First, one draws thevectors on a piece of graph paper, using a logicalsystem that treats the y axis as the north-southplane, and the x axis as the east-west plane. Eachvector should be in the form of an arrow point-ing in the appropriate direction.

Having drawn all the vectors, the onlyremaining one is between the point where thecar’s journey ends and the starting point—thatis, the resultant. The number of sides to the


Statics andEquilibrium


resulting shape is always one more than the num-ber of vectors being added; the final side is theresultant.

In this particular case, the answer is fairlyeasy. Because the car traveled north 5 mi and ulti-mately moved east by 5 mi, returning to a posi-tion of 5 mi north, the segment from the result-ant forms the hypotenuse of an equilateral (thatis, all sides equal) right triangle. By applying thePythagorean theorem, which states that thesquare of the length of the hypotenuse is equal tothe sum of the squares of the other two sides, onequickly arrives at a figure of 7.07 m (11.4 km) ina northeasterly direction. This is the car’s net dis-placement.

Calculating Force and Ten-sion in Equilibrium

Using vector sums, it is possible to make a num-ber of calculations for objects in equilibrium, butthese calculations are somewhat more challeng-ing than those in the car illustration. One form ofequilibrium calculation involves finding tension,or the force exerted by a supporting object on anobject in equilibrium—a force that is alwaysequal to the amount of weight supported.(Another way of saying this is that if the tensionon the supporting object is equal to the weight itsupports, then the supported object is in equilib-rium.)

In calculations for tension, it is best to treatthe supporting object—whether it be a rope, pic-ture hook, horizontal strut or some other item—as though it were weightless. One should beginby drawing a free-body diagram, a sketch show-ing all the forces acting on the supported object.It is not necessary to show any forces (other thanweight) that the object itself exerts, since thosedo not contribute to its equilibrium.

RESOLVING X AND Y COMPO-

NENTS. As with the distance vector graphdiscussed above, next one must equate theseforces to the x and y axes. The distance graphexample involved only segments already parallelto x and y, but suppose—using the numbersalready discussed—the graph had called for thecar to move in a perfect 45°-angle to the north-east along a distance of 7.07 mi. It would thenhave been easy to resolve this distance into an xcomponent (5 mi east) and a y component (5 minorth)—which are equal to the other two sides ofthe equilateral triangle.

This resolution of x and y components ismore challenging for calculations involving equi-librium, but once one understands the principleinvolved, it is easy to apply. For example, imaginea box suspended by two ropes, neither of whichis at a 90°-angle to the box. Instead, each rope isat an acute angle, rather like two segments of achain holding up a sign.

The x component will always be the productof tension (that is, weight) multiplied by thecosine of the angle. In a right triangle, one angleis always equal to 90°, and thus by definition, theother two angles are acute, or less than 90°. Theangle of either rope is acute, and in fact, the ropeitself may be considered the hypotenuse of animaginary triangle. The base of the triangle is thex axis, and the angle between the base and thehypotenuse is the one under consideration.

Hence, we have the use of the cosine, whichis the ratio between the adjacent leg (the base) ofthe triangle and the hypotenuse. Regardless ofthe size of the triangle, this figure is a constant forany particular angle. Likewise, to calculate the ycomponent of the angle, one uses the sine, or theratio between the opposite side and thehypotenuse. Keep in mind, once again, that theadjacent leg for the angle is by definition thesame as the x axis, just as the opposite leg is thesame as the y axis. The cosine (abbreviated cos),then, gives the x component of the angle, as thesine (abbreviated sin) does the y component.


Equilibrium and Center ofGravity in Real Objects

Before applying the concept of vector sums tomatters involving equilibrium, it is first necessaryto clarify the nature of equilibrium itself—whatit is and what it is not. Earlier it was stated that anobject is in equilibrium if the vector sum of theforces acting on it are equal to zero—as long asthose forces meet at a common point.

This is an important stipulation, because it ispossible to have lines of force that cancel oneanother out, but nonetheless cause an object tomove. If a force of a certain magnitude is appliedto the right side of an object, and a line of forceof equal magnitude meets it exactly from the left,then the object is in equilibrium. But if the line of



force from the right is applied to the top of theobject, and the line of force from the left to thebottom, then they do not meet at a commonpoint, and the object is not in equilibrium.Instead, it is experiencing torque, which willcause it to rotate.

VARIETIES OF EQUILIBRIUM.

There are two basic conditions of equilibrium.The term “translational equilibrium” describesan object that experiences no linear (straight-line) acceleration; on the other hand, an objectexperiencing no rotational acceleration (a com-ponent of torque) is said to be in rotational equi-librium.

Typically, an object at rest in a stable situa-tion experiences both linear and rotational equi-librium. But equilibrium itself is not necessarilystable. An empty glass sitting on a table is in sta-ble equilibrium: if it were tipped over slightly—that is, with a force below a certain threshold—then it would return to its original position. Thisis true of a glass sitting either upright or upside-down.

Now imagine if the glass were somehowpropped along the edge of a book sitting on thetable, so that the bottom of the glass formed thehypotenuse of a triangle with the table as its baseand the edge of the book as its other side. Theglass is in equilibrium now, but unstable equilib-rium, meaning that a slight disturbance—a forcefrom which it could recover in a stable situa-tion—would cause it to tip over.

If, on the other hand, the glass were lying onits side, then it would be in a state of neutralequilibrium. In this situation, the application offorce alongside the glass will not disturb its equi-librium. The glass will not attempt to seek stableequilibrium, nor will it become more unstable;rather, all other things being equal, it will remainneutral.

CENTER OF GRAVITY. Center ofgravity is the point in an object at which theweight below is equal to the weight above, theweight in front equal to the weight behind, andthe weight to the left equal to the weight on theright. Every object has just one center of gravity,and if the object is suspended from that point, itwill not rotate.

One interesting aspect of an object’s centerof gravity is that it does not necessarily have to bewithin the object itself. When a swimmer ispoised in a diving stance, as just before the start-


ing bell in an Olympic competition, the swim-mer’s center of gravity is to the front—some dis-tance from his or her chest. This is appropriate,since the objective is to get into the water asquickly as possible once the race starts.

By contrast, a sprinter’s stance places thecenter of gravity well within the body, or at leastfirmly surrounded by the body—specifically, atthe place where the sprinter’s rib cage touches theforward knee. This, too, fits with the needs of theathlete in the split-second following the startinggun. The sprinter needs to have as much tractionas possible to shoot forward, rather than forwardand downward, as the swimmer does.

Tension Calculations

In the earlier discussion regarding the method ofcalculating tension in equilibrium, two of thethree steps of this process were given: first, drawa free-body diagram, and second, resolve theforces into x and y components. The third step isto set the force components along each axis equalto zero—since, if the object is truly in equilibri-um, the sum of forces will indeed equal zero. Thismakes it possible, finally, to solve the equationsfor the net tension.

A GLASS SITTING ON A TABLE IS IN A STATE OF STABLE

EQUILIBRIUM. (Photograph by John Wilkes Studio/Corbis. Repro-




Imagine a picture that weighs 100 lb (445 N)suspended by a wire, the left side of which may becalled segment A, and the right side segment B.The wire itself is not perfectly centered on thepicture-hook: A is at a 30° angle, and B on a 45°angle. It is now possible to find the tension onboth.

First, one can resolve the horizontal compo-nents by the formula Fx = TBx + TAx = 0, meaningthat the x component of force is equal to theproduct of tension for the x component of B,added to the product of tension for the x compo-nent of A, which in turn is equal to zero. Giventhe 30°-angle of A, Ax = 0.866, which is the cosineof 30°. Bx is equal to cos 45°, which equals 0.707.(Recall the earlier discussion of distance, inwhich a square with sides 5 mi long wasdescribed: its hypotenuse was 7.07 mi, and 5/7.07= 0.707.)

Because A goes off to the left from the pointat which the picture is attached to the wire, thisplaces it on the negative portion of the x axis.Therefore, the formula can now be restated asTB(0.707)–TA(0.866) = 0. Solving for TB revealsthat it is equal to TA(0.866/0.707) = (1.22)TA.This will be substituted for TB in the formula forthe total force along the y component.

However, the y-force formula is somewhatdifferent than for x: since weight is exerted alongthe y axis, it must be subtracted. Thus, the for-mula for the y component of force is Fy = TAy +TBy–w = 0. (Note that the y components of bothA and B are positive: by definition, this must beso for an object suspended from some height.)

Substituting the value for TB obtained above,(1.22)TA, makes it possible to complete the equa-tion. Since the sine of 30° is 0.5, and the sine of45° is 0.707—the same value as its cosine—onecan state the equation thus: TA(0.5) +(1.22)TA(0.707)–100 lb = 0. This can be restatedas TA(0.5 + (1.22 • 0.707)) = TA(1.36) = 100 lb.Hence, TA = (100 lb/1.36) = 73.53 lb. Since TB =(1.22)TA, this yields a value of 89.71 lb for TB.

Note that TA and TB actually add up to con-siderably more than 100 lb. This, however, isknown as an algebraic sum—which is very simi-lar to an arithmetic sum, inasmuch as algebra issimply a generalization of arithmetic. What isimportant here, however, is the vector sum, andthe vector sum of TA and TB equals 100 lb.

CALCULATING CENTER OF

GRAVITY. Rather than go through anotherlengthy calculation for center of gravity, we willexplain the principles behind such calculations.


IN THE STARTING BLOCKS, A SPRINTER’S CENTER OF GRAVITY IS ALIGNED ALONG THE RIB CAGE AND FORWARD KNEE,THUS MAXIMIZING THE RUNNER’S ABILITY TO SHOOT FORWARD OUT OF THE BLOCKS. (Photograph by Ronnen Eshel/Corbis.




It is easy to calculate the center of gravity for aregular shape, such as a cube or sphere—assum-ing, of course, that the mass and therefore theweight is evenly distributed throughout theobject. In such a case, the center of gravity is thegeometric center. For an irregular object, howev-er, center of gravity must be calculated.

An analogy regarding United States demo-graphics may help to highlight the differencebetween geometric center and center of gravity.The geographic center of the U.S., which is anal-ogous to geometric center, is located near thetown of Castle Rock in Butte County, SouthDakota. (Because Alaska and Hawaii are so farwest of the other 48 states—and Alaska, with itsgreat geographic area, is far to the north—thedata is skewed in a northwestward direction. Thegeographic center of the 48 contiguous states isnear Lebanon, in Smith County, Kansas.)

The geographic center, like the geometriccenter of an object, constitutes a sort of balancepoint in terms of physical area: there is as muchU.S. land to the north of Castle Rock, SouthDakota, as to the south, and as much to the eastas to the west. The population center is more likethe center of gravity, because it is a measure, insome sense, of “weight” rather than of volume—though in this case concentration of people issubstituted for concentration of weight. Putanother way, the population center is the balancepoint of the population, if it were assumed thatevery person weighed the same amount.

Naturally, the population center has beenshifting westward ever since the first U.S. censusin 1790, but it is still skewed toward the east:though there is far more U.S. land west of theMississippi River, there are still more people eastof it. Hence, according to the 1990 U.S. census,the geographic center is some 1,040 mi (1,664km) in a southeastward direction from the pop-ulation center: just northwest of Steelville, Mis-souri, and a few miles west of the Mississippi.

The United States, obviously, is an “irregularobject,” and calculations for either its geographicor its population center represent the mastery ofnumerous mathematical principles. How, then,does one find the center of gravity for a muchsmaller irregular object? There are a number ofmethods, all rather complex.

To measure center of gravity in purely phys-ical terms, there are a variety of techniques relat-

ing to the shape of the object to be measured.There is also a mathematical formula, whichinvolves first treating the object as a conglomera-tion of several more easily measured objects.Then the x components for the mass of each“sub-object” can be added, and divided by thecombined mass of the object as a whole. Thesame can be done for the y components.

Using Equilibrium Calcula-tions

One reason for making center of gravity calcula-tions is to ensure that the net force on an objectpasses through that center. If it does not, theobject will start to rotate—and for an airplane,for instance, this could be disastrous. Hence, thebuilders and operators of aircraft make exceed-ingly detailed, complicated calculations regard-ing center of gravity. The same is true for ship-builders and shipping lines: if a ship’s center ofgravity is not vertically aligned with the focalpoint of the buoyant force exerted on it by thewater, it may well sink.

In the case of ships and airplanes, the shapesare so irregular that center of gravity calculationsrequire intensive analyses of the many compo-nents. Hence, a number of companies that supplymeasurement equipment to the aerospace andmaritime industries offer center of gravity meas-urement instruments that enable engineers tomake the necessary calculations.

On dry ground, calculations regarding equi-librium are likewise quite literally a life and deathmatter. In the earlier illustration, the object inequilibrium was merely a picture hanging from awire—but what if it were a bridge or a building?The results of inaccurate estimates of net forcecould affect the lives of many people. Hence,structural engineers make detailed analyses ofstress, once again using series of calculations thatmake the picture-frame illustration above looklike the simplest of all arithmetic problems.

WHERE TO LEARN MORE


“Determining Center of Gravity” National Aeronauticsand Space Administration (Web site).<http://www.grc.nasa.gov/WWW/K-12/airplane/cg.html> (March 19, 2001).





KEY TERMS


CENTER OF GRAVITY: The point on

an object at which the total weights on

either side of all axes (x, y, and z) are iden-

tical. Each object has just one center of

gravity, and if it is suspended from that

point, it will be in a state of perfect rota-

tional equilibrium.

COSINE: For an acute (less than 90°)

angle in a right triangle, the cosine (abbre-

viated cos) is the ratio between the adja-

cent leg and the hypotenuse. Regardless of

the size of the triangle, this figure is a con-

stant for any particular angle.

DISPLACEMENT: Change in position.

EQUILIBRIUM: A state in which vector

sum for all lines of force on an object is

equal to zero. An object that experiences no

linear acceleration is said to be in transla-

tional equilibrium, and one that experi-

ences no rotational acceleration is referred

to as being in rotational equilibrium. An

object may also be in stable, unstable, or

neutral equilibrium.



FREE-BODY DIAGRAM: A sketch

showing all the outside forces acting on an

object in equilibrium.

HYPOTENUSE: In a right triangle, the

side opposite the right angle.

RESULTANT: The sum of two or more

vectors, which measures the net change in

distance and direction.

RIGHT TRIANGLE: A triangle that

includes a right (90°) angle. The other

two angles are, by definition, acute, or less

than 90°.



Mass, time, and speed are all scalars. The

opposite of a scalar is a vector.

SINE: For an acute (less than 90°) angle

in a right triangle, the sine (abbreviated

sin) is the ratio between the opposite leg

and the hypotenuse. Regardless of the size

of the triangle, this figure is a constant for

any particular angle.

STATICS: The study of bodies at rest.

Those bodies may be acted upon by a vari-

ety of forces, but as long as the vector sum

for all those lines of force is equal to zero,

the body itself is said to be in a state of

equilibrium.

TENSION: The force exerted by a sup-

porting object on an object in equilibri-

um—a force that is always equal to the

amount of weight supported.


both magnitude and direction. Force is a

vector; so too is acceleration, a component

of force; and likewise weight, a variety of

force. The opposite of a vector is a scalar.

VECTOR SUM: A calculation, made by

different methods according to the factor

being analyzed—for instance, velocity or

force—that yields the net result of all the

vectors applied in a particular situation.


particular direction. Velocity is thus a vec-

tor quantity.



multiplied by the acceleration due to

gravity.

KEY TERMS



“Equilibrium and Statics” (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u313c.html> (March 19, 2001).

“Exploratorium Snack: Center of Gravity.” The Explorato-rium (Web site). <http://www.exploratorium.edu/snacks/center_of_gravity.html> (March 19, 2001).

Faivre d’Arcier, Marima. What Is Balance? Illustrated byVolker Theinhardt. New York: Viking Kestrel, 1986.

Taylor, Barbara. Weight and Balance. Photographs byPeter Millard. New York: F. Watts, 1990.

“Where Is Your Center of Gravity?” The K-8 AeronauticsInternet Textbook (Web site). <http://wing.ucdavis.edu/Curriculums/Forces_Motion/center_howto.html> (March 19, 2001).

Wood, Robert W. Mechanics Fundamentals. Illustrated byBill Wright. Philadelphia, PA: Chelsea House, 1997.

Zubrowski, Bernie. Mobiles: Building and Experimentingwith Balancing Toys. Illustrated by Roy Doty. NewYork: Morrow Junior Books, 1993.




PRESSUREPressure

CONCEPTPressure is the ratio of force to the surface areaover which it is exerted. Though solids exert pres-sure, the most interesting examples of pressureinvolve fluids—that is, gases and liquids—and inparticular water and air. Pressure plays a numberof important roles in daily life, among them itsfunction in the operation of pumps andhydraulic presses. The maintenance of ordinaryair pressure is essential to human health andwell-being: the body is perfectly suited to theordinary pressure of the atmosphere, and if thatpressure is altered significantly, a person mayexperience harmful or even fatal side-effects.

HOW IT WORKS

Force and Surface Area

When a force is applied perpendicular to a sur-face area, it exerts pressure on that surface equalto the ratio of F to A, where F is the force and Athe surface area. Hence, the formula for pressure(p) is p = F/A. One interesting consequence ofthis ratio is the fact that pressure can increase ordecrease without any change in force—in otherwords, if the surface becomes smaller, the pres-sure becomes larger, and vice versa.

If one cheerleader were holding anothercheerleader on her shoulders, with the girl abovestanding on the shoulder blades of the girl below,the upper girl’s feet would exert a certain pres-sure on the shoulders of the lower girl. This pres-sure would be equal to the upper girl’s weight (F,which in this case is her mass multiplied by thedownward acceleration due to gravity) dividedby the surface area of her feet. Suppose, then, that

the upper girl executes a challenging acrobaticmove, bringing her left foot up to rest against herright knee, so that her right foot alone exerts thefull force of her weight. Now the surface area onwhich the force is exerted has been reduced tohalf its magnitude, and thus the pressure on thelower girl’s shoulder is twice as great.

For the same reason—that is, that reductionof surface area increases net pressure—a well-delivered karate chop is much more effectivethan an open-handed slap. If one were to slap aboard squarely with one’s palm, the only likelyresult would be a severe stinging pain on thehand. But if instead one delivered a blow to theboard, with the hand held perpendicular—pro-vided, of course, one were an expert in karate—the board could be split in two. In the firstinstance, the area of force exertion is large andthe net pressure to the board relatively small,whereas in the case of the karate chop, the surfacearea is much smaller—and hence, the pressure ismuch larger.

Sometimes, a greater surface area is prefer-able. Thus, snowshoes are much more effectivefor walking in snow than ordinary shoes orboots. Ordinary footwear is not much larger thanthe surface of one’s foot, perfectly appropriate forwalking on pavement or grass. But with deepsnow, this relatively small surface area increasesthe pressure on the snow, and causes one’s feet tosink. The snowshoe, because it has a surface areasignificantly larger than that of a regular shoe,reduces the ratio of force to surface area andtherefore, lowers the net pressure.

The same principle applies with snow skisand water skis. Like a snowshoe, a ski makes itpossible for the skier to stay on the surface of the


Pressure


snow, but unlike a snowshoe, a ski is long andthin, thus enabling the skier to glide more effec-tively down a snow-covered hill. As for skiing onwater, people who are experienced at this sportcan ski barefoot, but it is tricky. Most beginnersrequire water skis, which once again reduce thenet pressure exerted by the skier’s weight on thesurface of the water.

Measuring Pressure

Pressure is measured by a number of units in theEnglish and metric—or, as it is called in the sci-entific community, SI—systems. Because p =F/A, all units of pressure represent some ratio offorce to surface area. The principle SI unit iscalled a pascal (Pa), or 1 N/m2. A newton (N),the SI unit of force, is equal to the force requiredto accelerate 1 kilogram of mass at a rate of 1meter per second squared. Thus, a Pascal is equalto the pressure of 1 newton over a surface area of1 square meter.

In the English or British system, pressure ismeasured in terms of pounds per square inch,abbreviated as lbs./in2. This is equal to 6.89 • 103

Pa, or 6,890 Pa. Scientists—even those in theUnited States, where the British system of unitsprevails—prefer to use SI units. However, theBritish unit of pressure is a familiar part of anAmerican driver’s daily life, because tire pressurein the United States is usually reckoned in termsof pounds per square inch. (The recommendedtire pressure for a mid-sized car is typically 30-35 lb/in2.)

Another important measure of pressure isthe atmosphere (atm), which the average pres-sure exerted by air at sea level. In English units,this is equal to 14.7 lbs./in2, and in SI units to1.013 • 105 Pa—that is, 101,300 Pa. There are alsotwo other specialized units of pressure measure-ment in the SI system: the bar, equal to 105 Pa,and the torr, equal to 133 Pa. Meteorologists, sci-entists who study weather patterns, use the mil-libar (mb), which, as its name implies, is equal to0.001 bars. At sea level, atmospheric pressure isapproximately 1,013 mb.

THE BAROMETER. The torr, onceknown as the “millimeter of mercury,” is equal tothe pressure required to raise a column of mer-cury (chemical symbol Hg) 1 mm. It is namedfor the Italian physicist Evangelista Torricelli(1608-1647), who invented the barometer, aninstrument for measuring atmospheric pressure.

The barometer, constructed by Torricelli in1643, consisted of a long glass tube filled withmercury. The tube was open at one end, andturned upside down into a dish containing moremercury: hence, the open end was submerged inmercury while the closed end at the top consti-tuted a vacuum—that is, an area in which thepressure is much lower than 1 atm.

The pressure of the surrounding air pusheddown on the surface of the mercury in the bowl,while the vacuum at the top of the tube providedan area of virtually no pressure, into which themercury could rise. Thus, the height to which themercury rose in the glass tube represented nor-mal air pressure (that is, 1 atm.) Torricelli dis-covered that at standard atmospheric pressure,the column of mercury rose to 760 millimeters.

The value of 1 atm was thus established asequal to the pressure exerted on a column ofmercury 760 mm high at a temperature of 0°C(32°F). Furthermore, Torricelli’s invention even-tually became a fixture both of scientific labora-

IN THE INSTANCE OF ONE CHEERLEADER STANDING ON

ANOTHER’S SHOULDERS, THE CHEERLEADER’S FEET

EXERT DOWNWARD PRESSURE ON HER PARTNER’SSHOULDERS. THE PRESSURE IS EQUAL TO THE GIRL’SWEIGHT DIVIDED BY THE SURFACE AREA OF HER FEET.(Photograph by James L. Amos/Corbis. Reproduced by permission.)


Pressure both cases, the force is always perpendicular tothe walls.

In each of these three characteristics, it isassumed that the container is finite: in otherwords, the fluid has nowhere else to go. Hence,the second statement: the external pressure exert-ed on the fluid is transmitted uniformly. Notethat the preceding statement was qualified by theterm “external”: the fluid itself exerts pressurewhose force component is equal to its weight.Therefore, the fluid on the bottom has muchgreater pressure than the fluid on the top, due tothe weight of the fluid above it.

Third, the pressure on any small surface ofthe fluid is the same, regardless of that surface’sorientation. In other words, an area of fluid per-pendicular to the container walls experiences thesame pressure as one parallel or at an angle to thewalls. This may seem to contradict the first prin-ciple, that the force is perpendicular to the wallsof the container. In fact, force is a vector quanti-ty, meaning that it has both magnitude anddirection, whereas pressure is a scalar, meaningthat it has magnitude but no specific direction.


Pascal’s Principle and theHydraulic Press

The three characteristics of fluid pressuredescribed above have a number of implicationsand applications, among them, what is known asPascal’s principle. Like the SI unit of pressure,Pascal’s principle is named after Blaise Pascal(1623-1662), a French mathematician and physi-cist who formulated the second of the three state-ments: that the external pressure applied on afluid is transmitted uniformly throughout theentire body of that fluid. Pascal’s principlebecame the basis for one of the importantmachines ever developed, the hydraulic press.

A simple hydraulic press of the variety usedto raise a car in an auto shop typically consists oftwo large cylinders side by side. Each cylindercontains a piston, and the cylinders are connect-ed at the bottom by a channel containing fluid.Valves control flow between the two cylinders.When one applies force by pressing down the pis-ton in one cylinder (the input cylinder), thisyields a uniform pressure that causes output in


tories and of households. Since changes inatmospheric pressure have an effect on weatherpatterns, many home indoor-outdoor ther-mometers today also include a barometer.

Pressure and Fluids

In terms of physics, both gases and liquids arereferred to as fluids—that is, substances that con-form to the shape of their container. Air pressureand water pressure are thus specific subjectsunder the larger heading of “fluid pressure.” Afluid responds to pressure quite differently than asolid does. The density of a solid makes it resist-ant to small applications of pressure, but if thepressure increases, it experiences tension and,ultimately, deformation. In the case of a fluid,however, stress causes it to flow rather than todeform.

There are three significant characteristics ofthe pressure exerted on fluids by a container. Firstof all, a fluid in a container experiencing noexternal motion exerts a force perpendicular tothe walls of the container. Likewise, the con-tainer walls exert a force on the fluid, and in

THE AIR PRESSURE ON TOP OF MOUNT EVEREST, THE

WORLD’S TALLEST PEAK, IS VERY LOW, MAKING BREATH-ING DIFFICULT. MOST CLIMBERS WHO ATTEMPT TO SCALE

EVEREST THUS CARRY OXYGEN TANKS WITH THEM.SHOWN HERE IS JIM WHITTAKER, THE FIRST AMERICAN

TO CLIMB EVEREST. (Photograph by Galen Rowell/Corbis. Repro-



Pressurethe second cylinder, pushing up a piston thatraises the car.

In accordance with Pascal’s principle, thepressure throughout the hydraulic press is thesame, and will always be equal to the ratiobetween force and pressure. As long as that ratiois the same, the values of F and A may vary. In thecase of an auto-shop car jack, the input cylinderhas a relatively small surface area, and thus, theamount of force that must be applied is relative-ly small as well. The output cylinder has a rela-tively large surface area, and therefore, exerts arelatively large force to lift the car. This, com-bined with the height differential between thetwo cylinders (discussed in the context ofmechanical advantage elsewhere in this book),makes it possible to lift a heavy automobile witha relatively small amount of effort.

THE HYDRAULIC RAM. The carjack is a simple model of the hydraulic press inoperation, but in fact, Pascal’s principle has manymore applications. Among these is the hydraulicram, used in machines ranging from bulldozersto the hydraulic lifts used by firefighters and util-ity workers to reach heights. In a hydraulic ram,however, the characteristics of the input and out-put cylinders are reversed from those of a carjack.

The input cylinder, called the master cylin-der, has a large surface area, whereas the outputcylinder (called the slave cylinder) has a smallsurface area. In addition—though again, this is afactor related to mechanical advantage ratherthan pressure, per se—the master cylinder isshort, whereas the slave cylinder is tall. Owing tothe larger surface area of the master cylindercompared to that of the slave cylinder, thehydraulic ram is not considered efficient in termsof mechanical advantage: in other words, theforce input is much greater than the force output.

Nonetheless, the hydraulic ram is as well-suited to its purpose as a car jack. Whereas thejack is made for lifting a heavy automobilethrough a short vertical distance, the hydraulicram carries a much lighter cargo (usually just oneperson) through a much greater vertical range—to the top of a tree or building, for instance.

Exploiting Pressure Differ-ences

PUMPS. A pump utilizes Pascal’s princi-ple, but instead of holding fluid in a single con-


tainer, a pump allows the fluid to escape. Specif-ically, the pump utilizes a pressure difference,causing the fluid to move from an area of higherpressure to one of lower pressure. A very simpleexample of this is a siphon hose, used to drawpetroleum from a car’s gas tank. Sucking on oneend of the hose creates an area of low pressurecompared to the relatively high-pressure area ofthe gas tank. Eventually, the gasoline will comeout of the low-pressure end of the hose. (Andwith luck, the person siphoning will be able toanticipate this, so that he does not get a mouth-ful of gasoline!)

The piston pump, more complex, but stillfairly basic, consists of a vertical cylinder alongwhich a piston rises and falls. Near the bottom ofthe cylinder are two valves, an inlet valve throughwhich fluid flows into the cylinder, and an outletvalve through which fluid flows out of it. On thesuction stroke, as the piston moves upward, theinlet valve opens and allows fluid to enter thecylinder. On the downstroke, the inlet valve clos-es while the outlet valve opens, and the pressureprovided by the piston on the fluid forces itthrough the outlet valve.

One of the most obvious applications of thepiston pump is in the engine of an automobile.In this case, of course, the fluid being pumped isgasoline, which pushes the pistons by providing aseries of controlled explosions created by thespark plug’s ignition of the gas. In another vari-ety of piston pump—the kind used to inflate abasketball or a bicycle tire—air is the fluid beingpumped. Then there is a pump for water, whichpumps drinking water from the ground It mayalso be used to remove desirable water from anarea where it is a hindrance, for instance, in thebottom of a boat.

BERNOULLI ’S PRINCIPLE.

Though Pascal provided valuable understandingwith regard to the use of pressure for performingwork, the thinker who first formulated generalprinciples regarding the relationship betweenfluids and pressure was the Swiss mathematicianand physicist Daniel Bernoulli (1700-1782).Bernoulli is considered the father of fluidmechanics, the study of the behavior of gases andliquids at rest and in motion.

While conducting experiments with liquids,Bernoulli observed that when the diameter of apipe is reduced, the water flows faster. This sug-gested to him that some force must be acting


Pressure upon the water, a force that he reasoned mustarise from differences in pressure. Specifically,the slower-moving fluid in the wider area of pipehad a greater pressure than the portion of thefluid moving through the narrower part of thepipe. As a result, he concluded that pressure andvelocity are inversely related—in other words, asone increases, the other decreases.

Hence, he formulated Bernoulli’s principle,which states that for all changes in movement,the sum of static and dynamic pressure in a fluidremain the same. A fluid at rest exerts static pres-sure, which is commonly meant by “pressure,” asin “water pressure.” As the fluid begins to move,however, a portion of the static pressure—pro-portional to the speed of the fluid—is convertedto what is known as dynamic pressure, or thepressure of movement. In a cylindrical pipe, stat-ic pressure is exerted perpendicular to the surfaceof the container, whereas dynamic pressure isparallel to it.

According to Bernoulli’s principle, thegreater the velocity of flow in a fluid, the greaterthe dynamic pressure and the less the static pres-sure: in other words, slower-moving fluid exertsgreater pressure than faster-moving fluid. Thediscovery of this principle ultimately made pos-sible the development of the airplane.

As fluid moves from a wider pipe to a nar-rower one, the volume of that fluid that moves agiven distance in a given time period does notchange. But since the width of the narrower pipeis smaller, the fluid must move faster (that is,with greater dynamic pressure) in order to movethe same amount of fluid the same distance inthe same amount of time. One way to illustratethis is to observe the behavior of a river: in awide, unconstricted region, it flows slowly, but ifits flow is narrowed by canyon walls, then itspeeds up dramatically.

Bernoulli’s principle ultimately became thebasis for the airfoil, the design of an airplane’swing when seen from the end. An airfoil isshaped like an asymmetrical teardrop laid on itsside, with the “fat” end toward the airflow. As airhits the front of the airfoil, the airstream divides,part of it passing over the wing and part passingunder. The upper surface of the airfoil is curved,however, whereas the lower surface is muchstraighter.

As a result, the air flowing over the top has agreater distance to cover than the air flowing

under the wing. Since fluids have a tendency tocompensate for all objects with which they comeinto contact, the air at the top will flow faster tomeet with air at the bottom at the rear end of thewing. Faster airflow, as demonstrated byBernoulli, indicates lower pressure, meaning thatthe pressure on the bottom of the wing keeps theairplane aloft.

Buoyancy and Pressure

One hundred and twenty years before the firstsuccessful airplane flight by the Wright brothersin 1903, another pair of brothers—the Mont-golfiers of France—developed another means offlight. This was the balloon, which relied on anentirely different principle to get off the ground:buoyancy, or the tendency of an object immersedin a fluid to float. As with Bernoulli’s principle,however, the concept of buoyancy is related topressure.

In the third century B.C., the Greek mathe-matician, physicist, and inventor Archimedes (c.287-212 B.C.) discovered what came to be knownas Archimedes’s principle, which holds that thebuoyant force of an object immersed in fluid isequal to the weight of the fluid displaced by theobject. This is the reason why ships float: becausethe buoyant, or lifting, force of them is less thanequal to the weight of the water they displace.

The hull of a ship is designed to displace ormove a quantity of water whose weight is greaterthan that of the vessel itself. The weight of thedisplaced water—that is, its mass multiplied bythe downward acceleration caused by gravity—isequal to the buoyant force that the ocean exertson the ship. If the ship weighs less than the waterit displaces, it will float; but if it weighs more, itwill sink.

The factors involved in Archimedes’s princi-ple depend on density, gravity, and depth ratherthan pressure. However, the greater the depthwithin a fluid, the greater the pressure that push-es against an object immersed in the fluid. More-over, the overall pressure at a given depth in afluid is related in part to both density and gravi-ty, components of buoyant force.

PRESSURE AND DEPTH. Thepressure that a fluid exerts on the bottom of itscontainer is equal to dgh, where d is density, g theacceleration due to gravity, and h the depth of thecontainer. For any portion of the fluid, h is equalto its depth within the container, meaning that



Pressure

the deeper one goes, the greater the pressure.Furthermore, the total pressure within the fluidis equal to dgh + pexternal, where pexternal is the pres-sure exerted on the surface of the fluid. In a pis-ton-and-cylinder assembly, this pressure comesfrom the piston, but in water, the pressure comesfrom the atmosphere.

In this context, the ocean may be viewed as atype of “container.” At its surface, the air exertsdownward pressure equal to 1 atm. The densityof the water itself is uniform, as is the downwardacceleration due to gravity; the only variable,then, is h, or the distance below the surface. Atthe deepest reaches of the ocean, the pressure isincredibly great—far more than any humanbeing could endure. This vast amount of pressurepushes upward, resisting the downward pressureof objects on its surface. At the same time, if aboat’s weight is dispersed properly along its hull,the ship maximizes area and minimizes force,thus exerting a downward pressure on the surfaceof the water that is less than the upward pressureof the water itself. Hence, it floats.

Pressure and the HumanBody

AIR PRESSURE. The Montgolfiersused the principle of buoyancy not to float on the

water, but to float in the sky with a craft lighterthan air. The particulars of this achievement arediscussed elsewhere, in the context of buoyancy;but the topic of lighter-than-air flight suggestsanother concept that has been alluded to severaltimes throughout this essay: air pressure.

Just as water pressure is greatest at the bot-tom of the ocean, air pressure is greatest at thesurface of the Earth—which, in fact, is at the bot-tom of an “ocean” of air. Both air and water pres-sure are examples of hydrostatic pressure—thepressure that exists at any place in a body of fluiddue to the weight of the fluid above. In the caseof air pressure, air is pulled downward by theforce of Earth’s gravitation, and air along the sur-face has greater pressure due to the weight (afunction of gravity) of the air above it. At greatheights above Earth’s surface, however, the gravi-tational force is diminished, and, thus, the airpressure is much smaller.

In ordinary experience, a person’s body issubjected to an impressive amount of pressure.Given the value of atmospheric pressure discussed earlier, if one holds out one’s hand—assuming that the surface is about 20 in2

(0.129 m2)—the force of the air resting on it isnearly 300 lb (136 kg)! How is it, then, that one’s


THIS YELLOW DIVING SUIT, CALLED A “NEWT SUIT,” IS SPECIALLY DESIGNED TO WITHSTAND THE ENORMOUS WATER

PRESSURE THAT EXISTS AT LOWER DEPTHS OF THE OCEAN. (Photograph by Amos Nachoum/Corbis. Reproduced by permission.)


Pressure

hand is not crushed by all this weight? The rea-son is that the human body itself is under pres-sure, and that the interior of the body exerts apressure equal to that of the air.


ATMOSPHERE: A measure of pres-

sure, abbreviated “atm” and equal to the

average pressure exerted by air at sea level.

In English units, this is equal to 14.7

pounds per square inch, and in SI units to

101,300 pascals.

BAROMETER: An instrument for

measuring atmospheric pressure.


immersed in a fluid to float.



container.

FLUID MECHANICS: The study of

the behavior of gases and liquids at rest

and in motion.

HYDROSTATIC PRESSURE: the

pressure that exists at any place in a body of

fluid due to the weight of the fluid above.

PASCAL: The principle SI or metric

unit of pressure, abbreviated “Pa” and

equal to 1 N/m2.

PASCAL’S PRINCIPLE: A statement,

formulated by French mathematician and

physicist Blaise Pascal (1623-1662), which

holds that the external pressure applied on

a fluid is transmitted uniformly through-

out the entire body of that fluid.



tion perpendicular to that surface. The for-

mula for pressure (p) is p = F/A, where F is

force and A the surface area.

KEY TERMS

THE RESPONSE TO CHANGES

IN AIR PRESSURE. The human body is,in fact, suited to the normal air pressure of 1 atm,and if that external pressure is altered, the bodyundergoes changes that may be harmful or evenfatal. A minor example of this is the “popping” inthe ears that occurs when one drives through themountains or rides in an airplane. With changesin altitude come changes in pressure, and thus,the pressure in the ears changes as well.

As noted earlier, at higher altitudes, the airpressure is diminished, which makes it harder tobreathe. Because air is a gas, its molecules have atendency to be non-attractive: in other words,when the pressure is low, they tend to move awayfrom one another, and the result is that a personat a high altitude has difficulty getting enough airinto his or her lungs. Runners competing in the1968 Olympics at Mexico City, a town in themountains, had to train in high-altitude environ-ments so that they would be able to breathe dur-ing competition. For baseball teams competingin Denver, Colorado (known as “the Mile-HighCity”), this disadvantage in breathing is compen-sated by the fact that lowered pressure and resist-ance allows a baseball to move more easilythrough the air.

If a person is raised in such a high-altitudeenvironment, of course, he or she becomes usedto breathing under low air pressure conditions.In the Peruvian Andes, for instance, people spendtheir whole lives at a height more than twice asgreat as that of Denver, but a person from a low-altitude area should visit such a locale only aftertaking precautions. At extremely great heights, ofcourse, no human can breathe: hence airplanecabins are pressurized. Most planes are equippedwith oxygen masks, which fall from the ceiling ifthe interior of the cabin experiences a pressuredrop. Without these masks, everyone in the cabinwould die.

BLOOD PRESSURE. Another as-pect of pressure and the human body is bloodpressure. Just as 20/20 vision is ideal, doctors rec-ommend a target blood pressure of “120 over80”—but what does that mean? When a person’sblood pressure is measured, an inflatable cuff iswrapped around the upper arm at the same levelas the heart. At the same time, a stethoscope isplaced along an artery in the lower arm to mon-itor the sound of the blood flow. The cuff isinflated to stop the blood flow, then the pressure


Pressureis released until the blood just begins flowingagain, producing a gurgling sound in the stetho-scope.

The pressure required to stop the blood flowis known as the systolic pressure, which is equalto the maximum pressure produced by the heart.After the pressure on the cuff is reduced until theblood begins flowing normally—which is reflect-ed by the cessation of the gurgling sound in thestethoscope—the pressure of the artery is meas-ured again. This is the diastolic pressure, or thepressure that exists within the artery betweenstrokes of the heart. For a healthy person, systolicpressure should be 120 torr, and diastolic pres-sure 80 torr.

WHERE TO LEARN MORE

“Atmospheric Pressure: The Force Exerted by the Weight ofAir” (Web site). <http://kids.earth.nasa.gov/archive/air_pressure/> (April 7, 2001).


“Blood Pressure” (Web site). <http://www.mckinley.uiuc.edu/health-info/dis-cond/bloodpr/bloodpr.html>(April 7, 2001).

Clark, John Owen Edward. The Atmosphere. New York:Gloucester Press, 1992.

Cobb, Allan B. Super Science Projects About Oceans. NewYork: Rosen, 2000.

“The Physics of Underwater Diving: Pressure Lesson”(Web site). <http://www.uncwil.edu/nurc/aquarius/lessons/pressure.html> (April 7, 2001).

Provenzo, Eugene F. and Asterie Baker Provenzo. 47Easy-to-Do Classic Experiments. Illustrations by PeterA. Zorn, Jr. New York: Dover Publications, 1989.

“Understanding Air Pressure” USA Today (Web site).<http://www.usatoday.com/weather/wbarocx.html>(April 7, 2001).

Zubrowski, Bernie. Balloons: Building and Experimentingwith Inflatable Toys. Illustrated by Roy Doty. NewYork: Morrow Junior Books, 1990.




E L AST IC I T YElasticity

CONCEPTUnlike fluids, solids do not respond to outsideforce by flowing or easily compressing. The termelasticity refers to the manner in which solidsrespond to stress, or the application of force overa given unit area. An understanding of elastici-ty—a concept that carries with it a rather exten-sive vocabulary of key terms—helps to illuminatethe properties of objects from steel bars to rubberbands to human bones.

HOW IT WORKS

Characteristics of a Solid

A number of parameters distinguish solids fromfluids, a term that in physics includes both gasesand liquids. Solids possess a definite volume anda definite shape, whereas gases have neither; liq-uids have no definite shape.

At the molecular level, particles of solidstend to be precise in their arrangement and closeto one another. Liquid molecules are close inproximity (though not as much so as solid mole-cules), and their arrangement is random, whilegas molecules are both random in arrangementand far removed in proximity. Gas molecules areextremely fast-moving, and exert little or noattraction toward one another. Liquid moleculesmove at moderate speeds and exert a moderateattraction, but solid particles are slow-moving,and have a strong attraction to one another.

One of several factors that distinguishessolids from fluids is their relative response topressure. Gases tend to be highly compressible,meaning that they respond well to pressure. Liq-uids tend to be noncompressible, yet because oftheir fluid characteristics, they experience exter-

nal pressure uniformly. If one applies pressure toa quantity of water in a closed container, thepressure is equal everywhere in the water. By con-trast, if one places a champagne glass upright ina vise and applies pressure until it breaks, chancesare that the stem or the base of the glass will beunaffected, because the pressure is not distrib-uted equally throughout the glass.

If the surface of a solid is disturbed, it willresist, and if the force of the disturbance is suffi-ciently strong, it will deform—for instance, whena steel plate begins to bend under pressure. Thisdeformation will be permanent if the force ispowerful enough, as in the above example of theglass in a vise. By contrast, when the surface of afluid is disturbed, it tends to flow.

Types of Stress

Deformation occurs as a result of stress, whetherthat stress be in the form of tension, compres-sion, or shear. Tension occurs when equal andopposite forces are exerted along the ends of anobject. These operate on the same line of action,but away from each other, thus stretching theobject. A perfect example of an object under ten-sion is a rope in the middle of a tug-of-war com-petition. The adjectival form of “tension” is “ten-sile”: hence the term “tensile stress,” which will bediscussed later.

Earlier, stress was defined as the applicationof force over a given unit area, and in fact, theformula for stress can be written as F/A, where Fis force and A area. This is also the formula forpressure, though in order for an object to beunder pressure, the force must be applied in adirection perpendicular to—and in the samedirection as—its surface. The one form of stress


Elasticity


that clearly matches these parameters is compres-sion, produced by the action of equal and oppo-site forces, whose effect is to reduce the length ofa material. Thus compression (for example,crushing an aluminum can in one’s hand) is botha form of stress and a form of pressure.

Note that compression was defined as reduc-ing length, yet the example given involved areduction in what most people would call the“width” or diameter of the aluminum can. Infact, width and height are the same as length, forthe purposes of most discussions in physics.Length is, along with time, mass, and electric cur-rent, one of the fundamental units of measureused to express virtually all other physical quan-tities. Width and height are simply lengthexpressed in terms of other planes, and withinthe subject of elasticity, it is not important to dis-tinguish between these varieties of length. (Bycontrast, when discussing gravitational attrac-tion—which is always vertical—it is obviouslynecessary to distinguish between “verticallength,” or height, and horizontal length.)

The third variety of stress is shear, whichoccurs when a solid is subjected to equal andopposite forces that do not act along the sameline, and which are parallel to the surface area ofthe object. If a thick hardbound book is lying flat,and a person places a finger on the spine andpushes the front cover away from the spine sothat the covers and pages no longer constituteparallel planes, this is an example of shear. Stressresulting from shear is called shearing stress.

Hooke’s Law and ElasticLimit

To sum up the three varieties of stress, tensionstretches an object, compression shrinks it, andshear twists it. In each case, the object isdeformed to some degree. This deformation isexpressed in terms of strain, or the ratio betweenchange in dimension and the original dimen-sions of the object. The formula for strain isδL/Lo, where δL is the change in length (δ, theGreek letter delta, means “change” in scientificnotation) and Lo the original length.

Hooke’s law, formulated by English physicistRobert Hooke (1635-1703), relates strain tostress. Hooke’s law can be stated in simple termsas “the strain is proportional to the stress,” andcan also be expressed in a formula, F = ks, whereF is the applied force, s, the resulting change in

dimension, and k, a constant whose value is relat-ed to the nature and size of the object understress. The harder the material, the higher thevalue of k; furthermore, the value of k is directlyproportional to the object’s cross-sectional areaor thickness.

The elastic limit of a given solid is the maxi-mum stress to which it can be subjected withoutexperiencing permanent deformation. Elasticlimit will be discussed in the context of severalexamples below; for now, it is important merelyto know that Hooke’s law is applicable only aslong as the material in question has not reachedits elastic limit. The same is true for any modulusof elasticity, or the ratio between a particulartype of applied stress and the strain that results.(The term “modulus,” whose plural is “moduli,”is Latin for “small measure.”)

Moduli of Elasticity

In cases of tension or compression, the modulusof elasticity is Young’s modulus. Named afterEnglish physicist Thomas Young (1773-1829),Young’s modulus is simply the ratio between F/Aand δL/Lo—in other words, stress divided bystrain. There are also moduli describing thebehavior of objects exposed to shearing stress(shear modulus), and of objects exposed to com-pressive stress from all sides (bulk modulus).

Shear modulus is the relationship of shear-ing stress to shearing strain. This can beexpressed as the ratio between F/A and φ. Thelatter symbol, the Greek letter phi, stands for theangle of shear—that is, the angle of deformationalong the sides of an object exposed to shearingstress. The greater the amount of surface area A,the less that surface will be displaced by the forceF. On the other hand, the greater the amount offorce in proportion to A, the greater the value ofφ, which measures the strain of an objectexposed to shearing stress. (The value of φ, how-ever, will usually be well below 90°, and certain-ly cannot exceed that magnitude.)

With tensile and compressive stress, A is asurface perpendicular to the direction of appliedforce, but with shearing stress, A is parallel to F.Consider again the illustration used above, of athick hardbound book lying flat. As noted, whenone pushes the front cover from the side so thatthe covers and pages no longer constitute parallelplanes, this is an example of shear. If one pulledthe spine and the long end of the pages away


Elasticity


from one another, that would be tensile stress,whereas if one pushed in on the sides of the pagesand spine, that would be compressive stress.Shearing stress, by contrast, would stress only thefront cover, which is analogous to A for anyobject under shearing stress.

The third type of elastic modulus is bulkmodulus, which occurs when an object is sub-jected to compression from all sides—that is, vol-ume stress. Bulk modulus is the relationship ofvolume stress to volume strain, expressed as theratio between F/A and δV/Vo, where δV is thechange in volume and Vo is the original volume.


Elastic and Plastic Deforma-tion

As noted earlier, the elastic limit is the maximumstress to which a given solid can be subjectedwithout experiencing permanent deformation,referred to as plastic deformation. Plastic defor-mation describes a permanent change in shapeor size as a result of stress; by contrast, elasticdeformation is only a temporary change indimension.

A classic example of elastic deformation, andindeed, of highly elastic behavior, is a rubberband: it can be deformed to a length many timesits original size, but upon release, it returns to itsoriginal shape. Examples of plastic deformation,on the other hand, include the bending of a steelrod under tension or the breaking of a glassunder compression. Note that in the case of thesteel rod, the object is deformed without ruptur-ing—that is, without breaking or reducing topieces. The breaking of the glass, however, isobviously an instance of rupturing.

Metals and Elasticity

Metals, in fact, exhibit a number of interestingcharacteristics with regard to elasticity. With thenotable exception of cast iron, metals tend topossess a high degree of ductility, or the ability tobe deformed beyond their elastic limits withoutexperiencing rupture. Up to a certain point, theratio of tension to elongation for metals is high:in other words, a high amount of tension pro-duces only a small amount of elongation. Beyondthe elastic limit, however, the ratio is much lower:that is, a relatively small amount of tension pro-duces a high degree of elongation.

Because of their ductility, metals are highlymalleable, and, therefore, capable of experienc-

THE MACHINE PICTURED HERE ROLLS OVER STEEL IN ORDER TO BEND IT INTO PIPES. BECAUSE OF ITS ELASTIC

NATURE, STEEL CAN BE BENT WITHOUT BREAKING. (Photograph by Vince Streano/Corbis. Reproduced by permission.)


Elasticity

ing mechanical deformation through metallurgi-cal processes, such as forging, rolling, and extru-sion. Cold extrusion involves the application ofhigh pressure—that is, a high bulk modulus—toa metal without heating it, and is used on mate-rials such as tin, zinc, and copper to change theirshape. Hot extrusion, on the other hand, involvesheating a metal to a point of extremely high mal-leability, and then reshaping it. Metals may alsobe melted for the purposes of casting, or pouringthe molten material into a mold.

ULTIMATE STRENGTH. The ten-sion that a material can withstand is called itsultimate strength, and due to their ductile prop-erties, most metals possess a high value of ulti-mate strength. It is possible, however, for a metalto break down due to repeated cycles of stressthat are well below the level necessary to ruptureit. This occurs, for instance, in metal machinessuch as automobile engines that experience ahigh frequency of stress cycles during operation.

The high ultimate strength of metals, both intension and compression, makes them useful in anumber of structural capacities. Steel has an ulti-mate compressive strength 25 times as great asconcrete, and an ultimate tensile strength 250times as great. For this reason, when concrete ispoured for building bridges or other large struc-


tures, steel rods are inserted in the concrete.Called “rebar” (for “reinforced bars”), the steelrods have ridges along them in order to bondmore firmly with the concrete as it dries. As aresult, reinforced concrete has a much greaterability than plain concrete to withstand tensionand compression.

Steel Bars and RubberBands Under Stress

CRYSTALLINE MATERIALS. Metalsare crystalline materials, meaning that they arecomposed of solids called crystals. Particles ofcrystals are highly ordered, with a definite geo-metric arrangement repeated in all directions,rather like a honeycomb. (It should be noted,however, that the crystals are not necessarily asuniform in size as the “cells” of the honeycomb.)The atoms of a crystal are arranged in orderlyrows, bound to one another by strongly attractiveforces that act like microscopic springs.

Just as a spring tends to return to its originallength, the highly attractive atoms in a steel bar,when it is stretched, tend to restore it to its orig-inal dimensions. Likewise, it takes a great deal offorce to pull apart the atoms. When the metal issubjected to plastic deformation, the atoms move

RUBBER BANDS, LIKE THE ONES SHOWN HERE FORMED INTO A BALL, ARE A CLASSIC EXAMPLE OF ELASTIC DEFOR-MATION. (Photograph by Matthew Klein/Corbis. Reproduced by permission.)


Elasticity

to new positions and form new bonds. Theatoms are incapable of forming bonds; however,when the metal has been subjected to stressexceeding its ultimate strength, at that point, themetal breaks.

The crystalline structure of metal influencesits behavior under high temperatures. Heat caus-es atoms to vibrate, and in the case of metals, thismeans that the “springs” are stretching and com-pressing. As temperature increases, so do thevibrations, thus increasing the average distancebetween atoms. For this reason, under extremelyhigh temperature, the elastic modulus of themetal decreases, and the metal becomes lessresistant to stress.

POLYMERS AND ELASTOM-

ERS. Rubber is so elastic in behavior that ineveryday life, the term “elastic” is most often usedfor objects containing rubber: the waistband on apair of underwear, for instance. The long, thinmolecules of rubber, which are arranged side-by-side, are called “polymers,” and the super-elasticpolymers in rubber are called “elastomers.” Thechemical bonds between the atoms in a polymer

are flexible, and tend to rotate, producing kinksalong the length of the molecule.

When a piece of rubber is subjected to ten-sion, as, for instance, if one pulls a rubber bandby the ends, the kinks and loops in the elas-tomers straighten. Once the stress is released,however, the elastomers immediately return totheir original shape. The more “kinky” the poly-mers, the higher the elastic modulus, and hence,the more capable the item is of stretching andrebounding.

It is interesting to note that steel and rubber,materials that are obviously quite different, areboth useful in part for the same reason: theirhigh elastic modulus when subjected to tension,and their strength under stress. But a rubberband exhibits behaviors under high temperaturesthat are quite different from that of a metal:when heated, rubber contracts. It does so quitesuddenly, in fact, suggesting that the added ener-gy of the heat allows the bonds in the elastomersto begin rotating again, thus restoring the kinkedshape of the molecules.

Bones

The tensile strength in bone fibers comes fromthe protein collagen, while the compressivestrength is largely due to the presence of inor-ganic (non-living) salt crystals. It may be hard tobelieve, but bone actually has an ultimatestrength—both in tension and compression—greater than that of concrete!

The ultimate strength of most materials isrendered in factors of 108 N/m2—that is,100,000,000 newtons (the metric unit of force)per square meter. For concrete under tensilestress, the ultimate strength is 0.02, whereas forbone, it is 1.3. Under compressive stress, the val-ues are 0.2 and 1.7, respectively. In fact, the ulti-mate tensile strength of bone is close to that ofcast iron (1.7), though the ultimate compressivestrength of cast iron (5.5) is much higher thanfor bone.

Even with these figures, it may be hard tounderstand how bone can be stronger than con-crete, but that is largely because the volume ofconcrete used in most situations is much greaterthan the volume of any bone in the body of ahuman being. By way of explanation, consider apiece of concrete no bigger than a typical bone:under relatively small amounts of stress, it wouldcrumble.


A HUMAN BONE HAS A GREATER “ULTIMATE STRENGTH”THAN THAT OF CONCRETE. (Ecoscene/Corbis. Reproduced by per-

mission.)


Elasticity


ANGLE OF SHEAR: The angle of

deformation on the sides of an object

exposed to shearing stress. Its symbol is f

(the Greek letter phi), and its value will

usually be well below 90°.

BULK MODULUS: The modulus of

elasticity for a material subjected to com-

pression on all surfaces—that is, volume

stress. Bulk modulus is the relationship of

volume stress to volume strain, expressed

as the ratio between F/A and dV/Vo, where

dV is the change in volume and Vo is the

original volume.

COMPRESSION: A form of stress

produced by the action of equal and oppo-

site forces, whose effect is to reduce the

length of a material. Compression is a form

of pressure. When compressive stress is

applied to all surfaces of a material, this is

known as volume stress.

DUCTILITY: A property whereby a

material is capable of being deformed far

beyond its elastic limit without experienc-

ing rupture—that is, without breaking.

Most metals other than cast iron are high-

ly ductile.

ELASTIC DEFORMATION: A tempo-

rary change in shape or size experienced by

a solid subjected to stress. Elastic deforma-

tion is thus less severe than plastic defor-

mation.

ELASTIC LIMIT: The maximum stress

to which a given solid can be subjected

without experiencing plastic deforma-

tion—that is, without being permanently

deformed.

ELASTICITY: The response of solids to

stress.

HOOKE’S LAW: A principle of elastic-

ity formulated by English physicist Robert

Hooke (1635-1703), who discovered that

strain is proportional to stress. Hooke’s law

can be written as a formula, F = ks, where

F is the applied force, s the resulting change

in dimension, and k a constant whose value

is related to the nature and size of the

object being subjected to stress. Hooke’s

law applies only when the elastic limit has

not been exceeded.

LENGTH: In discussions of elasticity,

“length” refers to an object’s dimensions on

any given plane, thus, it can be used not

only to refer to what is called length in

everyday language, but also to width or

height.

MODULUS OF ELASTICITY: The

ratio between a type of applied stress (that

is, tension, compression, and shear) and

the strain that results in the object to which

stress has been applied. Elastic moduli—

including Young’s modulus, shearing mod-

ulus, and bulk modulus—are applicable

only as long as the object’s elastic limit has

not been reached.

PLASTIC DEFORMATION: A perma-

nent change in shape or size experienced

by a solid subjected to stress. Plastic defor-

mation is thus more severe than elastic

deformation.



tion perpendicular to, and in the same

direction as, that surface.

KEY TERMS


Elasticity


WHERE TO LEARN MORE


“Dictionary of Metallurgy” Steelmill.com: The Polish SteelIndustry Directory (Web site). <http://www.steelmill.com/DICTIONARY/Diction-ary.htm> (April 9,2001).

“Engineering Processes.” eFunda.com (Web site).<http://www.efunda.com/processes/processes_home/process.cfm> (April 9, 2001).

Gibson, Gary. Making Shapes. Illustrated by Tony Ken-yon. Brookfield, CT: Copper Beech Books, 1996.

“Glossary of Materials Testing Terms” (Web site).<http://www.instron.com/apps/glossary> (April 9,2001).

Goodwin, Peter H. Engineering Projects for Young Scien-tists. New York: Franklin Watts, 1987.

Johnston, Tom. The Forces with You! Illustrated by SarahPooley. Milwaukee, WI: Gareth Stevens Publishing,1988.

SHEAR: A form of stress resulting

from equal and opposite forces that do not

act along the same line. If a thick hard-

bound book is lying flat, and one pushes

the front cover from the side so that the

covers and pages no longer constitute par-

allel planes, this is an example of shear.

SHEAR MODULUS: The modulus of

elasticity for an object exposed to shearing

stress. It is expressed as the ratio between

F/A and φ, where φ (the Greek letter phi)

stands for the angle of shear.

STRAIN: The ratio between the change

in dimension experienced by an object that

has been subjected to stress, and the origi-

nal dimensions of the object. The formula

for strain is dL/Lo, where dL is the change

in length and Lo the original length.

Hooke’s law, as well as the various moduli

of elasticity, relates strain to stress.

STRESS: In general terms, stress is any

attempt to deform a solid. Types of stress

include tension, compression, and shear.

More specifically, stress is the ratio of force

to unit area, F/A, where F is force and A

area. Thus, it is similar to pressure, and

indeed, compression is a form of pressure.

TENSION: A form of stress produced

by a force which acts to stretch a material.

The adjectival form of “tension” is “ten-

sile”: hence the terms “tensile stress” and

“tensile strain.”

ULTIMATE STRENGTH: The tension

that a material can withstand without rup-

turing. Due to their high levels of ductility,

most metals have a high value of ultimate

strength.

VOLUME STRESS: The stress that

occurs in a material when it is subjected to

compression from all sides. The modus of

elasticity for volume stress is the bulk mod-

ulus.

YOUNG’S MODULUS: A modulus of

elasticity describing the relationship

between stress to strain for objects under

either tension or compression. Named

after English physicist Thomas Young

(1773-1829), Young’s modulus is simply

the ratio between F/A and δL/Lo—in other

words, stress divided by strain.



155


WORK AND ENERGYWORK AND ENERGY

MECHAN ICAL ADVANTAGE ANDS IMPLE MACH INES

ENERGY



MECHAN ICAL ADVANTAGE AND

S IMPLE MACH INESMechanical Advantage and Simple Machines

CONCEPTWhen the term machine is mentioned, most peo-

ple think of complex items such as an automo-

bile, but, in fact, a machine is any device that

transmits or modifies force or torque for a spe-

cific purpose. Typically, a machine increases

either the force of the person operating it—an

aspect quantified in terms of mechanical advan-

tage—or it changes the distance or direction

across which that force can be operated. Even a

humble screw is a machine; so too is a pulley, and

so is one of the greatest machines ever invented:

the wheel. Virtually all mechanical devices are

variations on three basic machines: the lever, the

inclined plane, and the hydraulic press. From

these three, especially the first two, arose literally

hundreds of machines that helped define history,

and which still permeate daily life.

HOW IT WORKS

Machines and ClassicalMechanics

There are four known types of force in the uni-

verse: gravitational, electromagnetic, weak

nuclear, and strong nuclear. This was the order in

which the forces were identified, and the number

of machines that use each force descends in the

same order. The essay that follows will make lit-

tle or no reference to nuclear-powered machines.

Somewhat more attention will be paid to electri-

cal machines; however, to trace in detail the

development of forces in that context would

require a new and somewhat cumbersome

vocabulary.

Instead, the machines presented for consid-eration here depend purely on gravitational forceand the types of force explainable purely in agravitational framework. This is the realm ofclassical physics, a term used to describe the stud-ies of physicists from the time of Galileo Galilei(1564-1642) to the end of the nineteenth centu-ry. During this era, physicists were primarily con-cerned with large-scale interactions that wereeasily comprehended by the senses, as opposed tothe atomic behaviors that have become the sub-ject of modern physics.

Late in the classical era, the Scottish physicistJames Clerk Maxwell (1831-1879)—building onthe work of many distinguished predecessors—identified electromagnetic force. For most of theperiod, however, the focus was on gravitationalforce and mechanics, or the study of matter,motion, and forces. Likewise, the majority ofmachines invented and built during most of theclassical period worked according to the mechan-ical principles of plain gravitational force.

This was even true to some extent with thesteam engine, first developed late in the seven-teenth century and brought to fruition by Scot-land’s James Watt (1736-1819.) Yet the steamengine, though it involved ordinary mechanicalprocesses in part, represented a new type ofmachine, which used thermal energy. This is alsotrue of the internal-combustion engine; yet bothsteam- and gas-powered engines to some extentborrowed the structure of the hydraulic press,one of the three basic types of machine. Thencame the development of electronic power,thanks to Thomas Edison (1847-1931) and oth-ers, and machines became increasingly divorcedfrom basic mechanical laws.


MechanicalAdvantageand SimpleMachines

Mechanical Advantage

A common trait runs through all forms ofmachinery: mechanical advantage, or the ratio offorce output to force input. In the case of thelever, a simple machine that will be discussed indetail below, mechanical advantage is high. Insome machines, however, mechanical advantageis actually less than 1, meaning that the resultingforce is less than the applied force.

This does not necessarily mean that themachine itself has a flaw; on the contrary, it canmean that the machine has a different purposethan that of a lever. One example of this is thescrew: a screw with a high mechanical advan-tage—that is, one that rewarded the user’s inputof effort by yielding an equal or greater output—would be useless. In this case, mechanical advan-tage could only be achieved if the screw backedout from the hole in which it had been placed,and that is clearly not the purpose of a screw.

Here a machine offers an improvement interms of direction rather than force; likewisewith scissors or a fishing rod, both of which willbe discussed below, an improvement with regardto distance or range of motion is bought at theexpense of force. In these and many more cases,mechanical advantage alone does not measurethe benefit. Thus, it is important to keep in mindwhat was previously stated: a machine eitherincreases force output, or changes the force’s dis-tance or direction of operation.

Most machines, however, work best whenmechanical advantage is maximized. Yet me-chanical advantage—whether in theoreticalterms or real-life instances—can only go so high,because there are factors that limit it. For onething, the operator must give some kind of inputto yield an output; furthermore, in most situa-tions friction greatly diminishes output. Hence,in the operation of a car, for instance, one-quar-ter of the vehicle’s energy is expended simply onovercoming the resistance of frictional forces.

For centuries, inventors have dreamed ofcreating a mechanism with an almost infinitemechanical advantage. This is the much-sought-after “perpetual motion machine,” that wouldonly require a certain amount of initial input;after that, the machine would simply run on itsown forever. As output compounded over theyears, its ratio to input would become so highthat the figure for mechanical advantage wouldapproach infinity.


The heyday of classical mechanics—whenclassical studies in mechanics represented theabsolute cutting edge of experimentation—wasin the period from the beginning of the seven-teenth century to the beginning of the nine-teenth. One figure held a dominant position inthe world of physics during those two centuries,and indeed was the central figure in the history ofphysics between Galileo and Albert Einstein(1879-1955). This was Sir Isaac Newton (1642-1727), who discerned the most basic laws ofphysical reality—laws that govern everyday life,including the operation of simple machines.

Newton and his principles are essential tothe study that follows, but one other figuredeserves “equal billing”: the Greek mathemati-cian, physicist, and inventor Archimedes (c. 287-212 B.C.). Nearly 2,000 years before Newton,Archimedes explained and improved a numberof basic machines, most notably the lever.Describing the powers of the lever, he is said tohave promised,“Give me a lever long enough anda place to stand, and I will move the world.” Thishe demonstrated, according to one story, bymoving a fully loaded ship single-handedly withthe use of a lever, while remaining seated somedistance away.

THE LEVER, LIKE THIS HYDROELECTRIC ENGINE LEVER,IS A SIMPLE MACHINE THAT PERFECTLY ILLUSTRATES THE

CONCEPT OF MECHANICAL ADVANTAGE. (Photograph by E.O.

Hoppe/Corbis. Reproduced by permission.)


MechanicalAdvantageand Simple

Machines


A number of factors, most notably the exis-tence of friction, prevent the perpetual motionmachine from becoming anything other than apipe dream. In outer space, however, the near-absence of friction makes a perpetual motionmachine viable: hence, a space probe launchedfrom Earth can travel indefinitely unless or untilit enters the gravitational field of some otherbody in deep space.

The concept of a perpetual motion machine,at least on Earth, is only an idealization; yet ide-alization does have its place in physics. Physicistsdiscuss most concepts in terms of an idealizedstate. For instance, when illustrating the acceler-ation due to gravity experienced by a body in freefall, it is customary to treat such an event asthough it were taking place under conditionsdivorced from reality. To consider the effects offriction, air resistance, and other factors on thebody’s fall would create an impossibly complicat-ed problem—yet real-world situations are justthat complicated.

In light of this tendency to discuss physicalprocesses in idealized terms, it should be notedthat there are two types of mechanical advantage:theoretical and actual. Efficiency, as applied tomachines in its most specific scientific sense, isthe ratio of actual to theoretical mechanicaladvantage. This in some ways resembles the for-mula for mechanical advantage itself: once again,what is being measured is the relationshipbetween “output” (the real behavior of themachine) and “input” (the planned behavior ofthe machine).

As with other mechanical processes, theactual mechanical advantage of a machine is amuch more complicated topic than the theoreti-cal mechanical advantage. The gulf between thetwo, indeed, is enormous. It would be almostimpossible to address the actual behavior ofmachines within an environment frameworkthat includes complexities such as friction.

Each real-world framework—that is, eachphysical event in the real world—is just a bit dif-ferent from every other one, due to the manyvarieties of factors involved. By contrast, the ide-alized machines of physics problems behaveexactly the same way in one imaginary situationafter another, assuming outside conditions arethe same. Therefore, the only form of mechanicaladvantage that a physicist can easily discuss istheoretical. For that reason, the term “efficiency”

will henceforth be used as a loose synonym formechanical advantage—even though the techni-cal definition is rather different.

Types of Machines

The term “simple machine” is often used todescribe the labor-saving devices known to theancient world, most of which consisted of onlyone or two essential parts. Historical sources varyregarding the number of simple machines, butamong the items usually listed are levers, pulleys,winches, wheels and axles, inclined planes,wedges, and screws. The list, though long, canactually be reduced to just two items: levers andinclined planes. All the items listed after the leverand before the inclined plane—including thewheel and axle—are merely variations on thelever. The same goes for the wedge and the screw,with regard to the inclined plane.

In fact, all machines are variants on threebasic devices: the lever, the inclined plane, andthe hydraulic press. Each transmits or modifiesforce or torque, producing an improvement inforce, distance, or direction. The first two, whichwill receive more attention here, share severalaspects not true of the third. First of all, the leverand the inclined plane originated at the begin-ning of civilization, whereas the hydraulic press isa much more recent invention.

The lever appeared as early as 5000 B.C. inthe form of a simple balance scale, and within afew thousand years, workers in the Near East andIndia were using a crane-like lever called theshaduf to lift containers of water. The shaduf,introduced in Mesopotamia in about 3000 B.C.,consisted of a long wooden pole that pivoted ontwo upright posts. At one end of the lever was acounterweight, and at the other a bucket. Theoperator pushed down on the pole to fill thebucket with water, and then used the counter-weight to assist in lifting the bucket.

The inclined plane made its appearance inthe earliest days of civilization, when the Egyp-tians combined it with rollers in the building oftheir monumental structures, the pyramids.Modern archaeologists generally believe thatEgyptian work gangs raised the huge stoneblocks of the pyramids through the use of slop-ing earthen ramps. These were most probablybuilt up alongside the pyramid itself, and thenremoved when the structure was completed.




In contrast to the distant origins of the othertwo machines, the hydraulic press seems like amere youngster. Also, the first two clearly arose aspractical solutions first: by the time Archimedesachieved a conceptual understanding of thesemachines, they had been in use a long, long time.The hydraulic press, on the other hand, firstemerged from the theoretical studies of the bril-liant French mathematician and physicist BlaisePascal (1623-1662.) Nearly 150 years passedbefore the English inventor Joseph Bramah(1748-1814) developed a workable hydraulicpress in 1796, by which time Watt had alreadyintroduced his improved steam engine. TheIndustrial Revolution was almost underway.


The Lever

In its most basic form, the lever consists of a rigidbar supported at one point, known as the ful-crum. One of the simplest examples of a lever isa crowbar, which one might use to move a heavyobject, such as a rock. In this instance, the ful-crum could be the ground, though a more rigid

“artificial” fulcrum (such as a brick) would prob-ably be more effective.

As the operator of the crowbar pushes downon its long shaft, this constitutes an input offorce, variously termed applied force, effort force,or merely effort. Newton’s third law of motionshows that there is no such thing as an unpairedforce in the universe: every input of force in onearea will yield an output somewhere else. In thiscase, the output is manifested by dislodging thestone—that is, the output force, resistance force,or load.

Use of the lever gives the operator muchgreater lifting force than that available to a per-son who tried to lift with only the strength of hisor her own body. Like all machines, the leverlinks input to output, harnessing effort to yieldbeneficial results—in this case, by translating theinput effort into the output effort of a dislodgedstone. Note, however, the statement at the begin-ning of this paragraph: proper use of a lever actu-ally gives a person much greater force than he orshe would possess unaided. How can this be?

There is a close relationship between thebehavior of the lever and the concept of torque,as, for example, the use of a wrench to remove alug nut. A wrench, in fact, is a sort of lever (Class

THE HYDRAULIC PRESS, LIKE THE LIFT HOLDING UP THIS CAR IN A REPAIR SHOP, IS A RELATIVELY RECENT INVEN-TION THAT IS USED IN MANY MODERN DEVICES, FROM CAR JACKS TO TOILETS. (Photograph by Charles E. Rotkin/Corbis. Repro-




Machines

I—a distinction that will be explored below.) Inany object experiencing torque, the distance fromthe pivot point (the lug nut, in this case), to thearea where force is being applied is called themoment arm. On the wrench, this is the distancefrom the lug nut to the place where the operatoris pushing on the wrench handle. Torque is theproduct of force multiplied by moment arm, andthe greater the torque, the greater the tendency ofthe object to be put into rotation. As withmachines in general, the greater the input, thegreater the output.

The fact that torque is the product of forceand moment arm means that if one cannotincrease force, it is still possible to gain greatertorque by increasing the moment arm. This is thereason why, when one tries and fails to disengagea stubborn lug nut, it is a good idea to get alonger wrench. Likewise with a lever, greaterleverage can be gained without applying moreforce: all one needs is a longer lever arm.

As one might suspect, the lever arm is thedistance from the force input to the fulcrum, orfrom the fulcrum to the force output. If a car-penter is using a nail-puller on the head of ahammer to extract a nail from a board, the leverarm of force input would be from the carpenter’shand gripping the hammer handle to the placewhere the hammerhead rests against the board.The lever arm of force output would be from thehammerhead to the end of the nail-puller.

With a lever, the input force (that of the car-penter’s hand pulling back on the hammer han-dle) multiplied by the input lever arm is alwaysequal to the output force (that of the nail-pullerpulling up the nail) multiplied by the outputlever arm. The relationship between input andoutput force and lever arm then makes it possibleto determine a formula for the lever’s mechanicaladvantage.

Since FinLin = FoutLout (where F = force and L= lever arm), it is possible to set up an equationfor a lever’s mechanical advantage. Once again,mechanical advantage is always Fout/Fin, but witha lever, it is also Lin/Lout. Hence, the mechanicaladvantage of a lever is always the same as theinverse ratio of the lever arm. If the input arm is5 units long and the output arm is 1 unit long,the mechanical advantage will be 5, but if thepositions are reversed, it will be 0.2.

CLASSES OF LEVERS. Levers aredivided into three classes, depending on the rela-

tive positions of the input lever arm, the fulcrum,and the output arm or load. In a Class I lever,such as the crowbar and the wrench, the fulcrumis between the input arm and the output arm. Bycontrast, a Class II lever, for example, a wheelbar-row, places the output force (the load carried inthe barrow itself) between the input force (theaction of the operator lifting the handles) and thefulcrum, which in this case is the wheel.

Finally, there is the Class III lever, which isthe reverse of a Class II. Here, the input force isbetween the output force and the fulcrum. Thehuman arm itself is an example of a Class IIIlever: if one grasps a weight in one’s hand, one’sbent elbow is the fulcrum, the arm raising theweight is the input force, and the weight held inthe hand—now rising—is the output force. TheClass III lever has a mechanical advantage of lessthan 1, but what it loses in force output in gainsin range of motion.

The world abounds with levers. Among theClass I varieties in common use are a nail pulleron a hammerhead, described earlier, as well aspostal scales and pliers. A handcart, though itmight seem at first like a wheelbarrow, is actual-ly a Class I lever, because the wheel or fulcrum isbetween the input effort—the force of a person’shands gripping the handles—and the output,which is the lifting of the load in the handcartitself. Scissors constitute an interesting type ofClass I lever, because the force of the output (thecutting blades) is reduced in order to create agreater lever arm for the input, in this case thehandles gripped when cutting.

A handheld bottle opener provides an excel-lent illustration of a Class II lever. Here the ful-crum is on the far end of the opener, away fromthe operator: the top end of the opener ring,which rests atop the bottle cap. The cap itself isthe load, and one provides input force by pullingup on the opener handle, thus prying the capfrom the bottle with the lower end of the openerring. Nail clippers represent a type of combina-tion lever: the handle that one operates is a ClassII, while the cutting blades are a Class III.

Whereas Class II levers maximize force at theexpense of range of motion, Class III levers oper-ate in exactly the opposite fashion. When using afishing rod to catch a fish, the fisherman’s lefthand (assuming he is right-handed) constitutesthe fulcrum as it holds the rod just below the reelassembly. The right hand supplies the effort, jerk-




ing upward, while the fish is the load. The pur-pose here is not to raise a heavy object (one rea-son why a fishing rod may break if one catchestoo large a fish) but rather to use the increasedlever arm for one’s advantage in catching anobject at some distance. Similarly, a hammer,which constitutes a Class III lever, with the oper-ator’s wrist as fulcrum, magnifies the motion ofthe operator’s hand with a hammerhead that cutsa much wider arc.

Many machines that arose in the IndustrialAge are a combination of many levers—that is, acompound lever. In a manual typewriter orpiano, for instance, each key is a complex assem-bly of levers designed for a given task. An auto-mobile, too, uses multiple levers—most notably,a special variety known as the wheel and axle.

THE WHEEL AND AXLE. A wheelis a variation on a Class I lever, but it representssuch a stunning technological advancement thatit deserves to be considered on its own. Whendriving a car, the driver places input force on therim of the steering wheel, whose fulcrum is thecenter of the wheel. The output force is translat-ed along the steering column to the driveshaft.

The combination of wheel and axle over-comes one factor that tends to limit the effective-ness of most levers, regardless of class: limitedrange of motion. An axle is really a type of wheel,though it has a smaller radius, which means thatthe output lever arm is correspondingly smaller.Given what was already said about the equationfor mechanical advantage in a lever, this presentsa very fortunate circumstance.

When a wheel turns, it has a relatively largelever arm (the rim), that turns a relatively smalllever arm, the axle. Because the product of inputforce and input lever arm must equal outputforce multiplied by output lever arm, this meansthat the output force will be higher than theinput force. Therefore, the larger the wheel inproportion to the axle, the greater the mechani-cal advantage.

It is for this reason that large vehicles with-out power steering often have very large steeringwheels, which have a larger range of motion and,thus, a greater torque on the axle—that is, thesteering column. Some common examples of thewheel-and-axle principle in operation todayinclude a doorknob and a screwdriver; however,long before the development of the wheel andaxle, there were wheels alone.

There is nothing obvious about the wheel,and in fact, it is not nearly as old an invention asmost people think. Until the last few centuries,most peoples in sub-Saharan Africa, remote partsof central and northern Asia, the Americas, andthe Pacific Islands remained unaware of it. Thisdid not necessarily make them “primitive”: eventhe Egyptians who built the Great Pyramid ofCheops in about 2550 B.C. had no concept of thewheel.

What the Egyptians did have, however, wererollers—-most often logs, onto which a heavyobject was hoisted using a lever. From rollersdeveloped the idea of a sledge, a sled-like devicefor sliding large loads atop a set of rollers. Asledge appears in a Sumerian illustration fromabout 3500 B.C., the oldest known representationof a wheel-like object.

The transformation from the roller-and-sledge assembly to wheeled vehicles is not as easyas it might seem, and historians still disagree asto the connection. Whatever the case, it appearsthat the first true wheels originated in Sumer(now part of Iraq) in about 3500 B.C. These weretripartite wheels, made by attaching three piecesof wood and then cutting out a circle. This madea much more durable wheel than a sawed-off log,and also overcame the fact that few trees are per-fectly round.

During the early period of wheeled trans-portation, from 3500 to 2000 B.C., donkeys andoxen rather than horses provided the power, inpart because wheeled vehicles were not yet madefor the speeds that horses could achieve. Hence, itwas a watershed event when wheelmakers beganfashioning axles as machines separate from thewheel. Formerly, axles and wheels were made upof a single unit; separating them made cartsmuch more stable, especially when makingturns—and, as noted earlier, greatly increased themechanical advantage of the wheels themselves.

Transportation entered a new phase in about2000 B.C., when improvements in technologymade possible the development of spokedwheels. By heat-treating wood, it became possi-ble to bend the material slightly, and to attachspokes between the rim and hub of the wheel.When the wood cooled, the tension created amuch stronger wheel—capable of carrying heav-ier loads faster and over greater distances.

In China during the first century B.C., a newtype of wheeled vehicle—identified earlier as a




Machines

Class II lever—was born in the form of thewheelbarrow, or “wooden ox.” The wheelbarrow,whose invention the Chinese attributed to asemi-legendary figure named Ko Yu, was of suchvalue to the imperial army for moving arms andmilitary equipment that China’s rulers kept itsdesign secret for centuries.

In Europe, around the same time, chariotswere dying out, and it was a long time before thetechnology of wheeled transport improved. Thefirst real innovation came during the 1500s, withthe development of the horsedrawn coach. By1640, a German family was running a regularstagecoach service, and, in 1667, a new, light,two-wheeled carriage called a cabriolet made itsfirst appearance. Later centuries, of course, sawthe development of increasingly more sophisti-cated varieties of wheeled vehicles powered inturn by human effort (the bicycle), steam (thelocomotive), and finally, the internal combustionengine (the automobile.)

But the wheel was never just a machine fortransport: long before the first wheeled cartscame into existence, potters had been usingwheels that rotated in place to fashion perfectlyround objects, and in later centuries, wheelsgained many new applications. By 500 B.C., farm-ers in Greece and other parts of the Mediter-ranean world were using rotary mills powered bydonkeys. These could grind grain much fasterthan a person working with a hand-poweredgrindstone could hope to do, and in time, theGreeks found a means of powering their millswith a force more useful than donkeys: water.

The first waterwheels, turned by human oranimal power, included a series of buckets alongthe rim that made it possible to raise water fromthe river below and disperse it to other points. Byabout 70 B.C., however, Roman engineers recog-nized that they could use the power of water itselfto turn wheels and grind grain. Thus, the water-wheel became one of the first two rotor mecha-nisms in which an inanimate source (as opposedto the effort of humans or animals) createdpower to spin a shaft.

In this way, the waterwheel was a prototypefor the engine developed many centuries later.Indeed, in the first century A.D., Hero of Alexan-dria—who discovered the concept of steampower some 1,700 years before anyone took upthe idea and put it to use—proposed what hasbeen considered a prototype for the turbine

engine. However, for a variety of complex rea-sons, the ancient world was simply not ready forthe technological leap portended by such aninvention; and so, in terms of significant progressin the development of machines, Europe wasasleep for more than a millennium.

The other significant form of wheel poweredby an “inanimate” source was the windmill, firstmentioned in 85 B.C. by Antipater of Thessaloni-ca, who commented on a windmill he saw innorthern Greece. In this early version of thewindmill, the paddle wheel moved on a horizon-tal plane. However, the windmill did not takehold in Europe during ancient times, and, in fact,its true origins lie further east, and it did notbecome widespread until much later.

In the seventh century A.D., windmills beganto appear in the region of modern Iran andAfghanistan, and the concept spread to the Arabworld. Europeans in the Near East during theCrusades (1095-1291) observed the windmill,and brought the idea back to Europe with them.By the twelfth century Europeans had developedthe more familiar vertical mill.

Finally, there was a special variety of wheelthat made its appearance as early as 500 B.C.: thetoothed gearwheel. By 300 B.C., it was in usethroughout Egypt, and by about 270 B.C., Ctesi-bius of Alexandria (fl. c. 270-250 B.C.) hadapplied the gear in devising a constant-flowwater clock called a clepsydra.

Some 2,100 years after Ctesibius, toothedgears became a critical component of industrial-ization. The most common type is a spur gear, inwhich the teeth of the wheel are parallel to theaxis of rotation. Helical gears, by contrast, havecurved teeth in a spiral pattern at an angle totheir rotational axes. This means that severalteeth of one gearwheel are always in contact withseveral teeth of the adjacent wheel, thus provid-ing greater torque.

In bevel gears, the teeth are straight, as witha spur gear, but they slope at a 45°-angle relativeto their axes so that two gearwheels can fittogether at up to 90°-angles to one another with-out a change in speed. Finally, planetary gears aremade such that one or more smaller gearwheelscan fit within a larger gearwheel, which has teethcut on the inside rather than the outside.

Similar in concept to the gearwheel is the Vbelt drive, which consists of two wheels side byside, joined with a belt. Each of the wheels has




grooves cut in it for holding the belt, making thisa modification of the pulley, and the grooves pro-vide much greater gripping power for holdingthe belt in place. One common example of a Vbelt drive, combined with gearwheels, is a bicyclechain assembly.

PULLEYS. A pulley is essentially agrooved wheel on an axle attached to a frame,which in turn is attached to some form of rigidsupport such as a ceiling. A rope runs along thegrooves of the pulley, and one end is attached to a load while the other is controlled by theoperator.

In several instances, it has been noted that amachine may provide increased range of motionor position rather than power. So, this simplestkind of pulley, known as a single or fixed pulley,only offers the advantage of direction rather thanimproved force. When using Venetian blinds,there is no increase in force; the advantage of themachine is simply that it allows one to moveobjects upward and downward. Thus, the theo-retical mechanical advantage of a fixed pulley is 1(or almost certainly less under actual conditions,where friction is a factor).

Here it is appropriate to return toArchimedes, whose advancements in the under-standing of levers translated to improvements inpulleys. In the case of the lever, it was Archimedeswho first recognized that the longer the effortarm, the less effort one had to apply in raising theload. Likewise, with pulleys and related devices—cranes and winches—he explained and improvedthe way these machines worked.

The first crane device dates to about 1000B.C., but evidence from pictures suggests thatpulleys may have been in use as early as seventhousand years before. Several centuries beforeArchimedes’s time, the Greeks were using com-pound pulleys that contained several wheels andthus provided the operator with much greatermechanical advantage than a fixed pulley.Archimedes, who was also the first to recognizethe relationship between pulleys and levers, cre-ated the first fully realized block-and-tackle system using compound pulleys and cranes. Inthe late modern era, compound pulley systemswere used in applications such as elevators andescalators.

A compound pulley consists of two or morewheels, with at least one attached to the supportwhile the other wheel or wheels lift the load. A

rope runs from the support pulley down to theload-bearing wheel, wraps around that pulleyand comes back up to a fixed attachment on theupper pulley. Whereas the upper pulley is fixed,the load-bearing pulley is free to move, and rais-es the load as the rope is pulled below.

The simplest kind of compound pulley, withjust two wheels, has a mechanical advantage of 2.On a theoretical level, at least, it is possible to cal-culate the mechanical advantage of a compoundpulley with more wheels: the number is equal tothe segments of rope between the lower pulleysand the upper, or support pulley. In reality, how-ever, friction, which is high as ropes rub againstthe pulley wheels, takes its toll. Thus mechanicaladvantage is never as great as it might be.

A block-and-tackle, like a compound pulley,uses just one rope with a number of pulleywheels. In a block-and-tackle, however, thewheels are arranged along two axles, each ofwhich includes multiple pulley wheels that arefree to rotate along the axle. The upper row isattached to the support, and the lower row to theload. The rope connects them all, running fromthe first pulley in the upper set to the first in thelower set, then to the second in the upper set, andso on. In theory, at least, the mechanical advan-tage of a block-and-tackle is equal to the numberof wheels used, which must be an even num-ber—but again, friction diminishes the theoreti-cal mechanical advantage.

The Inclined Plane

To the contemporary mind, it is difficult enoughto think of a lever as a “machine”—but levers atleast have more than one part, unlike an inclinedplane. The latter, by contrast, is exactly what itseems to be: a ramp. Yet it was just such a rampstructure, as noted earlier, that probably enabledthe Egyptians to build the pyramids—a feat ofengineering so stunning that even today, somepeople refuse to believe that the ancient Egyp-tians could have achieved it on their own.

Surely, as anti-scientific proponents of vari-ous fantastic theories often insist, the building ofthe pyramids could only have been done withmachines provided by super-intelligent, extrater-restrial beings. Even in ancient times, the Greekhistorian Herodotus (c. 484-c. 424 B.C.) speculat-ed that the Egyptians must have used huge cranesthat had long since disappeared.




Machines

These bizarre guesses concerning the tech-nology for raising the pyramid’s giant blocksserve to highlight the brilliance of a gloriouslysimple machine that, in essence, doubles force. Ifone needs to move a certain weight to a certainheight, there are two options. One can eitherraise the weight straight upward, expending anenormous amount of effort, even with a pulleysystem; or one can raise the weight graduallyalong an inclined plane. The inclined plane is amuch wiser choice, because it requires half theeffort.

Why half? Imagine an inclined plane slopingevenly upward to the right. The plane exists in asort of frame that is equal in both length andheight to the dimensions of the plane itself. As wecan easily visualize, the plane takes up exactlyhalf of the frame, and this is true whether theslope is more than, less than, or equal to 45°. Forany plane in which the slope is more than 45°,however, the mechanical advantage will be lessthan 1, and it is indeed hard to imagine why any-one would use such a plane unless forced to do soby limitations on their horizontal space—forexample, when lifting a heavy object from a nar-row canyon.

The mechanical advantage of an inclinedplane is equal to the ratio between the distanceover which input force is applied and the dis-tance of output; or, more simply, the ratio oflength to height. If a man is pushing a crate up aramp 4 ft high and 8 ft long (1.22 m by 2.44 m),8 ft is the input distance and 4 ft the output dis-tance; hence, the mechanical advantage is 2. If theramp length were doubled to 16 ft (4.88 m), themechanical advantage would likewise double to4, and so on.

The concept of work, in terms of physics, hasspecific properties that are a subject unto them-selves; however, it is important here only to rec-ognize that work is the product of force (that is,effort) multiplied by distance. This means that ifone increases the distance, a much smaller quan-tity of force is needed to achieve the sameamount of work.

On an everyday level, it is easy to see this inaction. Walking or running up a gentle hill, obvi-ously, is easier than going up a steep hill. There-fore, if one’s primary purpose is to conserveeffort, it is best to choose the gentler hill. On theother hand, one may wish to minimize dis-tance—or, if moving for the purpose of exercise,

to maximize force input to burn calories. Ineither case, the steeper hill would be the betteroption.

WEDGES. The type of inclined planediscussed thus far is a ramp, but there are a num-ber of much smaller varieties of inclined plane atwork in the everyday world. A knife is an excel-lent example of one of the most common types,a wedge. Again, the mechanical advantage of awedge is the ratio of length to height, which, inthe knife, would be the depth of the blade com-pared to its cross-sectional width. Due to theways in which wedges are used, however, frictionplays a much greater role, therefore greatlyreducing the theoretical mechanical advantage.

Other types of wedges may be used with alever, as a form of fulcrum for raising objects. Or,a wedge may be placed under objects to stabilizethem, as for instance, when a person puts a fold-ed matchbook under the leg of a restaurant tableto stop it from wobbling. Wedges also stop otherobjects from moving: a triangular piece of woodunder a door will keep it from closing, and amore substantial wedge under the front wheels ofa car will stop it from rolling forward.

Variations of the wedge are everywhere.Consider all the types of cutting or chippingdevices that exist: scissors, chisels, ice picks, axes,splitting wedges (used with a mallet to split a logdown the center), saws, plows, electric razors, etc.Then there are devices that use a complex assem-bly of wedges working together. The part of a keyused to open a lock is really just a row of wedgesfor moving the pins inside the lock to the properposition for opening the door. Similarly, eachtooth in a zipper is a tiny wedge that fits tightlywith the adjacent teeth.

SCREWS. As the wheel is, without adoubt, the greatest conceptual variation on thelever, so the screw may be identified as a particu-larly cunning adaptation of an inclined plane.The uses of screws today are many and obvious,but as with wheels and axles, these machines havemore applications than are commonly recog-nized. Not only are there screws for holdingthings together, but there are screws such as thoseon vises, clamps, or monkey wrenches for apply-ing force to objects.

A screw is an inclined plane in the shape of ahelix, wrapped around an axis or cylinder. Inorder to determine its mechanical advantage, onemust first find the pitch, which is the distance




between adjacent threads. The other variable islever arm, which with a screwdriver is the radius,or on a wrench, the length from the crescent orclamp to the area of applied force. Obviously, thelever arm is much greater for a wrench, whichexplains why a wrench is sometimes preferable toa screwdriver, when removing a highly resistantmaterial screw or bolt.

When one rotates a screw of a given pitch,the applied force describes a circle whose areamay be calculated as 2πL, where L is the leverarm. This figure, when divided by the pitch, is thesame as the ratio between the distance of forceinput to force output. Either number is equal tothe mechanical advantage for a screw. As suggest-ed earlier, that mechanical advantage is usuallylow, because force input (screwing in the screw)takes place in a much greater range of motionthan force output (the screw working its way intothe surface). But this is exactly what the screw isdesigned to do, and what it lacks in mechanicaladvantage, it more than makes up in its holdingpower.

As with the lever and pulley, Archimedes didnot invent the screw, but he did greatly improvehuman understanding of it. Specifically, hedeveloped a mathematical formula for a simplespiral, and translated this into the highly practi-

cal Archimedes screw, a device for lifting water.

The invention consists of a metal pipe in a

corkscrew shape, which draws water upward as it

revolves. It proved particularly useful for lifting

water that had seeped into the lower parts of a

ship, and in many countries today, it remains in

use as a simple pump for drawing water out of

the ground.

Some historians maintain that Archimedes

did not invent the screw-type pump, but rather

saw an example of it in Egypt. In any case, he

clearly developed a practical version of the

device, and it soon gained application through-

out the ancient world. Archaeologists discovered

a screw-driven olive press in the ruins of Pom-

peii, destroyed by the eruption of Mt. Vesuvius

in A.D. 79, and Hero of Alexandria later men-

tioned the use of a screw-type machine in his

Mechanica.

Yet, Archimedes is the figure most widely

associated with the development of this won-

drous device. Hence, in 1837, when the Swedish-

American engineer John Ericsson (1803-1899)

demonstrated the use of a screw-driven ship’s

propeller, he did so on a craft he named the

Archimedes.


A SCREW, LIKE THIS CORKSCREW USED TO OPEN A BOTTLE OF WINE, IS AN INCLINED PLANE IN THE SHAPE OF A

HELIX, WRAPPED AROUND AN AXIS OR CYLINDER. (Ecoscene/Corbis. Reproduced by permission.)



Machines

From screws planted in wood to screws thatdrive ships at sea, the device is everywhere inmodern life. Faucets, corkscrews, drills, and meatgrinders are obvious examples. Though manytypes of jacks used for lifting an automobile or ahouse are levers, others are screw assemblies onwhich one rotates the handle along a horizontalaxis. In fact, the jack is a particularly interestingdevice. Versions of the jack represent all threetypes of simple machine: lever, inclined plane,and hydraulic press.

The Hydraulic Press

As noted earlier, the hydraulic press came intoexistence much, much later than the lever orinclined plane, and its birth can be seen withinthe context of a larger movement toward the useof water power, including steam. A little morethan a quarter-century after Pascal created thetheoretical framework for hydraulic power, hiscountryman Denis Papin (1647-1712) intro-duced the steam digester, a prototype for thepressure cooker. In 1687, Papin published a workdescribing a machine in which steam operated apiston—an early model for the steam engine.

Papin’s concept, which was on the absolutecutting edge of technological development atthat time, utilized not only steam power but alsothe very hydraulic concept that Pascal had iden-tified a few decades earlier. Indeed, the assemblyof pistons and cylinders that forms the centralcomponent of the internal-combustion enginereflects this hydraulic rule, discovered by Pascalin 1653. It was then that he formulated what isknown as Pascal’s principle: that the externalpressure applied on a fluid is transmitted uniformly throughout the entire body of thatfluid.

Inside a piston and cylinder assembly, one ofthe most basic varieties of hydraulic press, thepressure is equal to the ratio of force to the hori-zontal area of pressure. A simple hydraulic pressof the variety that might be used to raise a car inan auto shop typically consists of two large cylin-ders side by side, connected at the bottom by achannel in which valves control flow. When oneapplies force over a given area of input—that is,by pressing down on one cylinder—this yields auniform pressure that causes output in the sec-ond cylinder.

Once again, mechanical advantage is equalto the ratio of force output to force input, and fora hydraulic press, this can also be measured as theratio of area output to area input. Just as there isan inverse relationship between lever arm andforce in a lever, and between length and height inan inclined plane, so there is such a relationshipbetween horizontal area and force in a hydraulicpump. Consequently, in order to increase force,one should minimize area.

However, there is another factor to consider:height. The mechanical advantage of a hydraulicpump is equal to the vertical distance to whichthe input force is applied, divided by that of theoutput force. Hence, the greater the height of theinput cylinder compared to the output cylinder,the greater the mechanical advantage. And sincethese three factors—height, area, and force—work together, it is possible to increase the liftingforce and area by minimizing the height.

Consider once again the auto-shop car jack.Typically, the input cylinder will be relatively talland thin, and the output cylinder short andsquat. Because the height of the input cylinder islarge, the area of input will be relatively small, aswill the force of input. But according to Pascal’sprinciple, whatever the force applied on theinput, the pressure will be the same on the out-put. At the output end, where the car is raised,one needs a large amount of force and a relative-ly large lifting area. Therefore, height is mini-mized to increase force and area. If the outputarea is 10 times the size of the input area, aninput force of 1 unit will produce an output forceof 10 units—but in order to raise the weight by 1unit of height, the input piston must movedownward by 10 units.

This type of car jack provides a basic modelof the hydraulic press in operation, but, in fact,hydraulic technology has many more applica-tions. A hydraulic pump, whether for pumpingair into a tire or water from a basement, uses verymuch the same principle as the hydraulic jack. Sotoo does the hydraulic ram, used in machinesranging from bulldozers to the hydraulic liftsused by firefighters and utility workers to reachgreat heights.

In a hydraulic ram, however, the characteris-tics of the input and output cylinders arereversed from those of a car jack. The inputcylinder, called the master cylinder, is short andsquat, whereas the output cylinder—the slave





COMPOUND LEVER: A machine that

combines multiple levers to accomplish its

task. An example is a piano or manual

typewriter.

CLASS I LEVER: A lever in which the

fulcrum is between the input force and

output force. Examples include a crowbar,

a nail puller, and scissors.

CLASS II LEVER: A lever in which the

output force is between the input force and

the fulcrum. Class II levers, of which

wheelbarrows and bottle openers are

examples, maximize output force at the

expense of range of motion.

CLASS III LEVER: A lever in which

the input force is between the output force

and the fulcrum. Class III levers, of which

a fishing rod is an example, maximize

range of motion at the expense of output

force.

EFFICIENCY: The ratio of actual

mechanical advantage to theoretical

mechanical advantage.




another.

FULCRUM: The support point of a

lever.




INPUT: The effort supplied by the oper-

ator of a machine. In a Class I lever such as

a crowbar, input would be the energy one

expends by pushing down on the bar.

Input force is often called applied force,

effort force, or simply effort.

LEVER: One of the three basic varieties

of machine, a lever consists of a rigid bar

supported at one point, known as the ful-

crum.

LEVER ARM: On a lever, the distance

from the input force or the output force to

the fulcrum.

MACHINE: A device that transmits or

modifies force or torque for a specific pur-

pose.

MECHANICAL ADVANTAGE: The

ratio of force output to force input for a

machine.

MOMENT ARM: For an object experi-

encing torque, moment arm is the distance

from the pivot or balance point to the vec-

tor on which force is being applied.

Moment arm is always perpendicular to

the direction of force.

OUTPUT: The results achieved from the

operation of a machine. In a Class I lever

such as a crowbar, output is the moving of

a stone or other heavy load dislodged by

the crowbar. Output force is often called

the load or resistance force.

TORQUE: In general terms, torque is

turning force; in scientific terms, it is

the product of moment arm multiplied

by force.

KEY TERMS

cylinder—is tall and thin. The reason for thischange is that in objects using a hydraulic ram,height is more important than force output: they

are often raising people rather than cars. Whenthe slave cylinder exerts pressure on the stabilizerram above it (the bucket containing the firefight-



Machines

er, for example), it rises through a much largerrange of vertical motion than that of the fluidflowing from the master cylinder.

As noted earlier, the pistons of a car engineare hydraulic pumps—specifically, reciprocatinghydraulic pumps, so named because they allwork together. In scientific terms, “fluid” canmean either a liquid or a gas such as air; hence,there is an entire subset of hydraulic machinesthat are pneumatic, or air-powered. Among theseare power brakes in a car, pneumatic drills, andeven hovercrafts. As with the other two varietiesof simple machine, the hydraulic press is in evi-dence throughout virtually every nook and cran-ny of daily life. The pump in a toilet tank is a typeof hydraulic press, as is the inner chamber of apen. So too are aerosol cans, fire extinguishers,scuba tanks, water meters, and pressure gauges.

WHERE TO LEARN MORE

Archimedes (Web site). <http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html> (March 9,2001.)

Bains, Rae. Simple Machines. Mahwah, N.J.: Troll Associ-ates, 1985.


Canizares, Susan. Simple Machines. New York: Scholastic,1999.

Haslam, Andrew and David Glover. Machines. Photogra-phy by Jon Barnes. Chicago: World Book, 1998.

“Inventors Toolbox: The Elements of Machines” (Website). <http://www.mos.org/sln/Leonardo/Inven-torsToolbox.html> (March 9, 2001).


“Machines” (Web site). <http://www.galaxy.net:80/~k12/machines/index.s.html> (March 9, 2001).

“Motion, Energy, and Simple Machines” (Web site).<http://www.necc.mass.edu/MRVIS/MR3_13/start.html> (March 9, 2001).

O’Brien, Robert, and the Editors of Life. Machines. NewYork: Time-Life Books, 1964.

“Simple Machines” (Web site). <http://sln.fi.edu/qa97/spotlight3/spotlight3.html> (March 9, 2001).

Singer, Charles Joseph, et al., editors. A History of Tech-nology (8 vols.) Oxford, England: Clarendon Press,1954-84.




ENERGYEnergy

CONCEPTAs with many concepts in physics, energy—alongwith the related ideas of work and power—has ameaning much more specific, and in some waysquite different, from its everyday connotation.According to the language of physics, a personwho strains without success to pull a rock out ofthe ground has done no work, whereas a childplaying on a playground produces a great deal ofwork. Energy, which may be defined as the abili-ty of an object to do work, is neither created nordestroyed; it simply changes form, a concept that can be illustrated by the behavior of abouncing ball.

HOW IT WORKSIn fact, it might actually be more precise to saythat energy is the ability of “a thing” or “some-thing” to do work. Not only tangible objects(whether they be organic, mechanical, or electro-magnetic) but also non-objects may possessenergy. At the subatomic level, a particle with nomass may have energy. The same can be said of amagnetic force field.

One cannot touch a force field; hence, it isnot an object—but obviously, it exists. All onehas to do to prove its existence is to place a natu-ral magnet, such as an iron nail, within the mag-netic field. Assuming the force field is strongenough, the nail will move through space towardit—and thus the force field will have performedwork on the nail.

Work: What It Is and Is Not

Work may be defined in general terms as theexertion of force over a given distance. In order

for work to be accomplished, there must be a dis-placement in space—or, in colloquial terms,something has to be moved from point A topoint B. As noted earlier, this definition createsresults that go against the common-sense defini-tion of “work.”

A person straining, and failing, to pull a rockfrom the ground has performed no work (interms of physics) because nothing has beenmoved. On the other hand, a child on a play-ground performs considerable work: as she runsfrom the slide to the swing, for instance, she hasmoved her own weight (a variety of force) acrossa distance. She is even working when her move-ment is back-and-forth, as on the swing. Thistype of movement results in no net displacement,but as long as displacement has occurred at all,work has occurred.

Similarly, when a man completes a full push-up, his body is in the same position—parallel tothe floor, arms extended to support him—as hewas before he began it; yet he has accomplishedwork. If, on the other hand, he at the end of hisenergy, his chest is on the floor, straining but fail-ing, to complete just one more push-up, then heis not working. The fact that he feels as though hehas worked may matter in a personal sense, but itdoes not in terms of physics.

CALCULATING WORK. Work canbe defined more specifically as the product offorce and distance, where those two vectors areexerted in the same direction. Suppose one wereto drag a block of a certain weight across a givendistance of floor. The amount of force one exertsparallel to the floor itself, multiplied by the dis-tance, is equal to the amount of work exerted. Onthe other hand, if one pulls up on the block in a


Energy


position perpendicular to the floor, that forcedoes not contribute toward the work of draggingthe block across the floor, because it is not parallel to distance as defined in this particular situation.

Similarly, if one exerts force on the block atan angle to the floor, only a portion of that forcecounts toward the net product of work—a por-tion that must be quantified in terms oftrigonometry. The line of force parallel to thefloor may be thought of as the base of a triangle,with a line perpendicular to the floor as its sec-ond side. Hence there is a 90°-angle, making it aright triangle with a hypotenuse. The hypotenuseis the line of force, which again is at an angle tothe floor.

The component of force that counts towardthe total work on the block is equal to the totalforce multiplied by the cosine of the angle. Acosine is the ratio between the leg adjacent to anacute (less than 90°) angle and the hypotenuse.The leg adjacent to the acute angle is, of course,the base of the triangle, which is parallel to thefloor itself. Sizes of triangles may vary, but theratio expressed by a cosine (abbreviated cos)does not. Hence, if one is pulling on the block bya rope that makes a 30°-angle to the floor, then

force must be multiplied by cos 30°, which isequal to 0.866.

Note that the cosine is less than 1; hencewhen multiplied by the total force exerted, it willyield a figure 13.4% smaller than the total force.In fact, the larger the angle, the smaller thecosine; thus for 90°, the value of cos = 0. On theother hand, for an angle of 0°, cos = 1. Thus, iftotal force is exerted parallel to the floor—that is,at a 0°-angle to it—then the component of forcethat counts toward total work is equal to the totalforce. From the standpoint of physics, this wouldbe a highly work-intensive operation.

GRAVITY AND OTHER PECU-

LIARITIES OF WORK. The above dis-cussion relates entirely to work along a horizon-tal plane. On the vertical plane, by contrast, workis much simpler to calculate due to the presenceof a constant downward force, which is, ofcourse, gravity. The force of gravity acceleratesobjects at a rate of 32 ft (9.8 m)/sec2. The mass(m) of an object multiplied by the rate of gravi-tational acceleration (g) yields its weight, and theformula for work done against gravity is equal toweight multiplied by height (h) above somelower reference point: mgh.

WHILE THIS PLAYER DRIBBLES HIS BASKETBALL, THE BALL EXPERIENCES A COMPLEX ENERGY TRANSFER AS IT HITS

THE FLOOR AND BOUNCES BACK UP. (Photograph by David Katzenstein/Corbis. Reproduced by permission.)


Energy


Distance and force are both vectors—that is,quantities possessing both magnitude and direc-tion. Yet work, though it is the product of thesetwo vectors, is a scalar, meaning that only themagnitude of work (and not the direction overwhich it is exerted) is important. Hence mgh canrefer either to the upward work one exertsagainst gravity (that is, by lifting an object to acertain height), or to the downward work thatgravity performs on the object when it isdropped. The direction of h does not matter, andits value is purely relative, referring to the verticaldistance between one point and another.

The fact that gravity can “do work”—andthe irrelevance of direction—further illustrates

the truth that work, in the sense in which it isapplied by physicists, is quite different from“work” as it understood in the day-to-day world.There is a highly personal quality to the everydaymeaning of the term, which is completely lackingfrom its physics definition.

If someone carried a heavy box up fiveflights of stairs, that person would quite natural-ly feel justified in saying “I’ve worked.” Certainlyhe or she would feel that the work expended wasfar greater than that of someone who had simplyallowed the the elevator to carry the box up thosefive floors. Yet in terms of work done againstgravity, the work done on the box by the elevatoris exactly the same as that performed by the per-

HYDROELECTRIC DAMS, LIKE THE SHASTA DAM IN CALIFORNIA, SUPERBLY ILLUSTRATE THE PRINCIPLE OF ENERGY

CONVERSION. (Photograph by Charles E. Rotkin/Corbis. Reproduced by permission.)


Energyson carrying it upstairs. The identity of the“worker”—not to mention the sweat expendedor not expended—is irrelevant from the stand-point of physics.

Measurement of Work andPower

In the metric system, a newton (N) is the amountof force required to accelerate 1 kg of mass by 1meter per second squared (m/s2). Work is meas-ured by the joule (J), equal to 1 newton-meter (N• m). The British unit of force is the pound, andwork is measured in foot-pounds, or the workdone by a force of 1 lb over a distance of one foot.

Power, the rate at which work is accom-plished over time, is the same as work divided bytime. It can also be calculated in terms of forcemultiplied by speed, much like the force-multi-plied-by-distance formula for work. However, aswith work, the force and speed must be in thesame direction. Hence, the formula for power inthese terms is F • cos θ • v, where F=force,v=speed, and cos θ is equal to the cosine of theangle θ (the Greek letter theta) between F and thedirection of v.

The metric-system measure of power is thewatt, named after James Watt (1736-1819), theScottish inventor who developed the first fullyviable steam engine and thus helped inauguratethe Industrial Revolution. A watt is equal to 1joule per second, but this is such a small unit thatit is more typical to speak in terms of kilowatts,or units of 1,000 watts.

Ironically, Watt himself—like most people inthe British Isles and America—lived in a worldthat used the British system, in which the unit ofpower is the foot-pound per second. The latter,too, is very small, so for measuring the power ofhis steam engine, Watt suggested a unit based onsomething quite familiar to the people of histime: the power of a horse. One horsepower (hp)is equal to 550 foot-pounds per second.

SORTING OUT METRIC AND

BRITISH UNITS. The British system, ofcourse, is horridly cumbersome compared to themetric system, and thus it long ago fell out offavor with the international scientific communi-ty. The British system is the product of looselydeveloped conventions that emerged over time:for instance, a foot was based on the length of thereigning king’s foot, and in time, this becamestandardized. By contrast, the metric system was


created quite deliberately over a matter of just a

few years following the French Revolution, which

broke out in 1789. The metric system was adopt-

ed ten years later.

During the revolutionary era, French intel-

lectuals believed that every aspect of existence

could and should be treated in highly rational,

scientific terms. Out of these ideas arose much

folly—especially after the supposedly “rational”

leaders of the revolution began chopping off

people’s heads—but one of the more positive

outcomes was the metric system. This system,

based entirely on the number 10 and its expo-

nents, made it easy to relate one figure to anoth-

er: for instance, there are 100 centimeters in a

meter and 1,000 meters in a kilometer. This is

vastly more convenient than converting 12 inch-

es to a foot, and 5,280 feet to a mile.

IN THIS 1957 PHOTOGRAPH, ITALIAN OPERA SINGER

LUIGI INFANTINO TRIES TO BREAK A WINE GLASS BY

SINGING A HIGH “C” NOTE. CONTRARY TO POPULAR

BELIEF, THE NOTE DOES NOT HAVE TO BE A PARTICU-LARLY HIGH ONE TO BREAK THE GLASS: RATHER, THE

NOTE SHOULD BE ON THE SAME WAVELENGTH AS THE

GLASS’S OWN VIBRATIONS. WHEN THIS OCCURS,SOUND ENERGY IS TRANSFERRED DIRECTLY TO THE

GLASS, WHICH IS SHATTERED BY THIS SUDDEN NET

INTAKE OF ENERGY. (Hulton-Deutsch Collection/Corbis. Repro-



Energy For this reason, scientists—even those fromthe Anglo-American world—use the metric sys-tem for measuring not only horizontal space, butvolume, temperature, pressure, work, power, andso on. Within the scientific community, in fact,the metric system is known as SI, an abbreviationof the French Système International d’Unités—that is, “International System of Units.”

Americans have shown little interest inadopting the SI system, yet where power is con-cerned, there is one exception. For measuring thepower of a mechanical device, such as an auto-mobile or even a garbage disposal, Americans usethe British horsepower. However, for measuringelectrical power, the SI kilowatt is used. When anelectric utility performs a meter reading on afamily’s power usage, it measures that usage interms of electrical “work” performed for the fam-ily, and thus bills them by the kilowatt-hour.

Three Types of Energy

KINETIC AND POTENTIAL EN-

ERGY FORMULAE. Earlier, energy wasdefined as the ability of an object to accomplishwork—a definition that by this point hasacquired a great deal more meaning. There arethree types of energy: kinetic energy, or the ener-gy that something possesses by virtue of itsmotion; potential energy, the energy it possessesby virtue of its position; and rest energy, theenergy it possesses by virtue of its mass.

The formula for kinetic energy is KE = 1⁄2mv2. In other words, for an object of mass m,kinetic energy is equal to half the mass multi-plied by the square of its speed v. The actual der-ivation of this formula is a rather detailedprocess, involving reference to the second of thethree laws of motion formulated by Sir IsaacNewton (1642-1727.) The second law states thatF = ma, in other words, that force is equal to massmultiplied by acceleration. In order to under-stand kinetic energy, it is necessary, then, tounderstand the formula for uniform accelera-tion. The latter is vf

2 = v02 + 2as, where vf

2 is thefinal speed of the object, v0

2 its initial speed, aacceleration and s distance. By substituting val-ues within these equations, one arrives at the for-mula of 1⁄2 mv2 for kinetic energy.

The above is simply another form of thegeneral formula for work—since energy is, afterall, the ability to perform work. In order to pro-duce an amount of kinetic energy equal to 1⁄2 mv2

within an object, one must perform an amountof work on it equal to Fs. Hence, kinetic energyalso equals Fs, and thus the preceding paragraphsimply provides a means for translating that intomore specific terms.

The potential energy (PE) formula is muchsimpler, but it also relates to a work formulagiven earlier: that of work done against gravity.Potential energy, in this instance, is simply afunction of gravity and the distance h abovesome reference point. Hence, its formula is thesame as that for work done against gravity, mghor wh, where w stands for weight. (Note that thisrefers to potential energy in a gravitational field;potential energy may also exist in an electromag-netic field, in which case the formula would bedifferent from the one presented here.)

REST ENERGY AND ITS IN-

TRIGUING FORMULA. Finally, there isrest energy, which, though it may not sound veryexciting, is in fact the most intriguing—and themost complex—of the three. Ironically, the for-mula for rest energy is far, far more complex inderivation than that for potential or even kineticenergy, yet it is much more well-known withinthe popular culture.

Indeed, E = mc2 is perhaps the most famousphysics formula in the world—even more sothan the much simpler F = ma. The formula forrest energy, as many people know, comes fromthe man whose Theory of Relativity invalidatedcertain specifics of the Newtonian framework:Albert Einstein (1879-1955). As for what the for-mula actually means, that will be discussed later.


Falling and Bouncing Balls

One of the best—and most frequently used—illustrations of potential and kinetic energyinvolves standing at the top of a building, hold-ing a baseball over the side. Naturally, this is notan experiment to perform in real life. Due to itsrelatively small mass, a falling baseball does nothave a great amount of kinetic energy, yet in thereal world, a variety of other conditions (amongthem inertia, the tendency of an object to main-tain its state of motion) conspire to make a hit onthe head with a baseball potentially quite serious.



EnergyIf dropped from a great enough height, it couldbe fatal.

When one holds the baseball over the side ofthe building, potential energy is at a peak, butonce the ball is released, potential energy beginsto decrease in favor of kinetic energy. The rela-tionship between these, in fact, is inverse: as thevalue of one decreases, that of the other increas-es in exact proportion. The ball will only fall tothe point where its potential energy becomes 0,the same amount of kinetic energy it possessedbefore it was dropped. At the same point, kineticenergy will have reached maximum value, andwill be equal to the potential energy the ball pos-sessed at the beginning. Thus the sum of kineticenergy and potential energy remains constant,reflecting the conservation of energy, a subjectdiscussed below.

It is relatively easy to understand how theball acquires kinetic energy in its fall, but poten-tial energy is somewhat more challenging tocomprehend. The ball does not really “possess”the potential energy: potential energy resideswithin an entire system comprised by the ball,the space through which it falls, and the Earth.There is thus no “magic” in the reciprocal rela-tionship between potential and kinetic energy:both are part of a single system, which can beenvisioned by means of an analogy.

Imagine that one has a 20-dollar bill, thenbuys a pack of gum. Now one has, say, $19.20.The positive value of dollars has decreased by$0.80, but now one has increased “non-dollars”or “anti-dollars” by the same amount. After buy-ing lunch, one might be down to $12.00, mean-ing that “anti-dollars” are now up to $8.00. Thesame will continue until the entire $20.00 hasbeen spent. Obviously, there is nothing magicalabout this: the 20-dollar bill was a closed system,just like the one that included the ball and theground. And just as potential energy decreasedwhile kinetic energy increased, so “non-dollars”increased while dollars decreased.

BOUNCING BACK. The example ofthe baseball illustrates one of the most funda-mental laws in the universe, the conservation ofenergy: within a system isolated from all otheroutside factors, the total amount of energyremains the same, though transformations ofenergy from one form to another take place. Aninteresting example of this comes from the case

of another ball and another form of verticalmotion.

This time instead of a baseball, the ballshould be one that bounces: any ball will do,from a basketball to a tennis ball to a superball.And rather than falling from a great height, thisone is dropped through a range of motion ordi-nary for a human being bouncing a ball. It hitsthe floor and bounces back—during which timeit experiences a complex energy transfer.

As was the case with the baseball droppedfrom the building, the ball (or more specifically,the system involving the ball and the floor) pos-sesses maximum potential energy prior to beingreleased. Then, in the split-second before itsimpact on the floor, kinetic energy will be at amaximum while potential energy reaches zero.

So far, this is no different than the baseballscenario discussed earlier. But note what happenswhen the ball actually hits the floor: it stops foran infinitesimal fraction of a moment. What hashappened is that the impact on the floor (whichin this example is assumed to be perfectly rigid)has dented the surface of the ball, and this sapsthe ball’s kinetic energy just at the moment whenthe energy had reached its maximum value. Inaccordance with the energy conservation law,that energy did not simply disappear: rather, itwas transferred to the floor.

Meanwhile, in the wake of its huge energyloss, the ball is motionless. An instant later, how-ever, it reabsorbs kinetic energy from the floor,undents, and rebounds. As it flies upward, itskinetic energy begins to diminish, but potentialenergy increases with height. Assuming that theperson who released it catches it at exactly thesame height at which he or she let it go, thenpotential energy is at the level it was before theball was dropped.

WHEN A BALL LOSES ITS

BOUNCE. The above, of course, takes littleaccount of energy “loss”—that is, the transfer ofenergy from one body to another. In fact, a partof the ball’s kinetic energy will be lost to the floorbecause friction with the floor will lead to anenergy transfer in the form of thermal, or heat,energy. The sound that the ball makes when itbounces also requires a slight energy loss; butfriction—a force that resists motion when thesurface of one object comes into contact with thesurface of another—is the principal culpritwhere energy transfer is concerned.



Energy Of particular importance is the way the ballresponds in that instant when it hits bottom andstops. Hard rubber balls are better suited for thispurpose than soft ones, because the harder therubber, the greater the tendency of the moleculesto experience only elastic deformation. What thismeans is that the spacing between moleculeschanges, yet their overall position does not.

If, however, the molecules change positions,this causes them to slide against one another,which produces friction and reduces the energythat goes into the bounce. Once the internal fric-tion reaches a certain threshold, the ball is“dead”—that is, unable to bounce. The deaderthe ball is, the more its kinetic energy turns intoheat upon impact with the floor, and the lessenergy remains for bouncing upward.

Varieties of Energy in Action

The preceding illustration makes several refer-ences to the conversion of kinetic energy to ther-mal energy, but it should be stressed that thereare only three fundamental varieties of energy:potential, kinetic, and rest. Though heat is oftendiscussed as a form unto itself, this is done onlybecause the topic of heat or thermal energy iscomplex: in fact, thermal energy is simply a resultof the kinetic energy between molecules.

To draw a parallel, most languages permitthe use of only three basic subject-predicate con-structions: first person (“I”), second person(“you”), and third person (“he/she/it.”) Yet with-in these are endless varieties such as singular andplural nouns or various temporal orientations ofverbs: present (“I go”); present perfect (“I havegone”); simple past (“I went”); past perfect (“Ihad gone.”) There are even “moods,” such as thesubjunctive or hypothetical, which permit theconstruction of complex thoughts such as “Iwould have gone.” Yet for all this variety in termsof sentence pattern—actually, a degree of varietymuch greater than for that of energy types—allsubject-predicate constructions can still be iden-tified as first, second, or third person.

One might thus describe thermal energy as amanifestation of energy, rather than as a discreteform. Other such manifestations include electro-magnetic (sometimes divided into electrical andmagnetic), sound, chemical, and nuclear. Theprinciples governing most of these are similar:for instance, the positive or negative attraction

between two electromagnetically charged parti-cles is analogous to the force of gravity.

MECHANICAL ENERGY. One termnot listed among manifestations of energy ismechanical energy, which is something differentaltogether: the sum of potential and kinetic ener-gy. A dropped or bouncing ball was used as aconvenient illustration of interactions within alarger system of mechanical energy, but theexample could just as easily have been a rollercoaster, which, with its ups and downs, quiteneatly illustrates the sliding scale of kinetic andpotential energy.

Likewise, the relationship of Earth to theSun is one of potential and kinetic energy trans-fers: as with the baseball and Earth itself, theplanet is pulled by gravitational force toward thelarger body. When it is relatively far from theSun, it possesses a higher degree of potentialenergy, whereas when closer, its kinetic energy ishighest. Potential and kinetic energy can also beillustrated within the realm of electromagnetic,as opposed to gravitational, force: when a nail issome distance from a magnet, its potential ener-gy is high, but as it moves toward the magnet,kinetic energy increases.

ENERGY CONVERSION IN A

DAM. A dam provides a beautiful illustrationof energy conversion: not only from potential tokinetic, but from energy in which gravity pro-vides the force component to energy based inelectromagnetic force. A dam big enough to beused for generating hydroelectric power forms avast steel-and-concrete curtain that holds backmillions of tons of water from a river or otherbody. The water nearest the top—the “head” ofthe dam—thus has enormous potential energy.

Hydroelectric power is created by allowingcontrolled streams of this water to flow down-ward, gathering kinetic energy that is then trans-ferred to powering turbines. Dams in popularvacation spots often release a certain amount ofwater for recreational purposes during the day.This makes it possible for rafters, kayakers, andothers downstream to enjoy a relatively fast-flow-ing river. (Or, to put it another way, a stream withhigh kinetic energy.) As the day goes on, howev-er, the sluice-gates are closed once again to buildup the “head.” Thus when night comes, and ener-gy demand is relatively high as people retreat totheir homes, vacation cabins, and hotels, the damis ready to provide the power they need.



EnergyOTHER MANIFESTATIONS OF

ENERGY. Thermal and electromagneticenergy are much more readily recognizable man-ifestations of energy, yet sound and chemicalenergy are two forms that play a significant partas well. Sound, which is essentially nothing morethan the series of pressure fluctuations within amedium such as air, possesses enormous energy:consider the example of a singer hitting a certainnote and shattering a glass.

Contrary to popular belief, the note does nothave to be particularly high: rather, the noteshould be on the same wavelength as the glass’sown vibrations. When this occurs, sound energyis transferred directly to the glass, which is shat-tered by this sudden net intake of energy. Soundwaves can be much more destructive than that:not only can the sound of very loud music causepermanent damage to the ear drums, but also,sound waves of certain frequencies and decibellevels can actually drill through steel. Indeed,sound is not just a by-product of an explosion; itis part of the destructive force.

As for chemical energy, it is associated withthe pull that binds together atoms within largermolecular structures. The formation of watermolecules, for instance, depends on the chemicalbond between hydrogen and oxygen atoms. Thecombustion of materials is another example ofchemical energy in action.

With both chemical and sound energy, how-ever, it is easy to show how these simply reflectthe larger structure of potential and kinetic ener-gy discussed earlier. Hence sound, for instance, ispotential energy when it emerges from a source,and becomes kinetic energy as it moves toward areceiver (for example, a human ear). Further-more, the molecules in a combustible materialcontain enormous chemical potential energy,which becomes kinetic energy when released in a fire.

Rest Energy and Its NuclearManifestation

Nuclear energy is similar to chemical energy,though in this instance, it is based on the bindingof particles within an atom and its nucleus. But itis also different from all other kinds of energy,because its force component is neither gravita-tional nor electromagnetic, but based on one oftwo other known varieties of force: strongnuclear and weak nuclear. Furthermore, nuclear

energy—to a much greater extent than thermalor chemical energy—involves not only kineticand potential energy, but also the mysterious,extraordinarily powerful, form known as restenergy.

Throughout this discussion, there has beenlittle mention of rest energy; yet it is ever-pres-ent. Kinetic and potential energy rise and fallwith respect to one another; but rest energychanges little. In the baseball illustration, forinstance, the ball had the same rest energy at thetop of the building as it did in flight—the samerest energy, in fact, that it had when sitting on theground. And its rest energy is enormous.

NUCLEAR WARFARE. This bringsback the subject of the rest energy formula: E =mc2, famous because it made possible the cre-ation of the atomic bomb. The latter, which for-tunately has been detonated in warfare only twicein history, brought a swift end to World War IIwhen the United States unleashed it againstJapan in August 1945. From the beginning, it wasclear that the atom bomb possessed staggeringpower, and that it would forever change the waynations conducted their affairs in war and peace.

Yet the atom bomb involved only nuclear fis-sion, or the splitting of an atom, whereas thehydrogen bomb that appeared just a few yearsafter the end of World War II used an even morepowerful process, the nuclear fusion of atoms.Hence, the hydrogen bomb upped the ante to amuch greater extent, and soon the two nuclearsuperpowers—the United States and the SovietUnion—possessed the power to destroy most ofthe life on Earth.

The next four decades were marked by asuperpower struggle to control “the bomb” as itcame to be known—meaning any and all nuclearweapons. Initially, the United States controlled allatomic secrets through its heavily guarded Man-hattan Project, which created the bombs usedagainst Japan. Soon, however, spies such as Juliusand Ethel Rosenberg provided the Soviets withU.S. nuclear secrets, ensuring that the dictator-ship of Josef Stalin would possess nuclear capa-bilities as well. (The Rosenbergs were executedfor treason, and their alleged innocence became acelebrated cause among artists and intellectuals;however, Soviet documents released since thecollapse of the Soviet empire make it clear thatthey were guilty as charged.)



Energy





tors, the total amount of energy re-mains



COSINE: For an acute (less than 90°)

in a right triangle, the cosine (abbreviated

cos) is the ratio between the adjacent leg

and the hypotenuse. Regardless of the size

of the triangle, this figure is a constant for

any particular angle.

ENERGY: The ability of an object (or

in some cases a non-object, such as a mag-

netic force field) to accomplish work.




another.

HORSEPOWER: The British unit of

power, equal to 550 foot-pounds per

second.

HYPOTENUSE: In a right triangle, the

side opposite the right angle.

JOULE: The SI measure of work. One

joule (1 J) is equal to the work required

to accelerate 1 kilogram of mass by 1

meter per second squared (1 m/s2) over a

distance of 1 meter. Due to the small size

of the joule, however, it is often replaced

by the kilowatt-hour, equal to 3.6 million

(3.6 • 106) J.



MATTER: Physical substance that occu-

pies space, has mass, is composed of atoms

(or in the case of subatomic particles, is

part of an atom), and is convertible into

energy.

MECHANICAL ENERGY: The sum of

potential energy and kinetic energy within

a system.



position.

POWER: The rate at which work is

accomplished over time, a figure rendered

mathematically as work divided by time.

KEY TERMS

Both nations began building up missile arse-nals. It was not, however, just a matter of theUnited States and the Soviet Union. By the 1970s,there were at least three other nations in the“nuclear club”: Britain, France, and China. Therewere also other countries on the verge of devel-oping nuclear bombs, among them India andIsrael. Furthermore, there was a great threat thata terrorist leader such as Libya’s Muammar al-Qaddafi would acquire nuclear weapons and dothe unthinkable: actually use them.

Though other nations acquired nuclearweapons, however, the scale of the two super-power arsenals dwarfed all others. And at theheart of the U.S.-Soviet nuclear competition was

a sort of high-stakes chess game—to use ametaphor mentioned frequently during the1970s. Soviet leaders and their American coun-terparts both recognized that it would be the endof the world if either unleashed their nuclearweapons; yet each was determined to be able tomeet the other’s ever-escalating nuclear threat.

United States President Ronald Reaganearned harsh criticism at home for his nuclearbuildup and his hard line in negotiations withSoviet President Mikhail Gorbachev; but as aresult of this one-upmanship, he put the Sovietsinto a position where they could no longer com-pete. As they put more and more money intonuclear weapons, they found themselves less and


Energy


less able to uphold their already weak economicsystem. This was precisely Reagan’s purpose inusing American economic might to outspend theSoviets—or, in the case of the proposed multi-trillion-dollar Strategic Defense Initiative (SDIor “Star Wars”)—threatening to outspend them.The Soviets expended much of their economicenergy in competing with U.S. military strength,and this (along with a number of other complexfactors), spelled the beginning of the end of theCommunist empire.

E = mc2. The purpose of the precedinghistorical brief is to illustrate the epoch-makingsignificance of a single scientific formula: E =mc2. It ended World War II and ensured that no

war like it would ever happen again—but

brought on the specter of global annihilation. It

created a superpower struggle—yet it also ulti-

mately helped bring about the end of Soviet

totalitarianism, thus opening the way for a

greater level of peace and economic and cultural

exchange than the world has ever known. Yet

nuclear arsenals still remain, and the nuclear

threat is far from over.

So just what is this literally earth-shattering

formula? E stands for rest energy, m for mass, and

c for the speed of light, which is 186,000 mi

(297,600 km) per second. Squared, this yields an

almost unbelievably staggering number.

The SI unit of power is the watt, while the

British unit is the foot-pound per second.

The latter, because it is small, is usually

reckoned in terms of horsepower.

REST ENERGY: The energy an object

possesses by virtue of its mass.

RIGHT TRIANGLE: A triangle that

includes a right (90°) angle. The other two

angles are, by definition, acute or less

than 90°.



SI: An abbreviation of the French

Système International d’Unités, which

means “International System of Units.”

This is the term within the scientific com-

munity for the entire metric system, as

applied to a wide variety of quantities

ranging from length, weight and volume to

work and power, as well as electromag-

netic units.

SYSTEM: In discussions of energy, the

term “system” refers to a closed set of inter-

actions free from interference by outside

factors. An example is the baseball dropped

from a height to illustrate potential energy

and kinetic energy the ball, the space

through which it falls, and the ground

below together form a system.


both magnitude and direction.

WATT: The metric unit of power, equal

to 1 joule per second. Because this is such a

small unit, scientists and engineers typical-

ly speak in terms of kilowatts, or units of

1,000 watts.

WORK: The exertion of force over a

given distance. Work is the product of force

and distance, where force and distance are

exerted in the same direction. Hence the

actual formula for work is F • cos θ • s,

where F = force, s = distance, and cos θ is

equal to the cosine of the angle θ (the

Greek letter theta) between F and s. In the

metric or SI system, work is measured by

the joule (J), and in the British system by

the foot-pound.



Energy Hence, even an object of insignificant masspossesses an incredible amount of rest energy.The baseball, for instance, weighs only about0.333 lb, which—on Earth, at least—converts to0.15 kg. (The latter is a unit of mass, as opposedto weight.) Yet when factored into the rest energyequation, it yields about 3.75 billion kilowatt-hours—enough to provide an American homewith enough electrical power to last it more than156,000 years!

How can a mere baseball possess such ener-gy? It is not the baseball in and of itself, but itsmass; thus every object with mass of any kindpossesses rest energy. Often, mass energy can bereleased in very small quantities through purelythermal or chemical processes: hence, when a fireburns, an almost infinitesimal portion of thematter that went into making the fire is convert-ed into energy. If a stick of dynamite thatweighed 2.2 lb (1 kg) exploded, the portion of itthat “disappeared” would be equal to 6 parts outof 100 billion; yet that portion would cause ablast of considerable proportions.

As noted much earlier, the derivation of Ein-stein’s formula—and, more to the point, how hecame to recognize the fundamental principlesinvolved—is far beyond the scope of this essay.What is important is the fact, hypothesized byEinstein and confirmed in subsequent experi-ments, that matter is convertible to energy, a factthat becomes apparent when matter is accelerat-ed to speeds close to that of light.

Physicists do not possess a means for pro-pelling a baseball to a speed near that of light—or of controlling its behavior and capturing its

energy. Instead, atomic energy—whether of thewartime or peacetime varieties (that is, in powerplants)—involves the acceleration of mere atom-ic particles. Nor is any atom as good as another.Typically physicists use uranium and otherextremely rare minerals, and often, they furtherprocess these minerals in highly specialized ways.It is the rarity and expense of those minerals,incidentally—not the difficulty of actually put-ting atomic principles to work—that has keptsmaller nations from developing their ownnuclear arsenals.

WHERE TO LEARN MORE


Berger, Melvin. Sound, Heat and Light: Energy at Work.Illustrated by Anna DiVito. New York: Scholastic,1992.

Gardner, Robert. Energy Projects for Young Scientists. NewYork: F. Watts, 1987.

“Kinetic and Potential Energy” Thinkquest (Web site).<http://library.thinkquest.org/2745/data/ke.htm>(March 12, 2001).

Snedden, Robert. Energy. Des Plaines, IL: Heinemann,Library, 1999.


“Work and Energy” (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/energtoc.html>(March 12, 2001).

World of Coasters (Web site). <http://www.worldofcoasters.com> (March 12, 2001).

Zubrowski, Bernie. Raceways: Having Fun with Balls andTracks. Illustrated by Roy Doty. New York: Morrow,1985.



181


T HERMODYNAM ICSTHERMODYNAM ICS

GAS LAWS

MOLECULAR DYNAM ICS

STRUCTURE OF MATTER

THERMODYNAM ICS

HEAT

TEMPERATURE

THERMAL EXPANS ION



GAS L AWSGas Laws

CONCEPTGases respond more dramatically to temperatureand pressure than do the other three basic typesof matter (liquids, solids and plasma). For gases,temperature and pressure are closely related tovolume, and this allows us to predict their behav-ior under certain conditions. These predictionscan explain mundane occurrences, such as thefact that an open can of soda will soon lose itsfizz, but they also apply to more dramatic, life-and-death situations.

HOW IT WORKSOrdinary air pressure at sea level is equal to 14.7pounds per square inch, a quantity referred to asan atmosphere (atm). Because a pound is a unitof force and a kilogram a unit of mass, the met-ric equivalent is more complex in derivation.A newton (N), or 0.2248 pounds, is the metricunit of force, and a pascal (Pa)—1 newton persquare meter—the unit of pressure. Hence, anatmosphere, expressed in metric terms, is 1.013� 105 Pa.

Gases vs. Solids and Liq-uids: A Strikingly DifferentResponse

Regardless of the units you use, however, gasesrespond to changes in pressure and temperaturein a remarkably different way than do solids orliquids. Using a small water sample, say, 0.2642gal (1 l), an increase in pressure from 1-2 atm willdecrease the volume of the water by less than0.01%. A temperature increase from 32° to 212°F(0 to 100°C) will increase its volume by only 2%The response of a solid to these changes is even

less dramatic; however, the reaction of air (acombination of oxygen, nitrogen, and othergases) to changes in pressure and temperature isradically different.

For air, an equivalent temperature increasewould result in a volume increase of 37%, and anequivalent pressure increase will decrease thevolume by a whopping 50%. Air and other gasesalso have a boiling point below room tempera-ture, whereas the boiling point for water is high-er than room temperature and that of solids ismuch higher. The reason for this striking differ-ence in response can be explained by comparingall three forms of matter in terms of their overallstructure, and in terms of their molecular behav-ior. (Plasma, a gas-like state found, for instance,in stars and comets’ tails, does not exist on Earth,and therefore it will not be included in the com-parisons that follow.)

Molecular Structure Deter-mines Reaction

Solids possess a definite volume and a definiteshape, and are relatively noncompressible: forinstance, if you apply extreme pressure to a steelplate, it will bend, but not much. Liquids have adefinite volume, but no definite shape, and tendto be noncompressible. Gases, on the other hand,possess no definite volume or shape, and arecompressible.

At the molecular level, particles of solidstend to be definite in their arrangement and closein proximity—indeed, part of what makes a solid“solid,” in the everyday meaning of that term, isthe fact that its constituent parts are basicallyimmovable. Liquid molecules, too, are close inproximity, though random in arrangement. Gas


Gas Laws


molecules, too, are random in arrangement, buttend to be more widely spaced than liquid mole-cules. Solid particles are slow moving, and have astrong attraction to one another, whereas gasparticles are fast-moving, and have little or noattraction. (Liquids are moderate in bothregards.)

Given these interesting characteristics ofgases, it follows that a unique set of parameters—collectively known as the “gas laws”—are neededto describe and predict their behavior. Most ofthe gas laws were derived during the eighteenthand nineteenth centuries by scientists whosework is commemorated by the association oftheir names with the laws they discovered. Thesemen include the English chemists Robert Boyle(1627-1691), John Dalton (1766-1844), andWilliam Henry (1774-1836); the French physi-cists and chemists J. A. C. Charles (1746-1823)and Joseph Gay-Lussac (1778-1850), and the Ital-ian physicist Amedeo Avogadro (1776-1856).

Boyle’s, Charles’s, and Gay-Lussac’s Laws

Boyle’s law holds that in isothermal conditions(that is, a situation in which temperature is keptconstant), an inverse relationship exists betweenthe volume and pressure of a gas. (An inverserelationship is a situation involving two vari-ables, in which one of the two increases in directproportion to the decrease in the other.) In thiscase, the greater the pressure, the less the volumeand vice versa. Therefore the product of the vol-ume multiplied by the pressure remains constantin all circumstances.

Charles’s law also yields a constant, but inthis case the temperature and volume are allowedto vary under isobarometric conditions—that is,a situation in which the pressure remains thesame. As gas heats up, its volume increases, andwhen it cools down, its volume reduces accord-ingly. Hence, Charles established that the ratio oftemperature to volume is constant.

By now a pattern should be emerging: bothof the aforementioned laws treat one parameter(temperature in Boyle’s, pressure in Charles’s) asunvarying, while two other factors are treated asvariables. Both in turn yield relationshipsbetween the two variables: in Boyle’s law, pres-sure and volume are inversely related, whereas inCharles’s law, temperature and volume aredirectly related.

In Gay-Lussac’s law, a third parameter, vol-ume, is treated as a constant, and the result is aconstant ratio between the variables of pressureand temperature. According to Gay-Lussac’s law,the pressure of a gas is directly related to itsabsolute temperature.

Absolute temperature refers to the Kelvinscale, established by William Thomson, LordKelvin (1824-1907). Drawing on Charles’s dis-covery that gas at 0°C (32°F) regularly contractedby about 1/273 of its volume for every Celsiusdegree drop in temperature, Thomson derivedthe value of absolute zero (-273.15°C or -459.67°F). Using the Kelvin scale of absolutetemperature, Gay-Lussac found that at lowertemperatures, the pressure of a gas is lower, whileat higher temperatures its pressure is higher.Thus, the ratio of pressure to temperature is aconstant.

Avogadro’s Law

Gay-Lussac also discovered that the ratio inwhich gases combine to form compounds can beexpressed in whole numbers: for instance, wateris composed of one part oxygen and two partshydrogen. In the language of modern science,this would be expressed as a relationship betweenmolecules and atoms: one molecule of watercontains one oxygen atom and two hydrogenatoms.

In the early nineteenth century, however, sci-entists had yet to recognize a meaningful distinc-tion between atoms and molecules. Avogadrowas the first to achieve an understanding of thedifference. Intrigued by the whole-number rela-tionship discovered by Gay-Lussac, Avogadroreasoned that one liter of any gas must containthe same number of particles as a liter of anoth-er gas. He further maintained that gas consists ofparticles—which he called molecules—that inturn consist of one or more smaller particles.

In order to discuss the behavior of mole-cules, it was necessary to establish a large quanti-ty as a basic unit, since molecules themselves arevery small. For this purpose, Avogadro estab-lished the mole, a unit equal to 6.022137 � 1023

(more than 600 billion trillion) molecules. Theterm “mole” can be used in the same way we usethe word “dozen.” Just as “a dozen” can refer totwelve cakes or twelve chickens, so “mole” alwaysdescribes the same number of molecules.


Gas LawsJust as one liter of water, or one liter of mer-cury, has a certain mass, a mole of any given sub-stance has its own particular mass, expressed ingrams. The mass of one mole of iron, forinstance, will always be greater than that of onemole of oxygen. The ratio between them is exact-ly the same as the ratio of the mass of one ironatom to one oxygen atom. Thus the mole makesif possible to compare the mass of one element orone compound to that of another.

Avogadro’s law describes the connectionbetween gas volume and number of moles.According to Avogadro’s law, if the volume of gasis increased under isothermal and isobarometricconditions, the number of moles also increases.The ratio between volume and number of molesis therefore a constant.

The Ideal Gas Law

Once again, it is easy to see how Avogadro’s lawcan be related to the laws discussed earlier, sincethey each involve two or more of the four param-eters: temperature, pressure, volume, and quanti-ty of molecules (that is, number of moles). Infact, all the laws so far described are broughttogether in what is known as the ideal gas law,sometimes called the combined gas law.

The ideal gas law can be stated as a formula,pV = nRT, where p stands for pressure, V for vol-ume, n for number of moles, and T for tempera-ture. R is known as the universal gas constant, afigure equal to 0.0821 atm • liter/mole • K. (Likemost terms in physics, this one is best expressedin metric rather than English units.)

Given the equation pV = nRT and the factthat R is a constant, it is possible to find the valueof any one variable—pressure, volume, numberof moles, or temperature—as long as one knowsthe value of the other three. The ideal gas law alsomakes it possible to discern certain relations:thus if a gas is in a relatively cool state, the prod-uct of its pressure and volume is proportionatelylow; and if heated, its pressure and volume prod-uct increases correspondingly. Thus

,

where p1V1 is the product of its initial pressureand its initial volume, T1 its initial temperature,

V=

T1

p1 1

V

T2

p2 2


p2V2 the product of its final volume and final

pressure, and T2 its final temperature.

Five Postulates Regardingthe Behavior of Gases

Five postulates can be applied to gases. These

more or less restate the terms of the earlier dis-

cussion, in which gases were compared to solids

and liquids; however, now those comparisons

can be seen in light of the gas laws.

First, the size of gas molecules is minuscule

in comparison to the distance between them,

making gas highly compressible. In other words,

there is a relatively high proportion of empty

space between gas molecules.

Second, there is virtually no force attracting

gas molecules to one another.

Third, though gas molecules move random-

ly, frequently colliding with one another, their

net effect is to create uniform pressure.

A FIRE EXTINGUISHER CONTAINS A HIGH-PRESSURE MIX-TURE OF WATER AND CARBON DIOXIDE THAT RUSHES

OUT OF THE SIPHON TUBE, WHICH IS OPENED WHEN THE

RELEASE VALVE IS DEPRESSED. (Photograph by Craig Lovell/

Corbis. Reproduced by permission.)


Gas Laws


Fourth, the elastic nature of the collisions

results in no net loss of kinetic energy, the ener-

gy that an object possesses by virtue of its

motion. If a stone is dropped from a height, it

rapidly builds kinetic energy, but upon hitting a

nonelastic surface such as pavement, most of that

kinetic energy is transferred to the pavement. In

the case of two gas molecules colliding, however,

A HOT-AIR BALLOON FLOATS BECAUSE THE AIR INSIDE IT IS NOT AS DENSE THAN THE AIR OUTSIDE. THE WAY IN

WHICH THE DENSITY OF THE AIR IN THE BALLOON IS REDUCED REFLECTS THE GAS LAWS. (Duomo/Corbis. Reproduced by

permission.)


Gas Lawsthey simply bounce off one another, only to col-lide with other molecules and so on, with nokinetic energy lost.

Fifth, the kinetic energy of all gas moleculesis directly proportional to the absolute tempera-ture of the gas.

Laws of Partial Pressure

Two gas laws describe partial pressure. Dalton’slaw of partial pressure states that the total pressure of a gas is equal to the sum of its partial pressures—that is, the pressure exerted by each component of the gas mixture. As noted earlier, air is composed mostly of nitrogenand oxygen. Along with these are small compo-nents carbon dioxide and gases collectivelyknown as the rare or noble gases: argon, helium,krypton, neon, radon, and xenon. Hence, thetotal pressure of a given quantity of air is equal tothe sum of the pressures exerted by each of thesegases.

Henry’s law states that the amount of gasdissolved in a liquid is directly proportional tothe partial pressure of the gas above the surfaceof the solution. This applies only to gases such asoxygen and hydrogen that do not react chemical-ly to liquids. On the other hand, hydrochloricacid will ionize when introduced to water: one ormore of its electrons will be removed, and itsatoms will convert to ions, which are either posi-tive or negative in charge.


Pressure Changes

OPENING A SODA CAN. Inside acan or bottle of carbonated soda is carbon diox-ide gas (CO2), most of which is dissolved in thedrink itself. But some of it is in the space (some-times referred to as “head space”) that makes upthe difference between the volume of the softdrink and the volume of the container.

At the bottling plant, the soda manufactureradds high-pressure carbon dioxide to the headspace in order to ensure that more CO2 will beabsorbed into the soda itself. This is in accor-dance with Henry’s law: the amount of gas (inthis case CO2) dissolved in the liquid (soda) isdirectly proportional to the partial pressure of

the gas above the surface of the solution—that is,the CO2 in the head space. The higher the pres-sure of the CO2 in the head space, the greater theamount of CO2 in the drink itself; and the greaterthe CO2 in the drink, the greater the “fizz” ofthe soda.

Once the container is opened, the pressurein the head space drops dramatically. Once again,Henry’s law indicates that this drop in pressurewill be reflected by a corresponding drop in theamount of CO2 dissolved in the soda. Over aperiod of time, the soda will release that gas, andwill eventually go “flat.”

FIRE EXTINGUISHERS. A fireextinguisher consists of a long cylinder with anoperating lever at the top. Inside the cylinder is atube of carbon dioxide surrounded by a quantityof water, which creates pressure around the CO2

tube. A siphon tube runs vertically along thelength of the extinguisher, with one opening nearthe bottom of the water. The other end opens ina chamber containing a spring mechanismattached to a release valve in the CO2 tube.

The water and the CO2 do not fill the entirecylinder: as with the soda can, there is “headspace,” an area filled with air. When the operatinglever is depressed, it activates the spring mecha-nism, which pierces the release valve at the top ofthe CO2 tube. When the valve opens, the CO2

spills out in the “head space,” exerting pressureon the water. This high-pressure mixture ofwater and carbon dioxide goes rushing out of thesiphon tube, which was opened when the releasevalve was depressed. All of this happens, ofcourse, in a fraction of a second—plenty of timeto put out the fire.

AEROSOL CANS. Aerosol cans aresimilar in structure to fire extinguishers, thoughwith one important difference. As with the fireextinguisher, an aerosol can includes a nozzlethat depresses a spring mechanism, which in turnallows fluid to escape through a tube. But insteadof a gas cartridge surrounded by water, most ofthe can’s interior is made up of the product (forinstance, deodorant), mixed with a liquid pro-pellant.

The “head space” of the aerosol can is filledwith highly pressurized propellant in gas form,and in accordance with Henry’s law, a correspon-ding proportion of this propellant is dissolved inthe product itself. When the nozzle is depressed,



Gas Laws the pressure of the propellant forces the productout through the nozzle.

A propellant, as its name implies, propels theproduct itself through the spray nozzle when thelatter is depressed. In the past, chlorofluorocar-bons (CFCs)—manufactured compounds con-taining carbon, chlorine, and fluorine atoms—were the most widely used form of propellant.Concerns over the harmful effects of CFCs on theenvironment, however, has led to the develop-ment of alternative propellants, most notablyhydrochlorofluorocarbons (HCFCs), CFC-likecompounds that also contain hydrogen atoms.

When the TemperatureChanges

A number of interesting things, some of themunfortunate and some potentially lethal, occurwhen gases experience a change in temperature.In these instances, it is possible to see the gaslaws—particularly Boyle’s and Charles’s—at work.

There are a number of examples of the dis-astrous effects that result from an increase in thetemperature of a product containing com-bustible gases, as with natural gas and petrole-um-based products. In addition, the pressure onthe gases in aerosol cans makes the cans highlyexplosive—so much so that discarded cans at acity dump may explode on a hot summer day. Yetthere are other instances when heating a gas canproduce positive effects.

A hot-air balloon, for instance, floatsbecause the air inside it is not as dense than theair outside. By itself, this fact does not depend onany of the gas laws, but rather reflects the conceptof buoyancy. However, the way in which the den-sity of the air in the balloon is reduced doesindeed reflect the gas laws.

According to Charles’s law, heating a gas willincrease its volume. Also, as noted in the first andsecond propositions regarding the behavior ofgases, gas molecules are highly nonattractive toone another, and therefore, there is a great deal ofspace between them. The increase in volumemakes that space even greater, leading to a signif-icant difference in density between the air in theballoon and the air outside. As a result, the bal-loon floats, or becomes buoyant.

Although heating a gas can be beneficial,cooling a gas is not always a wise idea. If someone

were to put a bag of potato chips into a freezer,thinking this would preserve their flavor, hewould be in for a disappointment. Much of whatmaintains the flavor of the chips is the pressur-ization of the bag, which ensures a consistentinternal environment in which preservativechemicals, added during the manufacture of thechips, can keep them fresh. Placing the bag in thefreezer causes a reduction in pressure, as per Gay-Lussac’s law, and the bag ends up a limp versionof its earlier self.

Propane tanks and tires offer an example ofthe pitfalls that may occur by either allowing agas to heat up or cool down by too much.Because most propane tanks are made accordingto strict regulations, they are generally safe, but itis not entirely inconceivable that an extremelyhot summer day could cause a defective tank toburst. Certainly the laws of physics are there: anincrease in temperature leads to an increase inpressure, in accordance with Gay-Lussac’s law,and could lead to an explosion.

Because of the connection between heat andpressure, propane trucks on the highways duringthe summer are subjected to weight tests toensure that they are not carrying too much of thegas. On the other hand, a drastic reduction intemperature could result in a loss in gas pressure.If a propane tank from Florida were transportedby truck during the winter to northern Canada,the pressure would be dramatically reduced bythe time it reached its destination.

Gas Reactions That Moveand Stop a Car

In operating a car, we experience two examples ofgas laws in operation. One of these, common toeveryone, is that which makes the car run: thecombustion of gases in the engine. The other is,fortunately, a less frequent phenomenon—but itcan and does save lives. This is the operation ofan air bag, which, though it is partly related tolaws of motion, depends also on the behaviorsexplained in Charles’s law.

With regard to the engine, when the driverpushes down on the accelerator, this activates athrottle valve that sprays droplets of gasolinemixed with air into the engine. (Older vehiclesused a carburetor to mix the gasoline and air, butmost modern cars use fuel-injection, whichsprays the air-gas combination without requiringan intermediate step.) The mixture goes into the



Gas Laws

cylinder, where the piston moves up, compress-ing the gas and air.

While the mixture is still compressed (highpressure, high density), an electric spark plugproduces a flash that ignites it. The heat from thiscontrolled explosion increases the volume of air,which forces the piston down into the cylinder.This opens an outlet valve, causing the piston torise and release exhaust gases.

As the piston moves back down again, aninlet valve opens, bringing another burst of gaso-line-air mixture into the chamber. The piston,whose downward stroke closed the inlet valve,now shoots back up, compressing the gas and airto repeat the cycle. The reactions of the gasoline

and air are what move the piston, which turns acrankshaft that causes the wheels to rotate.

So much for moving—what about stopping?Most modern cars are equipped with an airbag,which reacts to sudden impact by inflating. Thisprotects the driver and front-seat passenger, who,even if they are wearing seatbelts, may otherwisebe thrown against the steering wheel or dash-board..

But an airbag is much more complicatedthan it seems. In order for it to save lives, it mustdeploy within 40 milliseconds (0.04 seconds).Not only that, but it has to begin deflating beforethe body hits it. An airbag does not inflate if a carsimply goes over a bump; it only operates in sit-


IN CASE OF A CAR COLLISION, A SENSOR TRIGGERS THE AIR BAG TO INFLATE RAPIDLY WITH NITROGEN GAS. BEFORE

YOUR BODY REACHES THE BAG, HOWEVER, IT HAS ALREADY BEGUN DEFLATING. (Illustration by Hans & Cassidy. The Gale

Group.)


Gas Laws


ABSOLUTE TEMPERATURE: Tem-

perature in relation to absolute zero

(-273.15°C or -459.67°F). Its unit is the

Kelvin (K), named after William Thomson,

Lord Kelvin (1824-1907), who created the

scale. The Kelvin and Celsius scales are

directly related; hence, Celsius tempera-

tures can be converted to Kelvins (for

which neither the word or symbol for

“degree” are used) by adding 273.15.

AVOGADRO’S LAW: A statement,

derived by the Italian physicist Amedeo

Avogadro (1776-1856), which holds that as

the volume of gas increases under isother-

mal and isobarometric conditions, the

number of molecules (expressed in terms

of mole number), increases as well. Thus

the ratio of volume to mole number is a

constant.

BOYLE’S LAW: A statement, derived

by English chemist Robert Boyle (1627-

1691), which holds that for gases in

isothermal conditions, an inverse relation-

ship exists between the volume and pres-

sure of a gas. This means that the greater

the pressure, the less the volume and vice

versa, and therefore the product of pres-

sure multiplied by volume yields a constant

figure.

CHARLES’S LAW: A statement,

derived by French physicist and chemist

J. A. C. Charles (1746-1823), which holds

that for gases in isobarometric conditions,

the ratio between the volume and temper-

ature of a gas is constant. This means that

the greater the temperature, the greater the

volume and vice versa.

DALTON’S LAW OF PARTIAL PRES-

SURE: A statement, derived by the

English chemist John Dalton (1766-1844),

which holds that the total pressure of a gas

is equal to the sum of its partial pres-

KEY TERMS

uations when the vehicle experiences extreme

deceleration. When this occurs, there is a rapid

transfer of kinetic energy to rest energy, as with

the earlier illustration of a stone hitting concrete.

And indeed, if you were to smash against a fully

inflated airbag, it would feel like hitting con-

crete—with all the expected results.

The airbag’s sensor contains a steel ball

attached to a permanent magnet or a stiff spring.

The spring holds it in place through minor

mishaps in which an airbag would not be war-

ranted—for instance, if a car were simply to be

“tapped” by another in a parking lot. But in a case

of sudden deceleration, the magnet or spring

releases the ball, sending it down a smooth bore.

It flips a switch, turning on an electrical circuit.

This in turn ignites a pellet of sodium azide,

which fills the bag with nitrogen gas.

The events described in the above illustra-tion take place within 40 milliseconds—less timethan it takes for your body to come flying for-ward; and then the airbag has to begin deflatingbefore the body reaches it. At this point, the high-ly pressurized nitrogen gas molecules beginescaping through vents. Thus as your body hitsthe bag, the deflation of the latter is moving it inthe same direction that your body is going—onlymuch, much more slowly. Two seconds afterimpact, which is an eternity in terms of theprocesses involved, the pressure inside the baghas returned to 1 atm.

WHERE TO LEARN MORE


“Chemistry Units: Gas Laws.” (Web site).<http://bio.bio.rpi.edu/MS99/ausemaW/chem/gases.hmtl> (February 21, 2001).


Gas Laws


Laws of Gases. New York: Arno Press, 1981.


Mebane, Robert C. and Thomas R. Rybolt. Air and OtherGases. Illustrations by Anni Matsick. New York:Twenty-First Century Books, 1995.

“Tutorials—6.” <http://www.chemistrycoach.com/tutori-als-6.html> (February 21, 2001).

sures—that is, the pressure exerted by each

component of the gas mixture.

GAY-LUSSAC’S LAW: A statement,

derived by the French physicist and

chemist Joseph Gay-Lussac (1778-1850),

which holds that the pressure of a gas is

directly related to its absolute temperature.

Hence the ratio of pressure to absolute

temperature is a constant.

HENRY’S LAW: A statement, derived

by the English chemist William Henry

(1774-836), which holds that the amount

of gas dissolved in a liquid is directly pro-

portional to the partial pressure of the gas

above the solution. This holds true only for

gases, such as hydrogen and oxygen, that

are capable of dissolving in water without

undergoing ionization.

IDEAL GAS LAW: A proposition, also

known as the combined gas law, that draws

on all the gas laws. The ideal gas law can be

expressed as the formula pV = nRT, where

p stands for pressure, V for volume, n for

number of moles, and T for temperature. R

is known as the universal gas constant, a

figure equal to 0.0821 atm • liter/mole • K.





IONIZATION: A reaction in which an

atom or group of atoms loses one or more

electrons. The atoms are then converted to

ions, which are either wholly positive or

negative in charge.

ISOTHERMAL: Referring to a situa-

tion in which temperature is kept constant.

ISOBAROMETRIC: Referring to a sit-

uation in which pressure is kept constant.

MOLE: A unit equal to 6.022137 � 1023

molecules.




MOLECUL AR DYNAM ICSMolecular Dynamics

CONCEPTPhysicists study matter and motion, or matter inmotion. These forms of matter may be large, orthey may be far too small to be seen by the mosthigh-powered microscopes available. Such is therealm of molecular dynamics, the study and sim-ulation of molecular motion. As its name sug-gests, molecular dynamics brings in aspects ofdynamics, the study of why objects move as theydo, as well as thermodynamics, the study of therelationships between heat, work, and energy.Existing at the borders between physics andchemistry, molecular dynamics provides under-standing regarding the properties of matter—including phenomena such as the liquefaction ofgases, in which one phase of matter is trans-formed into another.

HOW IT WORKS

Molecules

The physical world is made up of matter, physicalsubstance that has mass; occupies space; is com-posed of atoms; and is, ultimately, convertible toenergy. On Earth, three principal phases of mat-ter exist, namely solid, liquid, and gas. The differ-ences between these three are, on the surface atleast, easily perceivable. Clearly, water is a liquid,just as ice is a solid and steam a gas. Yet, the waysin which various substances convert betweenphases are often complex, as are the interrela-tions between these phases. Ultimately, under-standing of the phases depends on an awarenessof what takes place at the molecular level.

An atom is the smallest particle of a chemi-cal element. It is not, however, the smallest thing

in the universe; atoms are composed of subatom-ic particles, including protons, neutrons, andelectrons. These subatomic particles are dis-cussed in the context of the structure of matterelsewhere in this volume, where they are exam-ined largely with regard to their electromagneticproperties. In the present context, the concern isprimarily with the properties of atomic andmolecular particles, in terms of mechanics, thestudy of bodies in motion, and thermodynamics.

An atom must, by definition, represent oneand only one chemical element, of which 109have been identified and named. It should benoted that the number of elements changes withcontinuing research, and that many of the ele-ments, particularly those discovered relativelyrecently—as, for instance, meitnerium (No. 109),isolated in the 1990s—are hardly part of every-day experience. So, perhaps 100 would be a bet-ter approximation; in any case, consider the mul-titude of possible ways in which the elements canbe combined.

Musicians have only seven tones at their dis-posal, and artists only seven colors—yet theymanage to create a seemingly infinite variety ofmutations in sound and sight, respectively. Thereare only 10 digits in the numerical system thathas prevailed throughout the West since the lateMiddle Ages, yet it is possible to use that systemto create such a range of numbers that all thebooks in all the libraries in the world could notcontain them. This gives some idea of the rangeof combinations available using the hundred-odd chemical elements nature has provided—inother words, the number of possible molecularcombinations that exist in the universe.


MolecularDynamics


THE STRUCTURE OF MOLE-

CULES. A molecule is a group of atoms

joined in a single structure. Often, these atoms

come from different elements, in which case the

molecule represents a particular chemical com-

pound, such as water, carbon dioxide, sodium

chloride (salt), and so on. On the other hand, a

molecule may consist only of one type of atom:

oxygen molecules, for instance, are formed by the

joining of two oxygen atoms.

As much as scientists understand about mol-

ecules and their structure, there is much that they

do not know. Molecules of water are fairly easy to

understand, because they have a simple, regular

structure that does not change. A water molecule

is composed of one oxygen atom joined by two

hydrogen atoms, and since the oxygen atom is

much larger than the two hydrogens, its shape

can be compared to a basketball with two soft-

balls attached. The scale of the molecule, of

course, is so small as to boggle the mind: to bor-

row an illustration from American physicist

Richard Feynman (1918-1988), if a basketball

were blown up to the size of Earth, the molecules

inside of it would not even be as large as an ordi-

nary-sized basketball.

As for the water molecule, scientists know anumber of things about it: the distance betweenthe two hydrogen atoms (measured in unitscalled an angstrom), and even the angle at whichthey join the oxygen atom. In the case of salt,however, the molecular structure is not nearly asuniform as that of water: atoms join together, butnot always in regular ways. And then there arecompounds far more complex than water or salt,involving numerous elements that fit together inprecise and complicated ways. But, once that dis-cussion is opened, one has stepped from therealm of physics into that of chemistry, and thatis not the intention here. Rather, the purpose ofthe foregoing and very cursory discussion ofmolecular structure is to point out that mole-cules are at the heart of all physical existence—and that the things we cannot see are every bit ascomplicated as those we can.

THE MOLE. Given the tiny—to use anunderstatement—size of molecules, how do sci-entists analyze their behavior? Today, physicistshave at their disposal electron microscopes andother advanced forms of equipment that make itpossible to observe activity at the atomic andmolecular levels. The technology that makes thispossible is beyond the scope of the present dis-

THIS HUGE LIQUEFIED NATURAL GAS CONTAINER WILL BE INSTALLED ON A SHIP. THE VOLUME OF THE LIQUEFIED GAS

IS FAR LESS THAN IT WOULD BE IF THE GAS WERE IN A VAPORIZED STATE, THUS ENABLING EASE AND ECONOMY IN

TRANSPORT. (Photograph by James L. Amos/Corbis. Reproduced by permission.)


MolecularDynamics


cussion. On the other hand, consider a muchsimpler question: how do physicists weigh mole-cules?

Obviously “a bunch” of iron (an elementknown by the chemical symbol Fe) weighs morethan “a bunch” of oxygen, but what exactly is “abunch”? Italian physicist Amedeo Avogadro(1776-1856), the first scientist to clarify the dis-tinction between atoms and molecules, created aunit that made it possible to compare the massesof various molecules. This is the mole, alsoknown as “Avogadro’s number,” a unit equal to6.022137 � 1023 (more than 600 billion trillion)molecules.

The term “mole” can be used in the sameway that the word “dozen” is used. Just as “adozen” can refer to twelve cakes or twelve chick-ens, so “mole” always describes the same numberof molecules. A mole of any given substance hasits own particular mass, expressed in grams. Themass of one mole of iron, for instance, will alwaysbe greater than that of one mole of oxygen. Theratio between them is exactly the same as theratio of the mass of one iron atom to one oxygenatom. Thus, the mole makes it possible to com-pare the mass of one element or compound tothat of another.

Molecular Attraction andMotion

Molecular dynamics can be understood primari-ly in terms of the principles of motion, identifiedby Sir Isaac Newton (1642-1727), principles thatreceive detailed discussion at several places inthis volume. However, the attraction betweenparticles at the atomic and molecular level can-not be explained by reference to gravitationalforce, also identified by Newton. For more than acentury, gravity was the only type of force knownto physicists, yet the pull of gravitation alone wastoo weak to account for the strong pull betweenatoms and molecules.

During the eighteenth century and earlynineteenth centuries, however, physicists andother scientists became increasingly aware ofanother form of interaction at work in theworld—one that could not be explained in grav-itational terms. This was the force of electricityand magnetism, which Scottish physicist JamesClerk Maxwell (1831-1879) suggested were dif-ferent manifestations of a “new” kind of force,electromagnetism. All subatomic particles pos-sess either a positive, negative, or neutral electri-cal charge. An atom usually has a neutral charge,meaning that it is composed of an equal numberof protons (positive) and electrons (negative). In

HOW SMALL ARE MOLECULES? IF THIS BASKETBALL WERE BLOWN UP TO THE SIZE OF EARTH, THE MOLECULES INSIDE

IT WOULD NOT BE AS BIG AS A REAL BASKETBALL. (Photograph by Dimitri Iundt/Corbis. Reproduced by permission.)


MolecularDynamics

certain situations, however, it may lose one ormore electrons and, thus, acquire a net charge,making it an ion.

Positive and negative charges attract oneanother, much as the north and south poles oftwo different magnets attract. (In fact, magnet-ism is simply an aspect of electromagnetic force.)Not only do the positive and negative elements ofan atom attract one another, but positive ele-ments in atoms attract negative elements in otheratoms, and vice versa. These interactions aremuch more complex than the preceding discus-sion suggests, of course; the important point isthat a force other than gravitation draws mattertogether at the atomic and molecular levels. Onthe other hand, the interactions that are criticalto the study of molecular dynamics are primari-ly mechanical, comprehensible from the stand-point of Newtonian dynamics.

MOLECULAR BEHAVIOR AND

PHASES OF MATTER. All molecules arein motion, and the rate of that motion is affectedby the attraction between them. This attractionor repulsion can be though of like a spring con-necting two molecules, an analogy that worksbest for solids, but in a limited way for liquids.Most molecular motion in liquids and gases iscaused by collisions with other molecules; evenin solids, momentum is transferred from onemolecule to the next along the “springs,” but ulti-mately the motion is caused by collisions. Hencemolecular collisions provide the mechanism bywhich heat is transferred between two bodies incontact.

The rate at which molecules move in rela-tion to one another determines phase of mat-ter—that is, whether a particular item can bedescribed as solid, liquid, or gas. The movementof molecules means that they possess kineticenergy, or the energy of movement, which ismanifested as thermal energy and measured bytemperature. Temperature is really nothing morethan molecules in motion, relative to one anoth-er: the faster they move, the greater the kineticenergy, and the greater the temperature.

When the molecules in a material moveslowly in relation to one another, they tend to beclose in proximity, and hence the force of attrac-tion between them is strong. Such a material iscalled a solid. In molecules of liquid, by contrast,the rate of relative motion is higher, so the mole-cules tend to be a little more spread out, and

therefore the force between them is weaker. Amaterial substance whose molecules move athigh speeds, and therefore exert little attractiontoward one another, is known as a gas. All formsof matter possess a certain (very large) amount ofenergy due to their mass; thermal energy, howev-er, is—like phase of matter—a function of theattractions between particles. Hence, solids gen-erally have less energy than liquids, and liquidsless energy than gases.


Kinetic Theories of Matter

English chemist John Dalton (1766-1844) wasthe first to recognize that nature is composed oftiny particles. In putting forward his idea, Daltonadopted a concept from the Greek philosopherDemocritus (c. 470-380 B.C.), who proposed thatmatter is made up of tiny units he called atomos,or “indivisible.”

Dalton recognized that the structure ofatoms in a particular element or compound isuniform, and maintained that compounds aremade up of compound atoms: in other words,that water, for instance, is composed of “wateratoms.” Soon after Dalton, however, Avogadroclarified the distinction between atoms and mol-ecules. Neither Dalton nor Avogadro offeredmuch in the way of a theory regarding atomic ormolecular behavior; but another scientist hadalready introduced the idea that matter at thesmallest levels is in a constant state of motion.

This was Daniel Bernoulli (1700-1782), aSwiss mathematician and physicist whose studiesof fluids—a term which encompasses both gasesand liquids—provided a foundation for the fieldof fluid mechanics. (Today, Bernoulli’s principle,which relates the velocity and pressure of fluids,is applied in the field of aerodynamics, andexplains what keeps an airplane aloft.) Bernoullipublished his fluid mechanics studies in Hydro-dynamica (1700-1782), a work in which he pro-vided the basis for what came to be known as thekinetic theory of gases.

BROWNIAN MOTION. Because hecame before Dalton and Avogadro, and, thus, didnot have the benefit of their atomic and molecu-lar theories, Bernoulli was not able to develop hiskinetic theory beyond the seeds of an idea. The



MolecularDynamics

subsequent elaboration of kinetic theory, whichis applied not only to gases but (with somewhatless effectiveness) to liquids and solids, in fact,resulted from an accidental discovery.

In 1827, Scottish botanist Robert Brown(1773-1858) was studying pollen grains under amicroscope, when he noticed that the grainsunderwent a curious zigzagging motion in thewater. The pollen assumed the shape of a colloid,a pattern that occurs when particles of one sub-stance are dispersed—but not dissolved—inanother substance. Another example of a col-loidal pattern is a puff of smoke.

At first, Brown assumed that the motion hada biological explanation—that is, that it resultedfrom life processes within the pollen—but later,he discovered that even pollen from long-deadplants behaved in the same way. He never under-stood what he was witnessing. Nor did a numberof other scientists, who began noticing otherexamples of what came to be known as Brownianmotion: the constant but irregular zigzagging ofcolloidal particles, which can be seen clearlythrough a microscope.

MAXWELL, BOLTZMANN, AND

THE MATURING OF KINETIC THE-

ORY. A generation after Brown’s time, kinetictheory came to maturity through the work ofMaxwell and Austrian physicist Ludwig E. Boltz-mann (1844-1906). Working independently, thetwo men developed a theory, later dubbed theMaxwell-Boltzmann theory of gases, whichdescribed the distribution of molecules in a gas.In 1859, Maxwell described the distribution ofmolecular velocities, work that became the foun-dation of statistical mechanics—the study oflarge systems—by examining the behavior oftheir smallest parts.

A year later, in 1860, Maxwell published apaper in which he presented the kinetic theory ofgases: the idea that a gas consists of numerousmolecules, relatively far apart in space, whichinteract by colliding. These collisions, he pro-posed, are responsible for the production of ther-mal energy, because when the velocity of themolecules increases—as it does after collision—the temperature increases as well. Eight yearslater, in 1868, Boltzmann independently appliedstatistics to the kinetic theory, explaining thebehavior of gas molecules by means of whatwould come to be known as statistical me-chanics.

Kinetic theory offered a convincing explana-tion of the processes involved in Brownianmotion. According to the kinetic view, whatBrown observed had nothing to do with thepollen particles; rather, the movement of thoseparticles was simply the result of activity on thepart of the water molecules. Pollen grains aremany thousands of times larger than water mol-ecules, but since there are so many molecules ineven one drop of water, and their motion is soconstant but apparently random, the water mol-ecules are bound to move a pollen grain onceevery few thousand collisions.

In 1905, Albert Einstein (1879-1955) ana-lyzed the behavior of particles subjected toBrownian motion. His work, and the confirma-tion of his results by French physicist Jean Bap-tiste Perrin (1870-1942), finally put an end to anyremaining doubts concerning the molecularstructure of matter. The kinetic explanation ofmolecular behavior, however, remains a theory.

Kinetic Theory and Gases

Maxwell’s and Boltzmann’s work helped explaincharacteristics of matter at the molecular level,but did so most successfully with regard to gases.Kinetic theory fits with a number of behaviorsexhibited by gases: their tendency to fill any con-tainer by expanding to fit its interior, forinstance, and their ability to be easily com-pressed.

This, in turn, concurs with the gas laws (dis-cussed in a separate essay titled “Gas Laws”)—forinstance, Boyle’s law, which maintains that pres-sure decreases as volume increases, and viceversa. Indeed, the ideal gas law, which shows aninverse relationship between pressure and vol-ume, and a proportional relationship betweentemperature and the product of pressure and vol-ume, is an expression of kinetic theory.

THE GAS LAWS ILLUSTRATED.

The operations of the gas laws are easy to visual-ize by means of kinetic theory, which portraysgas molecules as though they were millions uponbillions of tiny balls colliding at random. Inside acube-shaped container of gas, molecules are col-liding with every possible surface, but the neteffect of these collisions is the same as though themolecules were divided into thirds, each thirdcolliding with opposite walls inside the cube.



MolecularDynamics

If the cube were doubled in size, the mole-cules bouncing back and forth between two setsof walls would have twice as far to travel betweeneach collision. Their speed would not change, butthe time between collisions would double, thus,cutting in half the amount of pressure theywould exert on the walls. This is an illustration ofBoyle’s law: increasing the volume by a factor oftwo leads to a decrease in pressure to half of itsoriginal value.

On the other hand, if the size of the contain-er were decreased, the molecules would have lessdistance to travel from collision to collision. Thismeans they would be colliding with the wallsmore often, and, thus, would have a higherdegree of energy—and, hence, a higher tempera-ture. This illustrates another gas law, Charles’slaw, which relates volume to temperature: as oneof the two increases or decreases, so does theother. Thus, it can be said, in light of kinetic the-ory, that the average kinetic energy produced bythe motions of all the molecules in a gas is pro-portional to the absolute temperature of the gas.

GASES AND ABSOLUTE TEM-

PERATURE. The term “absolute tempera-ture” refers to the Kelvin scale, established byWilliam Thomson, Lord Kelvin (1824-1907).Drawing on Charles’s discovery that gas at 0°C(32°F) regularly contracts by about 1/273 of itsvolume for every Celsius degree drop in temper-ature, Thomson derived the value of absolutezero (-273.15°C or -459.67°F). The Kelvin andCelsius scales are directly related; hence, Celsiustemperatures can be converted to Kelvins byadding 273.15.

The Kelvin scale measures temperature inrelation to absolute zero, or 0K. (Units in theKelvin system, known as Kelvins, do not includethe word or symbol for degree.) But what isabsolute zero, other than a very cold tempera-ture? Kinetic theory provides a useful definition:the temperature at which all molecular move-ment in a gas ceases. But this definition requiressome qualification.

First of all, the laws of thermodynamicsshow the impossibility of actually reachingabsolute zero. Second, the vibration of atomsnever completely ceases: rather, the vibration ofthe average atom is zero. Finally, one element—helium—does not freeze, even at temperaturesnear absolute zero. Only the application of pres-sure will push helium past the freezing point.

Changes of Phase

Kinetic theory is more successful when applied togases than to liquids and solids, because liquidand solid molecules do not interact nearly as fre-quently as gas particles do. Nonetheless, theproposition that the internal energy of any sub-stance—gas, liquid, or solid—is at least partlyrelated to the kinetic energies of its moleculeshelps explain much about the behavior of matter.

The thermal expansion of a solid, forinstance, can be clearly explained in terms ofkinetic theory. As discussed in the essay on elas-ticity, many solids are composed of crystals, reg-ular shapes composed of molecules joined to oneanother, as though on springs. A spring that ispulled back, just before it is released, is an exam-ple of potential energy: the energy that an objectpossesses by virtue of its position. For a crys-talline solid at room temperature, potential ener-gy and spacing between molecules are relativelylow. But as temperature increases and the solidexpands, the space between molecules increas-es—as does the potential energy in the solid.

An example of a liquid displaying kineticbehavior is water in the process of vaporization.The vaporization of water, of course, occurs inboiling, but water need not be anywhere near theboiling point to evaporate. In either case, theprocess is the same. Speeds of molecules in anysubstance are distributed along a curve, meaningthat a certain number of molecules have speedswell below, or well above, the average. Thosewhose speeds are well above the average haveenough energy to escape the surface, and oncethey depart, the average energy of the remainingliquid is less than before. As a result, evaporationleads to cooling. (In boiling, of course, the con-tinued application of thermal energy to theentire water sample will cause more molecules toachieve greater energy, even as highly energizedmolecules leave the surface of the boiling wateras steam.)

The Phase Diagram

The vaporization of water is an example of achange of phase—the transition from one phaseof matter to another. The properties of any sub-stance, and the points at which it changes phase,are plotted on what is known as a phase diagram.The latter typically shows temperature along thex-axis, and pressure along the y-axis. It is alsopossible to construct a phase diagram that plots



MolecularDynamics

volume against temperature, or volume againstpressure, and there are even three-dimensionalphase diagrams that measure the relationshipbetween all three—volume, pressure, and tem-perature. Here we will consider the simpler two-dimensional diagram we have described.

For simple substances such as water and car-bon dioxide, the solid form of the substanceappears at a relatively low temperature, and atpressures anywhere from zero upward. The linebetween solids and liquids, indicating the tem-perature at which a solid becomes a liquid at anypressure above a certain level, is called the fusioncurve. Though it appears to be a line, it is indeedcurved, reflecting the fact that at high pressures,a solid well below the normal freezing point forthat substance may be melted to create a liquid.

Liquids occupy the area of the phase dia-gram corresponding to relatively high tempera-tures and high pressures. Gases or vapors, on theother hand, can exist at very low temperatures,but only if the pressure is also low. Above themelting point for the substance, gases exist athigher pressures and higher temperatures. Thus,the line between liquids and gases often looksalmost like a 45° angle. But it is not a straightline, as its name, the vaporization curve, indi-cates. The curve of vaporization reflects the factthat at relatively high temperatures and highpressures, a substance is more likely to be a gasthan a liquid.

CRITICAL POINT AND SUBLI-

MATION. There are several other interestingphenomena mapped on a phase diagram. One isthe critical point, which can be found at a placeof very high temperature and pressure along thevaporization curve. At the critical point, hightemperatures prevent a liquid from remaining aliquid, no matter how high the pressure. At thesame time, the pressure causes gas beyond thatpoint to become more and more dense, but dueto the high temperatures, it does not condenseinto a liquid. Beyond the critical point, the sub-stance cannot exist in anything other than thegaseous state. The temperature component of thecritical point for water is 705.2°F (374°C)—at218 atm, or 218 times ordinary atmosphericpressure. For helium, however, critical tempera-ture is just a few degrees above absolute zero.This is why helium is rarely seen in forms otherthan a gas.

There is also a certain temperature and pres-sure, called the triple point, at which some sub-stances—water and carbon dioxide are exam-ples—will be a liquid, solid, and gas all at once.Another interesting phenomenon is the sublima-tion curve, or the line between solid and gas. Atcertain very low temperatures and pressures, asubstance may experience sublimation, meaningthat a gas turns into a solid, or a solid into a gas,without passing through a liquid stage. A well-known example of sublimation occurs when “dryice,” which is made of carbon dioxide, vaporizesat temperatures above (-109.3°F [-78.5°C]). Car-bon dioxide is exceptional, however, in that itexperiences sublimation at relatively high pres-sures, such as those experienced in everyday life:for most substances, the sublimation pointoccurs at such a low pressure point that it is sel-dom witnessed outside of a laboratory.

Liquefaction of Gases

One interesting and useful application of phasechange is the liquefaction of gases, or the changeof gas into liquid by the reduction in its molecu-lar energy levels. There are two important prop-erties at work in liquefaction: critical tempera-ture and critical pressure. Critical temperature isthat temperature above which no amount ofpressure will cause a gas to liquefy. Critical pres-sure is the amount of pressure required to lique-fy the gas at critical temperature.

Gases are liquefied by one of three methods:(1) application of pressure at temperatures belowcritical; (2) causing the gas to do work againstexternal force, thus, removing its energy andchanging it to the liquid state; or (3) causing thegas to do work against some internal force. Thesecond option can be explained in terms of theoperation of a heat engine, as explored in theThermodynamics essay.

In a steam engine, an example of a heatengine, water is boiled, producing energy in theform of steam. The steam is introduced to acylinder, in which it pushes on a piston to drivesome type of machinery. In pushing against thepiston, the steam loses energy, and as a result,changes from a gas back to a liquid.

As for the use of internal forces to cool a gas,this can be done by forcing the vapor through asmall nozzle or porous plug. Depending on thetemperature and properties of the gas, such an



MolecularDynamics


ABSOLUTE ZERO: The temperature,

defined as 0K on the Kelvin scale, at which

the motion of molecules in a solid virtu-

ally ceases. Absolute zero is equal to

-459.67°F (-273.15°C).

ATOM: The smallest particle of a chem-

ical element. An atom can exist either

alone or in combination with other atoms

in a molecule.

BROWNIAN MOTION: The constant

but irregular zigzagging of colloidal parti-

cles, which can be seen clearly through a

microscope. The phenomenon is named

after Scottish botanist Robert Brown

(1773-1858), who first witnessed it but was

not able to explain it. The behavior exhib-

ited in Brownian motion provides evi-

dence for the kinetic theory of matter.

CHANGE OF PHASE: The transition

from one phase of matter to another.

CHEMICAL COMPOUND: A sub-

stance made up of atoms of more than one

chemical element. These atoms are usually

joined in molecules.

CHEMICAL ELEMENT: A substance

made up of only one kind of atom.

COLLOID: A pattern that occurs when

particles of one substance are dispersed—

but not dissolved—in another substance. A

puff of smoke in the air is an example of a

colloid, whose behavior is typically charac-

terized by Brownian motion.

CRITICAL POINT: A coordinate, plot-

ted on a phase diagram, above which a sub-

stance cannot exist in anything other than

the gaseous state. Located at a position of

very high temperature and pressure, the

critical point marks the termination of the

vaporization curve.

DYNAMICS: The study of why objects

move as they do. Dynamics is an element

of mechanics.


liquid, which tends to flow, and which con-

forms to the shape of its container. Unlike

solids, fluids are typically uniform in

molecular structure: for instance, one mol-

ecule of water is the same as another water

molecule.

FUSION CURVE: The boundary

between solid and liquid for any given sub-

stance, as plotted on a phase diagram.

GAS: A phase of matter in which mole-

cules exert little or no attraction toward

one another, and, therefore, move at high

speeds.

HEAT: Internal thermal energy that

flows from one body of matter to another.

KELVIN SCALE: Established by

William Thomson, Lord Kelvin (1824-

1907), the Kelvin scale measures tempera-

ture in relation to absolute zero, or 0K.

(Units in the Kelvin system, known as

Kelvins, do not include the word or symbol

for degree.) The Kelvin and Celsius scales

are directly related; hence, Celsius temper-

atures can be converted to Kelvins by

adding 273.15.



KINETIC THEORY OF GASES: The

idea that a gas consists of numerous mole-

cules, relatively far apart in space, which

interact by colliding. These collisions are

responsible for the production of thermal

energy, because when the velocity of the

molecules increases—as it does after colli-

sion—the temperature increases as well.

KEY TERMS


MolecularDynamics


operation may be enough to remove energy suf-ficient for liquefaction to take place. Sometimes,the process must be repeated before the gas fullycondenses into a liquid.

HISTORICAL BACKGROUND.

Like the steam engine itself, the idea of gas lique-faction is a product of the early Industrial Age.One of the pioneering figures in the field was thebrilliant English physicist Michael Faraday(1791-1867), who liquefied a number of high-critical temperature gases, such as carbon dioxide.

Half a century after Faraday, French physi-cist Louis Paul Cailletet (1832-1913) and Swisschemist Raoul Pierre Pictet (1846-1929) devel-oped the nozzle and porous-plug methods of liq-uefaction. This, in turn, made it possible to liq-

uefy gases with much lower critical temperatures,among them oxygen, nitrogen, and carbonmonoxide.

By the end of the nineteenth century, physi-cists were able to liquefy the gases with the low-est critical temperatures. James Dewar of Scot-land (1842-1923) liquefied hydrogen, whose crit-ical temperature is -399.5°F (-239.7°C). Sometime later, Dutch physicist Heike KamerlinghOnnes (1853-1926) successfully liquefied the gaswith the lowest critical temperature of them all:helium, which, as mentioned earlier, becomes agas at almost unbelievably low temperatures. Itscritical temperature is -449.9°F (-267.7°C), orjust 5.3K.

APPLICATIONS OF GAS LIQ-

UEFACTION. Liquefied natural gas (LNG)

KINETIC THEORY OF MATTER: The

application of the kinetic theory of gases to

all forms of matter. Since particles of liq-

uids and solids move much more slowly

than do gas particles, kinetic theory is not

as successful in this regard; however, the

proposition that the internal energy of any

substance is at least partly related to the

kinetic energies of its molecules helps

explain much about the behavior of

matter.

LIQUID: A phase of matter in which

molecules exert moderate attractions

toward one another, and, therefore, move

at moderate speeds.

MATTER: Physical substance that has

mass; occupies space; is composed of

atoms; and is ultimately convertible to

energy. There are several phases of matter,

including solids, liquids, and gases.


motion.


(more than 600 billion trillion) molecules.

Since their size makes it impossible to

weigh molecules in relatively small quanti-

ties; hence, the mole, devised by Italian

physicist Amedeo Avogadro (1776-1856),

facilitates comparisons of mass between

substances.

MOLECULAR DYNAMICS: The study

and simulation of molecular motion.

MOLECULE: A group of atoms, usual-

ly of more than one chemical element,

joined in a structure.

PHASE DIAGRAM: A chart, plotted

for any particular substance, identifying

the particular phase of matter for that sub-

stance at a given temperature and pressure

level. A phase diagram usually shows tem-

perature along the x-axis, and pressure

along the y-axis.

PHASES OF MATTER: The various

forms of material substance (matter),



MolecularDynamics


and liquefied petroleum gas (LPG), the latter amixture of by-products obtained from petrole-um and natural gas, are among the examples ofliquefied gas in daily use. In both cases, the vol-ume of the liquefied gas is far less than it wouldbe if the gas were in a vaporized state, thusenabling ease and economy in transport.

Liquefied gases are used as heating fuel formotor homes, boats, and homes or cabins inremote areas. Other applications of liquefiedgases include liquefied oxygen and hydrogen inrocket engines, and liquefied oxygen and petrole-um used in welding. The properties of liquefiedgases also figure heavily in the science of produc-ing and studying low-temperature environ-ments. In addition, liquefied helium is used instudying the behavior of matter at temperaturesclose to absolute zero.

A “New” Form of Matter?

Physicists at a Colorado laboratory in 1995revealed a highly interesting aspect of atomicmotion at temperatures approaching absolutezero. Some 70 years before, Einstein had predict-ed that, at extremely low temperatures, atomswould fuse to form one large “superatom.” Thishypothesized structure was dubbed the Bose-Einstein Condensate after Einstein and Satyen-dranath Bose (1894-1974), an Indian physicistwhose statistical methods contributed to thedevelopment of quantum theory.

Because of its unique atomic structure, theBose-Einstein Condensate has been dubbed a“new” form of matter. It represents a quantummechanical effect, relating to a cutting-edge areaof physics devoted to studying the properties of

which are defined primarily in terms of the

behavior exhibited by their atomic or

molecular structures. On Earth, three prin-

cipal phases of matter exist, namely solid,

liquid, and gas.

POTENTIAL ENERGY: The energy an

object possesses by virtue of its position.

SOLID: A phase of matter in which

molecules exert strong attractions toward

one another, and, therefore, move slowly.

STATISTICAL MECHANICS: A realm

of the physical sciences devoted to the

study of large systems by examining the

behavior of their smallest parts.

SUBLIMATION CURVE: The bound-

ary between solid and gas for any given

substance, as plotted on a phase diagram.







ronment.

TEMPERATURE: A measure of the

average kinetic energy—or molecular

translational energy in a system. Differ-

ences in temperature determine the direc-

tion of internal energy flow between two

systems when heat is being transferred.

THERMAL ENERGY: Heat energy, a

form of kinetic energy produced by the

movement of atomic or molecular parti-

cles. The greater the movement of these

particles, the greater the thermal energy.

THERMODYNAMICS: The study of

the relationships between heat, work, and

energy.

VAPORIZATION CURVE: The bound-

ary between liquid and gas for any given

substance as plotted on a phase diagram.



MolecularDynamics


subatomic particles and the interaction of matterwith radiation. Thus it is not directly related tomolecular dynamics; nonetheless, the Bose-Ein-stein Condensate is mentioned here as an exam-ple of the exciting work being performed at alevel beyond that addressed by moleculardynamics. Its existence may lead to a greaterunderstanding of quantum mechanics, and onan everyday level, the “superatom” may aid in the design of smaller, more powerful com-puter chips.

WHERE TO LEARN MORE

Cooper, Christopher. Matter. New York: DK Publishing,1999.

“Kinetic Theory of Gases: A Brief Review” University ofVirginia Department of Physics (Web site).<http://www.phys.virginia.edu/classes/252/kinetic_theory.html> (April 15, 2001).

“The Kinetic Theory Page” (Web site).<http://comp.uark.edu/~jgeabana/mol_dyn/> (April15, 2001).

Medoff, Sol and John Powers. The Student ChemistExplores Atoms and Molecules. Illustrated by NancyLou Gahan. New York: R. Rosen Press, 1977.

“Molecular Dynamics” (Web site).<http://www.biochem.vt.edu/courses/modeling/molecular_dynamics.html> (April 15, 2001).

“Molecular Simulation Molecular Dynamics Page” (Website).<http://www.phy.bris.ac.uk/research/theory/simula-tion/md.html> (April 15, 2001).

Santrey, Laurence. Heat. Illustrated by Lloyd Birming-ham. Mahwah, NJ: Troll Associates, 1985.

Strasser, Ben. Molecules in Motion. Illustrated by VernJorgenson. Pasadena, CA: Franklin Publications,1967.

Van, Jon. “U.S. Scientists Create a ‘Superatom.’” ChicagoTribune, July 14, 1995, p. 3.



S TRUCTURE OF MAT TERStructure of Matter

CONCEPTThe physical realm is made up of matter. OnEarth, matter appears in three clearly definedforms—solid, liquid, and gas—whose visible andperceptible structure is a function of behaviorthat takes place at the molecular level. Thoughthese are often referred to as “states” of matter, itis also useful to think of them as phases of mat-ter. This terminology serves as a reminder thatany one substance can exist in any of the threephases. Water, for instance, can be ice, liquid, orsteam; given the proper temperature and pres-sure, it may be solid, liquid, and gas all at once!But the three definite earthbound states of mat-ter are not the sum total of the material world: inouter space a fourth phase, plasma, exists—andthere may be still other varieties in the physicaluniverse.

HOW IT WORKS

Matter and Energy

Matter can be defined as physical substance thathas mass; occupies space; is composed of atoms;and is ultimately convertible to energy. A signifi-cant conversion of matter to energy, however,occurs only at speeds approaching that of thespeed of light, a fact encompassed in the famousstatement formulated by Albert Einstein (1879-1955), E = mc2.

Einstein’s formula means that every itempossesses a quantity of energy equal to its massmultiplied by the squared speed of light. Giventhe fact that light travels at 186,000 mi (297,600km) per second, the quantities of energy avail-

able from even a tiny object traveling at thatspeed are massive indeed. This is the basis forboth nuclear power and nuclear weaponry, eachof which uses some of the smallest particles inthe known universe to produce results that areboth amazing and terrifying.

The forms of matter that most people expe-rience in their everyday lives, of course, are trav-eling at speeds well below that of the speed oflight. Even so, transfers between matter and ener-gy take place, though on a much, much smallerscale. For instance, when a fire burns, only a tinyfraction of its mass is converted to energy. Therest is converted into forms of mass differentfrom that of the wood used to make the fire.Much of it remains in place as ash, of course, butan enormous volume is released into the atmos-phere as a gas so filled with energy that it gener-ates not only heat but light. The actual mass con-verted into energy, however, is infinitesimal.

CONSERVATION AND CON-

VERSION. The property of energy is, at alltimes and at all places in the physical universe,conserved. In physics, “to conserve” somethingmeans “to result in no net loss of” that particularcomponent—in this case, energy. Energy is neverdestroyed: it simply changes form. Hence, theconservation of energy, a law of physics statingthat within a system isolated from all other out-side factors, the total amount of energy remainsthe same, though transformations of energyfrom one form to another take place.

Whereas energy is perfectly conserved, mat-ter is only approximately conserved, as shownwith the example of the fire. Most of the matterfrom the wood did indeed turn into more mat-


Structureof Matter


ter—that is, vapor and ash. Yet, as also noted, a

tiny quantity of matter—too small to be per-

ceived by the senses—turned into energy.

The conservation of mass holds that total

mass is constant, and is unaffected by factors

such as position, velocity, or temperature, in any

system that does not exchange any matter with its

environment. This, however, is a qualified state-

ment: at speeds well below c (the speed of light),

it is essentially true, but for matter approaching c

and thus, turning into energy, it is not.

Consider an item of matter moving at thespeed of 100 mi (160 km)/sec. This is equal to360,000 MPH (576,000 km/h) and in terms ofthe speeds to which humans are accustomed, itseems incredibly fast. After all, the fastest anyhuman beings have ever traveled was about25,000 MPH (40,000 km/h), in the case of theastronauts aboard Apollo 11 in May 1969, and thespeed under discussion is more than 14 timesgreater. Yet 100 mi/sec is a snail’s pace comparedto c: in fact, the proportional difference betweenan actual snail’s pace and the speed of a human

AN ICEBERG FLOATS BECAUSE THE DENSITY OF ICE IS LOWER THAN WATER, WHILE ITS VOLUME IS GREATER, MAKING

THE ICEBERG BUOYANT. (Photograph by Ric Engenbright/Corbis. Reproduced by permission.)


Structureof Matter


walking is not as great. Yet even at this leisurelygait, equal to 0.00054c, a portion of mass equal to0.0001% (one-millionth of the total mass) con-verts to energy.

Matter at the Atomic Level

In his brilliant work Six Easy Pieces, Americanphysicist Richard Feynman (1918-1988) askedhis readers, “If, in some cataclysm, all of scientif-ic knowledge were to be destroyed, and only onesentence passed on to the next generations ofcreatures, what statement would contain themost information in the fewest words? I believe itis the atomic hypothesis (or the atomic fact, orwhatever you wish to call it) that all things aremade of atoms—little articles that move aroundin perpetual motion, attracting each other whenthey are a little distance apart, but repelling uponbeing squeezed into one another. In that sen-tence, you will see, there is an enormous amountof information about the world, if just a littleimagination and thinking are applied.”

Feynman went on to offer a powerful seriesof illustrations concerning the size of atoms rela-tive to more familiar objects: if an apple weremagnified to the size of Earth, for instance, theatoms in it would each be about the size of a reg-ular apple. Clearly atoms and other atomic parti-cles are far too small to be glimpsed by even themost highly powered optical microscope. Yet, it isthe behavior of particles at the atomic level thatdefines the shape of the entire physical world.Viewed from this perspective, it becomes easy tounderstand how and why matter is convertible toenergy. Likewise, the interaction between atomsand other particles explains why some types of matter are solid, others liquid, and still others, gas.

ATOMS AND MOLECULES. Anatom is the smallest particle of a chemical ele-ment. It is not, however, the smallest particle inthe universe; atoms are composed of subatomicparticles, including protons, neutrons, and elec-trons. But at the subatomic level, it is meaning-less to refer to, for instance, “an oxygen electron”:electrons are just electrons. An atom, then, is thefundamental unit of matter. Most of the sub-stances people encounter in the world, however,are not pure elements, such as oxygen or iron;they are chemical compounds, in which atoms ofmore than one element join together to formmolecules.

One of the most well-known molecularforms in the world is water, or H2O, composed oftwo hydrogen atoms and one oxygen atom. Thearrangement is extremely precise and nevervaries: scientists know, for instance, that the twohydrogen atoms join the oxygen atom (which ismuch larger than the hydrogen atoms) at anangle of 105° 3’. Other molecules are much morecomplex than those of water—some of themmuch, much more complex, which is reflected inthe sometimes unwieldy names required to iden-tify their chemical components.

ATOMIC AND MOLECULAR

THEORY. The idea of atoms is not new. Morethan 24 centuries ago, the Greek philosopherDemocritus (c. 470-380 B.C.) proposed that mat-ter is composed of tiny particles he called atom-os, or “indivisible.” Democritus was not, however,describing matter in a concrete, scientific way:his “atoms” were idealized, philosophical con-structs, not purely physical units.

Yet, he came amazingly close to identifyingthe fundamental structure of physical reality—much closer than any number of erroneous the-ories (such as the “four elements” of earth, air,fire, and water) that prevailed until moderntimes. English chemist John Dalton (1766-1844)was the first to identify what Feynman latercalled the “atomic hypothesis”: that nature iscomposed of tiny particles. In putting forwardhis idea, Dalton adopted Democritus’s word“atom” to describe these basic units.

Dalton recognized that the structure ofatoms in a particular element or compound isuniform. He maintained that compounds aremade up of compound atoms: in other words,that water, for instance, is a compound of “wateratoms.” Water, however, is not an element, andthus, it was necessary to think of its atomic com-position in a different way—in terms of mole-cules rather than atoms. Dalton’s contemporaryAmedeo Avogadro (1776-1856), an Italian physi-cist, was the first scientist to clarify the distinc-tion between atoms and molecules.

THE MOLE. Obviously, it is impracticalto weigh a single molecule, or even several thou-sand; what was needed, then, was a number largeenough to make possible practical comparisonsof mass. Hence, the mole, a quantity equal to“Avogadro’s number.” The latter, named afterAvogadro though not derived by him, is equal to6.022137 x 1023 (more than 600 billion trillion)molecules.


Structureof Matter

The term “mole” can be used in the sameway that the word “dozen” is used. Just as “adozen” can refer to twelve cakes or twelve chick-ens, so “mole” always describes the same numberof molecules. A mole of any given substance hasits own particular mass, expressed in grams. Themass of one mole of iron, for instance, will alwaysbe greater than that of one mole of oxygen. Theratio between them is exactly the same as theratio of the mass of one iron atom to one oxygenatom. Thus, the mole makes it possible to com-pare the mass of one element or compound tothat of another.

BROWNIAN MOTION AND KI-

NETIC THEORY. Contemporary to bothDalton and Avogadro was Scottish naturalistRobert Brown (1773-1858), who in 1827 stum-bled upon a curious phenomenon. While study-ing pollen grains under a microscope, Brownnoticed that the grains underwent a curiouszigzagging motion in the water. At first, heassumed that the motion had a biological expla-nation—that is, it resulted from life processeswithin the pollen—but later he discovered thateven pollen from long-dead plants behaved inthe same way.

Brown never understood what he was wit-nessing. Nor did a number of other scientists,who began noticing other examples of whatcame to be known as Brownian motion: the con-stant but irregular zigzagging of particles in apuff of smoke, for instance. Later, however, Scot-tish physicist James Clerk Maxwell (1831-1879)and others were able to explain it by what cameto be known as the kinetic theory of matter.

The kinetic theory, which is discussed indepth elsewhere in this book, is based on the ideathat molecules are constantly in motion: hence,the water molecules were moving the pollengrains Brown observed. Pollen grains are manythousands of times as large as water molecules,but there are so many molecules in just one drop of water, and their motion is so constantbut apparently random, that they are bound to move a pollen grain once every few thousandcollisions.

GROWTH IN UNDERSTANDING

THE ATOM. Einstein, who was born the yearMaxwell died, published a series of papers inwhich he analyzed the behavior of particles sub-jected to Brownian motion. His work, and theconfirmation of his results by French physicist

Jean Baptiste Perrin (1870-1942), finally put anend to any remaining doubts concerning themolecular structure of matter.

It may seem amazing that the molecular andatomic ideas were still open to question in theearly twentieth century; however, the vast major-ity of what is known today concerning the atomemerged after World War I. At the end of thenineteenth century, scientists believed the atomto be indivisible, but growing evidence concern-ing electrical charges in atoms brought with it theawareness that there must be something smallercreating those charges.

Eventually, physicists identified protons andelectrons, but the neutron, with no electricalcharge, was harder to discover: it was not identi-fied until 1932. After that point, scientists wereconvinced that just three types of subatomic par-ticles existed. However, subsequent activityamong physicists—particularly those in the fieldof quantum mechanics—led to the discovery ofother elementary particles, such as the photon.However, in this discussion, the only subatomicparticles whose behavior is reviewed are the pro-ton, electron, and neutron.

Motion and Attraction inAtoms and Molecules

At the molecular level, every item of matter in theworld is in motion. This may be easy enough toimagine with regard to air or water, since bothtend to flow. But what about a piece of paper, ora glass, or a rock? In fact, all molecules are in con-stant motion, and depending on the particularphase of matter, this motion may vary from amere vibration to a high rate of speed.

Molecular motion generates kinetic energy,or the energy of movement, which is manifestedas heat or thermal energy. Indeed, heat is reallynothing more than molecules in motion relativeto one another: the faster they move, the greaterthe kinetic energy, and the greater the heat.

The movement of atoms and molecules isalways in a straight line and at a constant veloci-ty, unless acted upon by some outside force. Infact, the motion of atoms and molecules is con-stantly being interfered with by outside forces,because they are perpetually striking one anoth-er. These collisions cause changes in direction,and may lead to transfers of energy from oneparticle to another.



Structureof Matter

ELECTROMAGNETIC FORCE

IN ATOMS. The behavior of molecules can-not be explained in terms of gravitational force.This force, and the motions associated with it,were identified by Sir Isaac Newton (1642-1727),and Newton’s model of the universe seemed toanswer most physical questions. Then in the latenineteenth century, Maxwell discovered a secondkind of force, electromagnetism. (There are twoother known varieties of force, strong and weaknuclear, which are exhibited at the subatomiclevel.) Electromagnetic force, rather than gravita-tion, explains the attraction between atoms.

Several times up to this point, the subatom-ic particles have been mentioned but notexplained in terms of their electrical charge,which is principal among their defining charac-teristics. Protons have a positive electrical charge,while neutrons exert no charge. These two typesof particles, which make up the vast majority ofthe atom’s mass, are clustered at the center, ornucleus. Orbiting around this nucleus are elec-trons, much smaller particles which exert a nega-tive charge.

Chemical elements are identified by thenumber of protons they possess. Hydrogen, firstelement listed on the periodic table of elements,has one proton and is thus identified as 1; car-bon, or element 6, has six protons, and so on.

An atom usually has a neutral charge, mean-ing that it is composed of an equal number ofprotons or electrons. In certain situations, how-ever, it may lose one or more electrons and thusacquire a net charge. Such an atom is called anion. But electrical charge, like energy, is con-served, and the electrons are not “lost” when anatom becomes an ion: they simply go elsewhere.

MOLECULAR BEHAVIOR AND

STATES OF MATTER. Positive and neg-ative charges interact at the molecular level in away that can be compared to the behavior ofpoles in a pair of magnets. Just as two north polesor two south poles repel one another, so likecharges—two positives, or two negatives—repel.Conversely, positive and negative charges exertan attractive force on one another similar to thatof a north pole and south pole in contact.

In discussing phases of matter, the attractionbetween molecules provides a key to distinguish-ing between states of matter. This is not to sayone particular phase of matter is a particularlygood conductor of electrical current, however.

For instance, certain solids—particularly metalssuch as copper—are extremely good conductors.But wood is a solid, too, and conducts electricalcurrent poorly.

The properties of various forms of matter,viewed from the larger electromagnetic picture,are a subject far beyond the scope of this essay. Inany case, the electromagnetic properties of con-cern in the present instance are not the onesdemonstrated at a macroscopic level—that is, inview of “the big picture.” Rather, the subject ofthe attractive force operating at the atomic ormolecular levels has been introduced to showthat certain types of material have a greater inter-molecular attraction.

As previously stated, all matter is in motion.The relative speed of that motion, however, is afunction of the attraction between molecules,which in turn defines a material according to oneof the phases of matter. When the molecules in amaterial exert a strong attraction toward oneanother, they move slowly, and the material iscalled a solid. Molecules of liquid, by contrast,exert a moderate attraction and move at moder-ate speeds. A material substance whose moleculesexert little or no attraction, and therefore, moveat high speeds, is known as a gas.

These comparisons of molecular speed andattraction, obviously, are relative. Certainly, it iseasy enough in most cases to distinguish betweenone phase of matter and another, but there aresome instances in which they overlap. Examplesof these will follow, but first it is necessary to dis-cuss the phases of matter in the context of theirbehavior in everyday situations.


From Solid to Liquid

The attractions between particles have a numberof consequences in defining the phases of matter.The strong attractive forces in solids cause itsparticles to be positioned close together. Thismeans that particles of solids resist attempts tocompress them, or push them together. Becauseof their close proximity, solid particles are fixedin an orderly and definite pattern. As a result, asolid usually has a definite volume and shape.

A crystal is a type of solid in which the con-stituent parts are arranged in a simple, definite



Structureof Matter

geometric arrangement that is repeated in alldirections. Metals, for instance, are crystallinesolids. Other solids are said to be amorphous,meaning that they possess no definite shape.Amorphous solids—clay, for example—eitherpossess very tiny crystals, or consist of severalvarieties of crystal mixed randomly. Still othersolids, among them glass, do not contain crystals.

VIBRATIONS AND FREEZING.

Because of their strong attractions to one anoth-er, solid particles move slowly, but like all parti-cles of matter, they do move. Whereas the parti-cles in a liquid or gas move fast enough to be inrelative motion with regard to one another, how-ever, solid particles merely vibrate from a fixedposition.

This can be shown by the example of asinger hitting a certain note and shattering aglass. Contrary to popular belief, the note doesnot have to be particularly high: rather, the noteshould be on the same wavelength as the vibra-tion of the glass. When this occurs, sound energyis transferred directly to the glass, which shattersbecause of the sudden net intake of energy.

As noted earlier, the attraction and motionof particles in matter has a direct effect on heatand temperature. The cooler the solid, the slowerand weaker the vibrations, and the closer the par-ticles are to one another. Thus, most types ofmatter contract when freezing, and their densityincreases. Absolute zero, or 0K on the Kelvin scaleof temperature—equal to -459.67°F (-273°C)—is the point at which vibration virtually stops.Note that the vibration virtually stops, but doesnot stop entirely. In any event, the lowest temperature actually achieved, at a Finnishnuclear laboratory in 1993, is 2.8 • 10-10K, or0.00000000028K—still above absolute zero.

UNUSUAL CHARACTERISTICS

OF ICE. The behavior of water at the freez-ing/melting point is interesting and exceptional.Above 39.2°F (4°C) water, like most substances,expands when heated. But between 32°F (0°C)and that temperature, however, it actually con-tracts. And whereas most substances becomemuch denser with lowered temperatures, thedensity of water reaches its maximum at 39.2°F.Below that point, it starts to decrease again.

Not only does the density of ice begindecreasing just before freezing, but its volumeincreases. This is the reason ice floats: its weightis less than that of the water it has displaced, and

therefore, it is buoyant. Additionally, the buoyantqualities of ice atop very cold water explain whythe top of a lake may freeze, but lakes rarelyfreeze solid—even in the coldest of inhabitedregions.

Instead of freezing from the bottom up, as itwould if ice were less buoyant than the water, thelake freezes from the top down. Furthermore, iceis a poorer conductor of heat than water, and,thus, little of the heat from the water belowescapes. Therefore, the lake does not freeze com-pletely—only a layer at the top—and this helpspreserve animal and plant life in the body ofwater. On the other hand, the increased volumeof frozen water is not always good for humans:when water in pipes freezes, it may increase involume to the point where the pipe bursts.

MELTING. When heated, particles beginto vibrate more and more, and, therefore, movefurther apart. If a solid is heated enough, it losesits rigid structure and becomes a liquid. The tem-perature at which a solid turns into a liquid iscalled the melting point, and melting points aredifferent for different substances. For the mostpart, however, solids composed of heavier parti-cles require more energy—and, hence, highertemperatures—to induce the vibrations neces-sary for freezing. Nitrogen melts at -346°F (-210°C), ice at 32°F (0°C), and copper at 1,985°F(1,085°C). The melting point of a substance,incidentally, is the same as its freezing point: thedifference is a matter of orientation—that is,whether the process is one of a solid melting tobecome a liquid, or of a liquid freezing to becomea solid.

The energy required to change a solid to aliquid is called the heat of fusion. In melting, allthe heat energy in a solid (energy that exists dueto the motion of its particles) is used in breakingup the arrangement of crystals, called a lattice.This is why the water resulting from melted icedoes not feel any warmer than when it wasfrozen: the thermal energy has been expended,with none left over for heating the water. Once allthe ice is melted, however, the absorbed energyfrom the particles—now moving at much greaterspeeds than when the ice was in a solid state—causes the temperature to rise.

From Liquid to Gas

The particles of a liquid, as compared to those ofa solid, have more energy, more motion, and less



Structureof Matter

attraction to one another. The attraction, how-ever, is still fairly strong: thus, liquid particles arein close enough proximity that the liquid resistscompression.

On the other hand, their arrangement isloose enough that the particles tend to movearound one another rather than merely vibratingin place, as solid particles do. A liquid is thereforenot definite in shape. Both liquids and gases tendto flow, and to conform to the shape of their con-tainer; for this reason, they are together classifiedas fluids.

Owing to the fact that the particles in a liq-uid are not as close in proximity as those of asolid, liquids tend to be less dense than solids.The liquid phase of substance is thus inclined tobe larger in volume than its equivalent in solidform. Again, however, water is exceptional in thisregard: liquid water actually takes up less spacethan an equal mass of frozen water.

BOILING. When a liquid experiences anincrease in temperature, its particles take onenergy and begin to move faster and faster. Theycollide with one another, and at some point theparticles nearest the surface of the liquid acquireenough energy to break away from their neigh-bors. It is at this point that the liquid becomes agas or vapor.

As heating continues, particles throughoutthe liquid begin to gain energy and move faster,but they do not immediately transform into gas.The reason is that the pressure of the liquid,combined with the pressure of the atmosphereabove the liquid, tends to keep particles in place.Those particles below the surface, therefore,remain where they are until they acquire enoughenergy to rise to the surface.

The heated particle moves upward, leavingbehind it a hollow space—a bubble. A bubble isnot an empty space: it contains smaller trappedparticles, but its small weight relative to that ofthe liquid it disperses makes it buoyant. There-fore, a bubble floats to the top, releasing itstrapped particles as gas or vapor. At that point,the liquid is said to be boiling.

THE EFFECT OF ATMOSPHER-

IC PRESSURE. As they rise, the particlesthus have to overcome atmospheric pressure, andthis means that the boiling point for any liquiddepends in part on the pressure of the surround-ing air. This is why cooking instructions oftenvary with altitude: the greater the distance from

sea level, the less the air pressure, and the shorterthe required cooking time.

Atop Mt. Everest, Earth’s highest peak atabout 29,000 ft (8,839 m) above sea level, thepressure is approximately one-third normalatmospheric pressure. This means the air is one-third as dense as it is as sea level, which explainswhy mountain-climbers on Everest and other tallpeaks must wear oxygen masks to stay alive. Italso means that water boils at a much lower tem-perature on Everest than it does elsewhere. At sealevel, the boiling point of water is 212°F (100°C),but at 29,000 ft it is reduced by one-quarter, to158°F (70°C).

Of course, no one lives on the top of Mt.Everest—but people do live in Denver, Colorado,where the altitude is 5,577 ft (1,700 m) and theboiling point of water is 203°F (95°C). Given thelower boiling point, one might assume that foodwould cook faster in Denver than in New York,Los Angeles, or some other city close to sea level.In fact, the opposite is true: because heated parti-cles escape the water so much faster at high alti-tudes, they do not have time to acquire the ener-gy needed to raise the temperature of the water.It is for this reason that a recipe may contain astatement such as “at altitudes above XX feet, addXX minutes to cooking time.”

If lowered atmospheric pressure means alowered boiling point, what happens in outerspace, where there is no atmospheric pressure?Liquids boil at very, very low temperatures. Thisis one of the reasons why astronauts have to wearpressurized suits: if they did not, their bloodwould boil—even though space itself is incredi-bly cold.

LIQUID TO GAS AND BACK

AGAIN. Note that the process of a liquidchanging to a gas is similar to what occurs whena solid changes to a liquid: particles gain heat andtherefore energy, begin to move faster, break freefrom one another, and pass a certain thresholdinto a new phase of matter. And just as the freez-ing and melting point for a given substance arethe same temperature, the only difference beingone of orientation, the boiling point of a liquidtransforming into a gas is the same as the con-densation point for a gas turning into a liquid.

The behavior of water in boiling and con-densation makes possible distillation, one of theprincipal methods for purifying seawater in vari-ous parts of the world. First, the water is boiled,



Structureof Matter

then, it is allowed to cool and condense, thusforming water again. In the process, the waterseparates from the salt, leaving it behind in theform of brine. A similar separation takes placewhen salt water freezes: because salt, like mostsolids, has a much lower freezing point thanwater, very little of it remains joined to the waterin ice. Instead, the salt takes the form of a brinyslush.

GAS AND ITS LAWS. Havingreached the gaseous state, a substance takes oncharacteristics quite different from those of asolid, and somewhat different from those of a liq-uid. Whereas liquid particles exert a moderateattraction to one another, particles in a gas exertlittle to no attraction. They are thus free to move,and to move quickly. The shape and arrangementof gas is therefore random and indefinite—and,more importantly, the motion of gas particlesgive it much greater kinetic energy than the otherforms of matter found on Earth.

The constant, fast, and random motion ofgas particles means that they are always collidingand thereby transferring kinetic energy back andforth without any net loss. These collisions alsohave the overall effect of producing uniformpressure in a gas. At the same time, the charac-teristics and behavior of gas particles indicatethat they will tend not to remain in an open con-tainer. Therefore, in order to maintain any pres-sure on a gas—other than the normal atmos-pheric pressure exerted on the surface of the gasby the atmosphere (which, of course, is also agas)—it is necessary to keep it in a closed con-tainer.

There are a number of gas laws (examined inanother essay in this book) describing theresponse of gases to changes in pressure, temper-ature, and volume. Among these is Boyle’s law,which holds that when the temperature of a gasis constant, there is an inverse relationshipbetween volume and pressure: in other words,the greater the pressure, the less the volume, andvice versa. According to a second gas law,Charles’s law, for gases in conditions of constantpressure, the ratio between volume and tempera-ture is constant—that is, the greater the temper-ature, the greater the volume, and vice versa.

In addition, Gay-Lussac’s law shows that thepressure of a gas is directly related to its absolutetemperature on the Kelvin scale: the higher thetemperature, the higher the pressure, and vice

versa. Gay-Lussac’s law is combined, along withBoyle’s and Charles’s and other gas laws, in theideal gas law, which makes it possible to find thevalue of any one variable—pressure, volume,number of moles, or temperature—for a gas, aslong as one knows the value of the other three.

Other States of Matter

PLASMA. Principal among states ofmatter other than solid, liquid, and gas is plasma,which is similar to gas. (The term “plasma,” whenreferring to the state of matter, has nothing to dowith the word as it is often used, in reference toblood plasma.) As with gas, plasma particles col-lide at high speeds—but in plasma, the speeds areeven greater, and the kinetic energy levels evenhigher.

The speed and energy of these collisions isdirectly related to the underlying property thatdistinguishes plasma from gas. So violent are thecollisions between plasma particles that electronsare knocked away from their atoms. As a result,plasma does not have the atomic structure typi-cal of a gas; rather, it is composed of positive ionsand electrons. Plasma particles are thus electri-cally charged, and, therefore, greatly influencedby electrical and magnetic fields.

Formed at very high temperatures, plasma isfound in stars and comets’ tails; furthermore, thereaction between plasma and atomic particles inthe upper atmosphere is responsible for the auro-ra borealis or “northern lights.” Though notfound on Earth, plasma—ubiquitous in otherparts of the universe—may be the most plentifulamong the four principal states of matter.

QUASI-STATES. Among the quasi-states of matter discussed by physicists are sever-al terms that describe the structure in which par-ticles are joined, rather than the attraction andrelative movement of those particles. “Crys-talline,” “amorphous,” and “glassy” are all termsto describe what may be individual states of mat-ter; so too is “colloidal.”

A colloid is a structure intermediate in sizebetween a molecule and a visible particle, and ithas a tendency to be dispersed in another medi-um—as smoke, for instance, is dispersed in air.Brownian motion describes the behavior of mostcolloidal particles. When one sees dust floating ina ray of sunshine through a window, the lightreflects off colloids in the dust, which are driven



Structureof Matter

back and forth by motion in the air otherwiseimperceptible to the human senses.

DARK MATTER. The number of statesor phases of matter is clearly not fixed, and it isquite possible that more will be discovered inouter space, if not on Earth. One intriguing can-didate is called dark matter, so described becauseit neither reflects nor emits light, and is thereforeinvisible. In fact, luminous or visible matter mayvery well make up only a small fraction of themass in the universe, with the rest being taken upby dark matter.

If dark matter is invisible, how doastronomers and physicists know it exists? Byanalyzing the gravitational force exerted on visi-ble objects when there seems to be no visibleobject to account for that force. An example isthe center of our galaxy, the Milky Way, whichappears to be nothing more than a dark “halo.” Inorder to cause the entire galaxy to revolve aroundit in the same way that planets revolve around theSun, the Milky Way must contain a staggeringquantity of invisible mass.

Dark matter may be the substance at theheart of a black hole, a collapsed star whose massis so great that its gravitational field preventslight from escaping. It is possible, also, that darkmatter is made up of neutrinos, subatomic parti-cles thought to be massless. Perhaps, the theorygoes, neutrinos actually possess tiny quantities ofmass, and therefore in huge groups—a moletimes a mole times a mole—they might possessappreciable mass.

In addition, dark matter may be the decidingfactor as to whether the universe is infinite. Themore mass the universe possesses, the greater itsoverall gravity, and if the mass of the universe isabove a certain point, it will eventually begin tocontract. This, of course, would mean that it isfinite; on the other hand, if the mass is below thisthreshold, it will continue to expand indefinitely.The known mass of the universe is nowhere nearthat threshold—but, because the nature of darkmatter is still largely unknown, it is not possibleyet to say what effect its mass may have on thetotal equation.

A “NEW” FORM OF MATTER?

Physicists at the Joint Institute of LaboratoryAstrophysics in Boulder, Colorado, in 1995revealed a highly interesting aspect of atomicbehavior at temperatures approaching absolutezero. Some 70 years before, Einstein had predict-

ed that, at extremely low temperatures, atomswould fuse to form one large “superatom.” Thishypothesized structure was dubbed the Bose-Einstein Condensate (BEC) after Einstein andSatyendranath Bose (1894-1974), an Indianphysicist whose statistical methods contributedto the development of quantum theory.

Cooling about 2,000 atoms of the elementrubidium to a temperature just 170 billionths ofa degree Celsius above absolute zero, the physi-cists succeeded in creating an atom 100 microm-eters across—still incredibly small, but vast incomparison to an ordinary atom. The super-atom, which lasted for about 15 seconds, cooleddown all the way to just 20 billionths of a degreeabove absolute zero. The Colorado physicistswon the Nobel Prize in physics in 1997 for theirwork.

In 1999, researchers in a lab at Harvard Uni-versity also created a superatom of BEC, andused it to slow light to just 38 MPH (60.8km/h)—about 0.02% of its ordinary speed.Dubbed a “new” form of matter, the BEC maylead to a greater understanding of quantummechanics, and may aid in the design of smaller,more powerful computer chips.

States and Phases and InBetween

At places throughout this essay, references havebeen made variously to “phases” and “states” ofmatter. This is not intended to confuse, butrather to emphasize a particular point. Solids,liquids, and gases are referred to as “phases,”because substances on Earth—water, forinstance—regularly move from one phase toanother. This change, a function of temperature,is called (aptly enough) “change of phase.”

There is absolutely nothing incorrect inreferring to “states of matter.” But “phases ofmatter” is used in the present context as a meansof emphasizing the fact that most substances, atthe appropriate temperature and pressure, can besolid, liquid, or gas. In fact, a substance may evenbe solid, liquid, and gas.

An Analogy to Human Life

The phases of matter can be likened to the phas-es of a person’s life: infancy, babyhood, child-hood, adolescence, adulthood, old age. The tran-sition between these stages is indefinite, yet it is



Structureof Matter

easy enough to say when a person is at a certainstage.

At the transition point between adolescenceand adulthood—say, at seventeen years old—ayoung person may say that she is an adult, buther parents may insist that she is still an adoles-cent or a child. And indeed, she might qualify aseither. On the other hand, when she is thirty, itwould be ridiculous to assert that she is anythingother than an adult.

At the same time, a person at a certain agemay exhibit behaviors typically associated withanother age. A child, for instance, may behavelike an adult, or an adult like a baby. One inter-esting example of this is the relationship betweenage two and late adolescence. In both cases, theperson is in the process of individualizing, devel-oping an identity separate from that of his or herparents—yet clearly, there are also plenty of dif-ferences between a two-year-old and a seventeen-year-old.

As with the transitional phases in humanlife, in the borderline pressure levels and temper-atures for phases of matter it is sometimes diffi-cult to say, for instance, if a substance is fully aliquid or fully a gas. On the other hand, at a cer-tain temperature and pressure level, a substance

clearly is what it is: water at very low temperature

and pressure, for instance, is indisputably ice—

just as an average thirty-year-old is obviously an

adult. As for the second observation, that a per-

son at one stage in life may reflect characteristics

of another stage, this too is reflected in the

behavior of matter.

LIQUID CRYSTALS. A liquid crystal

is a substance that, over a specific range of tem-

perature, displays properties both of a liquid and

a solid. Below this temperature range, it is

unquestionably a solid, and above this range it is

just as obviously a liquid. In between, however,

liquid crystals exhibit a strange solid-liquid

behavior: like a liquid, their particles flow, but

like a solid, their molecules maintain specific

crystalline arrangements.

Long, wide, and placed alongside one anoth-

er, liquid crystal molecules exhibit interesting

properties in response to light waves. The speed

of light through a liquid crystal actually varies,

depending on whether the light is traveling along

the short or long sides of the molecules. These

differences in light speed may lead to a change in

the direction of polarization, or the vibration of

light waves.


THE RESPONSE OF LIQUID CRYSTALS TO LIGHT MAKES THEM USEFUL IN THE DISPLAYS USED ON LAPTOP COMPUT-ERS. (AFP/Corbis. Reproduced by permission.)


Structureof Matter


ATOM: The smallest particle of a chem-

ical element. An atom can exist either alone

or in combination with other atoms in a

molecule. Atoms are made up of protons,

neutrons, and electrons. In most cases, the

electrical charges in atoms cancel out one

another; but when an atom loses one or

more electrons, and thus has a net charge,

it becomes an ion.

CHEMICAL COMPOUND: A sub-

stance made up of atoms of more than one

chemical element. These atoms are usually

joined in molecules.

CHEMICAL ELEMENT: A substance

made up of only one kind of atom.







CONSERVATION OF MASS: A phys-

ical principle which states that total mass is

constant, and is unaffected by factors such

as position, velocity, or temperature, in any

system that does not exchange any matter

with its environment. Unlike the other

conservation laws, however, conservation

of mass is not universally applicable, but

applies only at speeds significant lower

than that of light—186,000 mi (297,600

km) per second. Close to the speed of light,

mass begins converting to energy.








ELECTRON: Negatively charged parti-

cles in an atom. Electrons, which spin

around the nucleus of protons and neu-

trons, constitute a very small portion of the

atom’s mass. In most atoms, the number of

electrons and protons is the same, thus

canceling out one another. When an atom

loses one or more electrons, however—

thus becoming an ion—it acquires a net

electrical charge.




another.


liquid, that tends to flow, and that con-

forms to the shape of its container. Unlike

solids, fluids are typically uniform in

molecular structure for instance, one mol-

ecule of water is the same as another water

molecule.

GAS: A phase of matter in which mole-

cules exert little or no attraction toward

one another, and therefore move at high

speeds.

ION: An atom that has lost or gained

one or more electrons, and thus has a net

electrical charge.

LIQUID: A phase of matter in which

molecules exert moderate attractions

toward one another, and therefore move at

moderate speeds.



atoms; and is ultimately (at speeds

approaching that of light) convertible to

energy. There are several phases of matter,

including solids, liquids, and gases.

KEY TERMS


Structureof Matter


The cholesteric class of liquid crystals is sonamed because the spiral patterns of lightthrough the crystal are similar to those whichappear in cholesterols. Depending on the physi-cal properties of a cholesteric liquid crystal, onlycertain colors may be reflected. The response ofliquid crystals to light makes them useful in liq-uid crystal displays (LCDs) found on laptopcomputer screens, camcorder views, and in otherapplications.

In some cholesteric liquid crystals, high tem-peratures lead to a reflection of shorter visiblelight waves, and lower temperatures to a displayof longer visible waves. Liquid crystal thermome-ters thus show red when cool, and blue as theyare warmed. This may seem a bit unusual tosomeone who does not understand why the ther-

mometer displays those colors, since people typ-ically associate red with heat and blue with cold.

THE TRIPLE POINT. A liquid crys-tal exhibits aspects of both liquid and solid, andthus, at certain temperatures may be classifiedwithin the crystalline quasi-state of matter. Onthe other hand, the phenomenon known as thetriple point shows how an ordinary substance,such as water or carbon dioxide, can actually be aliquid, solid, and vapor—all at once.

Again, water—the basis of all life on Earth—is an unusual substance in many regards. Forinstance, most people associate water as a gas orvapor (that is, steam) with very high tempera-tures. Yet, at a level far below normal atmospher-ic pressure, water can be a vapor at temperaturesas low as -4°F (-20 °C). (All of the pressure values


(more than 600 billion trillion) molecules.

Their size makes it impossible to weigh

molecules in relatively small quantities;

hence the mole facilitates comparisons of

mass between substances.

MOLECULE: A group of atoms, usual-

ly of more than one chemical element,

joined in a structure.

NEUTRON: A subatomic particle that

has no electrical charge. Neutrons are

found at the nucleus of an atom, alongside

protons.

PHASES OF MATTER: The various

forms of material substance (matter),

which are defined primarily in terms of the

behavior exhibited by their atomic or

molecular structures. On Earth, three prin-

cipal phases of matter exist, namely solid,

liquid, and gas. Other forms of matter

include plasma.

PLASMA: One of the phases of matter,

closely related to gas. Plasma apparently

does not exist on Earth, but is found, for

instance, in stars and comets’ tails. Con-

taining neither atoms nor molecules, plas-

ma is made up of electrons and positive

ions.

PROTON: A positively charged particle

in an atom. Protons and neutrons, which

together form the nucleus around which

electrons orbit, have approximately the

same mass—a mass that is many times

greater than that of an electron.

SOLID: A phase of matter in which

molecules exert strong attractions toward

one another, and therefore move slowly.







ronment.



Structureof Matter

in the discussion of water at or near the triplepoint are far below atmospheric norms: the pres-sure at which water would turn into a vapor at -4°F, for instance, is about 1/1000 normal atmos-pheric pressure.)

As everyone knows, at relatively low temper-atures, water is a solid—ice. But if the pressure ofice falls below a very low threshold, it will turnstraight into a gas (a process known as sublima-tion) without passing through the liquid stage.On the other hand, by applying enough pressure,it is possible to melt ice, and thereby transform itfrom a solid to a liquid, at temperatures below itsnormal freezing point.

The phases and changes of phase for a givensubstance at specific temperatures and pressurelevels can be plotted on a graph called a phasediagram, which typically shows temperature onthe x-axis and pressure on the y-axis. The phasediagram of water shows a line between the solidand liquid states that is almost, but not quite,exactly perpendicular to the x-axis: it slopesslightly upward to the left, reflecting the fact thatsolid ice turns into water with an increase ofpressure.

Whereas the line between solid and liquidwater is more or less straight, the divisionbetween these two states and water vapor iscurved. And where the solid-liquid line intersectsthe vaporization curve, there is a place called thetriple point. Just below freezing, in conditions

equivalent to about 0.7% of normal atmosphericpressure, water is a solid, liquid, and vapor all atonce.

WHERE TO LEARN MORE

Biel, Timothy L. Atom: Building Blocks of Matter. SanDiego, CA: Lucent Books, 1990.

Feynman, Richard. Six Easy Pieces: Essentials of PhysicsExplained by Its Most Brilliant Teacher. New intro-duction by Paul Davies. Cambridge, MA: PerseusBooks, 1995.

Hewitt, Sally. Solid, Liquid, or Gas? New York: Children’sPress, 1998.

“High School Chemistry Table of Contents—Solids andLiquids” Homeworkhelp.com (Web site). <http://www.homeworkhelp.com/homeworkhelp/freemember/text/chem/hig h/topic09.html> (April 10, 2001).

“Matter: Solids, Liquids, Gases.” Studyweb (Web site).<http://www.studyweb.com/links/4880.html> (April10, 2001).

“The Molecular Circus” (Web site). <http://www.cpo.com/Weblabs/circus.html> (April 10, 2001).

Paul, Richard. A Handbook to the Universe: Explorationsof Matter, Energy, Space, and Time for Beginning Sci-entific Thinkers. Chicago: Chicago Review Press,1993.

“Phases of Matter” (Web site). <http://pc65.frontier.osrhe.edu/hs/science/pphase.html> (April 10, 2001).

Royston, Angela. Solids, Liquids, and Gasses. Chicago:Heinemann Library, 2001.

Wheeler, Jill C. The Stuff Life’s Made Of: A Book AboutMatter. Minneapolis, MN: Abdo & Daughters Pub-lishing, 1996.




THERMODYNAM ICSThermodynamics

CONCEPTThermodynamics is the study of the relation-

ships between heat, work, and energy. Though

rooted in physics, it has a clear application to

chemistry, biology, and other sciences: in a sense,

physical life itself can be described as a con-

tinual thermodynamic cycle of transformations

between heat and energy. But these transforma-

tions are never perfectly efficient, as the second

law of thermodynamics shows. Nor is it possible

to get “something for nothing,” as the first law of

thermodynamics demonstrates: the work output

of a system can never be greater than the net

energy input. These laws disappointed hopeful

industrialists of the early nineteenth century,

many of whom believed it might be possible to

create a perpetual motion machine. Yet the laws

of thermodynamics did make possible such high-

ly useful creations as the internal combustion

engine and the refrigerator.

HOW IT WORKS

Historical Context

Machines were, by definition, the focal point of

the Industrial Revolution, which began in Eng-

land during the late eighteenth and early nine-

teenth centuries. One of the central preoccupa-

tions of both scientists and industrialists thus

became the efficiency of those machines: the

ratio of output to input. The more output that

could be produced with a given input, the greater

the production, and the greater the economic

advantage to the industrialists and (presumably)

society as a whole.

At that time, scientists and captains ofindustry still believed in the possibility of a per-petual motion machine: a device that, uponreceiving an initial input of energy, would con-tinue to operate indefinitely without furtherinput. As it emerged that work could be convert-ed into heat, a form of energy, it began to seempossible that heat could be converted directlyback into work, thus making possible the opera-tion of a perfectly reversible perpetual motionmachine. Unfortunately, the laws of thermody-namics dashed all those dreams.

SNOW’S EXPLANATION. Sometexts identify two laws of thermodynamics, whileothers add a third. For these laws, which will bediscussed in detail below, British writer and sci-entist C. P. Snow (1905-1980) offered a witty,nontechnical explanation. In a 1959 lecture pub-lished as The Two Cultures and the Scientific Rev-olution, Snow compared the effort to transformheat into energy, and energy back into heat again,as a sort of game.

The first law of thermodynamics, in Snow’sversion, teaches that the game is impossible towin. Because energy is conserved, and thus, itsquantities throughout the universe are always thesame, one cannot get “something for nothing” byextracting more energy than one put into amachine.

The second law, as Snow explained it, offersan even more gloomy prognosis: not only is itimpossible to win in the game of energy-workexchanges, one cannot so much as break even.Though energy is conserved, that does not meanthe energy is conserved within the machinewhere it is used: mechanical systems tend towardincreasing disorder, and therefore, it is impossi-


Thermo-dynamics


ble for the machine even to return to the originallevel of energy.

The third law, discovered in 1905, seems tooffer a possibility of escape from the conditionsimposed in the second law: at the temperature ofabsolute zero, this tendency toward breakdowndrops to a level of zero as well. But the third lawonly proves that absolute zero cannot beattained: hence, Snow’s third observation, that itis impossible to step outside the boundaries ofthis unwinnable heat-energy transformationgame.

Work and Energy

Work and energy, discussed at length elsewherein this volume, are closely related. Work is theexertion of force over a given distance to displaceor move an object. It is thus the product of forceand distance exerted in the same direction. Ener-gy is the ability to accomplish work.

There are many manifestations of energy,including one of principal concern in the presentcontext: thermal or heat energy. Other manifes-tations include electromagnetic (sometimesdivided into electrical and magnetic), sound,chemical, and nuclear energy. All these, however,can be described in terms of mechanical energy,

which is the sum of potential energy—the ener-

gy that an object has due to its position—and

kinetic energy, or the energy an object possesses

by virtue of its motion.

MECHANICAL ENERGY. Kinetic

energy relates to heat more clearly than does

potential energy, discussed below; however, it is

hard to discuss the one without the other. To use

a simple example—one involving mechanical

energy in a gravitational field—when a stone is

held over the edge of a cliff, it has potential ener-

gy. Its potential energy is equal to its weight

(mass times the acceleration due to gravity) mul-

tiplied by its height above the bottom of the

canyon below. Once it is dropped, it acquires

kinetic energy, which is the same as one-half its

mass multiplied by the square of its velocity.

Just before it hits bottom, the stone’s kinetic

energy will be at a maximum, and its potential

energy will be at a minimum. At no point can the

value of its kinetic energy exceed the value of the

potential energy it possessed before it fell: the

mechanical energy, or the sum of kinetic and

potential energy, will always be the same, though

the relative values of kinetic and potential energy

may change.

A WOMAN WITH A SUNBURNED NOSE. SUNBURNS ARE CAUSED BY THE SUN’S ULTRAVIOLET RAYS. (Photograph by Lester

V. Bergman/Corbis. Reproduced by permission.)


Thermo-dynamics

system. Rather than being “energy-in-residence,”heat is “energy-in-transit.”

This may be a little hard to comprehend, butit can be explained in terms of the stone-and-cliffkinetic energy illustration used above. Just as asystem can have no kinetic energy unless some-thing is moving within it, heat exists only whenenergy is being transferred. In the above illustra-tion of mechanical energy, when the stone wassitting on the ground at the top of the cliff, it wasanalogous to a particle of internal energy in bodyA. When, at the end, it was again on theground—only this time at the bottom of thecanyon—it was the same as a particle of internalenergy that has transferred to body B. Inbetween, however, as it was falling from one tothe other, it was equivalent to a unit of heat.

TEMPERATURE. In everyday life, peo-ple think they know what temperature is: a meas-ure of heat and cold. This is wrong for two rea-sons: first, as discussed below, there is no suchthing as “cold”—only an absence of heat. So,then, is temperature a measure of heat? Wrongagain.

Imagine two objects, one of mass M and theother with a mass twice as great, or 2M. Bothhave a certain temperature, and the question is,how much heat will be required to raise theirtemperature by equal amounts? The answer isthat the object of mass 2M requires twice asmuch heat to raise its temperature the sameamount. Therefore, temperature cannot possiblybe a measure of heat.

What temperature does indicate is the direc-tion of internal energy flow between bodies, andthe average molecular kinetic energy in transitbetween those bodies. More simply, though a bitless precisely, it can be defined as a measure ofheat differences. (As for the means by which athermometer indicates temperature, that isbeyond the parameters of the subject at hand; itis discussed elsewhere in this volume, in the con-text of thermal expansion.)

MEASURING TEMPERATURE

AND HEAT. Temperature, of course, can bemeasured either by the Fahrenheit or Centigradescales familiar in everyday life. Another tempera-ture scale of relevance to the present discussion isthe Kelvin scale, established by William Thom-son, Lord Kelvin (1824-1907).

Drawing on the discovery made by Frenchphysicist and chemist J. A. C. Charles (1746-


CONSERVATION OF ENERGY.

What mechanical energy does the stone possessafter it comes to rest at the bottom of the canyon?In terms of the system of the stone droppingfrom the cliffside to the bottom, none. Or, to putit another way, the stone has just as muchmechanical energy as it did at the very beginning.Before it was picked up and held over the side ofthe cliff, thus giving it potential energy, it waspresumably sitting on the ground away from theedge of the cliff. Therefore, it lacked potentialenergy, inasmuch as it could not be “dropped”from the ground.

If the stone’s mechanical energy—at least inrelation to the system of height between the cliffand the bottom—has dropped to zero, where didit go? A number of places. When it hit, the stonetransferred energy to the ground, manifested asheat. It also made a sound when it landed, andthis also used up some of its energy. The stoneitself lost energy, but the total energy in the uni-verse was unaffected: the energy simply left thestone and went to other places. This is an exam-ple of the conservation of energy, which is close-ly tied to the first law of thermodynamics.

But does the stone possess any energy at thebottom of the canyon? Absolutely. For one thing,its mass gives it an energy, known as mass or restenergy, that dwarfs the mechanical energy in thesystem of the stone dropping off the cliff. (Massenergy is the other major form of energy, asidefrom kinetic and potential, but at speeds wellbelow that of light, it is released in quantities thatare virtually negligible.) The stone may have elec-tromagnetic potential energy as well; and ofcourse, if someone picks it up again, it will havegravitational potential energy. Most important tothe present discussion, however, is its internalkinetic energy, the result of vibration among themolecules inside the stone.

Heat and Temperature

Thermal energy, or the energy of heat, is really aform of kinetic energy between particles at theatomic or molecular level: the greater the move-ment of these particles, the greater the thermalenergy. Heat itself is internal thermal energy thatflows from one body of matter to another. It isnot the same as the energy contained in a sys-tem—that is, the internal thermal energy of the


Thermo-dynamics

1823), that gas at 0°C (32°F) regularly contractsby about 1/273 of its volume for every Celsiusdegree drop in temperature, Thomson derivedthe value of absolute zero (discussed below) as -273.15°C (-459.67°F). The Kelvin and Celsiusscales are thus directly related: Celsius tempera-tures can be converted to Kelvins (for which nei-ther the word nor the symbol for “degree” areused) by adding 273.15.

MEASURING HEAT AND HEAT

CAPACITY. Heat, on the other hand, is meas-ured not by degrees (discussed along with thethermometer in the context of thermal expan-sion), but by the same units as work. Since ener-gy is the ability to perform work, heat or workunits are also units of energy. The principal unitof energy in the SI or metric system is the joule(J), equal to 1 newton-meter (N • m), and theprimary unit in the British or English system isthe foot-pound (ft • lb). One foot-pound is equalto 1.356 J, and 1 joule is equal to 0.7376 ft • lb.

Two other units are frequently used for heatas well. In the British system, there is the Btu, orBritish thermal unit, equal to 778 ft • lb. or 1,054J. Btus are often used in reference, for instance, tothe capacity of an air conditioner. An SI unit thatis also used in the United States—where Britishmeasures typically still prevail—is the kilocalo-rie. This is equal to the heat that must be addedto or removed from 1 kilogram of water tochange its temperature by 1°C. As its name sug-gests, a kilocalorie is 1,000 calories. A calorie isthe heat required to change the temperature in 1gram of water by 1°C—but the dietary Calorie(capital C), with which most people are familiaris the same as the kilocalorie.

A kilocalorie is identical to the heat capacityfor one kilogram of water. Heat capacity (some-times called specific heat capacity or specificheat) is the amount of heat that must be addedto, or removed from, a unit of mass for a givensubstance to change its temperature by 1°C. thisis measured in units of J/kg • °C (joules per kilo-gram-degree Centigrade), though for the sake ofconvenience it is typically rendered in terms ofkilojoules (1,000 joules): kJ/kg • °c. Expressedthus, the specific heat of water 4.185—which isfitting, since a kilocalorie is equal to 4.185 kJ.Water is unique in many aspects, with regard tospecific heat, in that it requires far more heat toraise the temperature of water than that of mer-cury or iron.


Hot and “Cold”

Earlier, it was stated that there is no such thing as“cold”—a statement hard to believe for someonewho happens to be in Buffalo, New York, orInternational Falls, Minnesota, during a Febru-ary blizzard. Certainly, cold is real as a sensoryexperience, but in physical terms, cold is not a“thing”—it is simply the absence of heat.

People will say, for instance, that they put anice cube in a cup of coffee to cool it, but in termsof physics, this description is backward: whatactually happens is that heat flows from the cof-fee to the ice, thus raising its temperature. Theresulting temperature is somewhere between thatof the ice cube and the coffee, but one cannotobtain the value simply by averaging the twotemperatures at the beginning of the transfer.

For one thing, the volume of the water in theice cube is presumably less than that of the waterin the coffee, not to mention the fact that theirdiffering chemical properties may have someminor effect on the interaction. Most important,however, is the fact that the coffee did not simplymerge with the ice: in transferring heat to the icecube, the molecules in the coffee expended someof their internal kinetic energy, losing furtherheat in the process.

COOLING MACHINES. Even cool-ing machines, such as refrigerators and air condi-tioners, actually use heat, simply reversing theusual process by which particles are heated. Therefrigerator pulls heat from its inner compart-ment—the area where food and other perish-ables are stored—and transfers it to the regionoutside. This is why the back of a refrigerator iswarm.

Inside the refrigerator is an evaporator, intowhich heat from the refrigerated compartmentflows. The evaporator contains a refrigerant—agas, such as ammonia or Freon 12, that readilyliquifies. This gas is released into a pipe from theevaporator at a low pressure, and as a result, itevaporates, a process that cools it. The pipe takesthe refrigerant to the compressor, which pumpsit into the condenser at a high pressure. Locatedat the back of the refrigerator, the condenser is along series of pipes in which pressure turns thegas into liquid. As it moves through the condens-



Thermo-dynamics

er, the gas heats, and this heat is released into theair around the refrigerator.

An air conditioner works in a similar man-ner. Hot air from the room flows into the evapo-rator, and a compressor circulates refrigerantfrom the evaporator to a condenser. Behind theevaporator is a fan, which draws in hot air fromthe room, and another fan pushes heat from thecondenser to the outside. As with a refrigerator,the back of an air conditioner is hot because it ismoving heat from the area to be cooled.

Thus, cooling machines do not defy theprinciples of heat discussed above; nor do theydefy the laws of thermodynamics that will be dis-cussed at the conclusion of this essay. In accor-dance with the second law, in order to move heatin the reverse of its usual direction, externalenergy is required. Thus, a refrigerator takes inenergy from a electric power supply (that is, theoutlet it is plugged into), and extracts heat.Nonetheless, it manages to do so efficiently,removing two or three times as much heat fromits inner compartment as the amount of energyrequired to run the refrigerator.

Transfers of Heat

It is appropriate now to discuss how heat is trans-ferred. One must remember, again, that in orderfor heat to be transferred from one point toanother, there must be a difference of tempera-ture between those two points. If an object orsystem has a uniform level of internal thermalenergy—no matter how “hot” it may be in ordi-nary terms—no heat transfer is taking place.

Heat is transferred by one of three methods:conduction, which involves successive molecularcollisions; convection, which requires the motionof hot fluid from one place to another; or radia-tion, which involves electromagnetic waves andrequires no physical medium for the transfer.

CONDUCTION. Conduction takesplace best in solids and particularly in metals,whose molecules are packed in relatively closeproximity. Thus, when one end of an iron rod isheated, eventually the other end will acquire heatdue to conduction. Molecules of liquid or non-metallic solids vary in their ability to conductheat, but gas—due to the loose attractionsbetween its molecules—is a poor conductor.

When conduction takes place, it is as thougha long line of people are standing shoulder to

shoulder, passing a secret down the line. In thiscase, however, the “secret” is kinetic thermalenergy. And just as the original phrasing of thesecret will almost inevitably become garbled bythe time it gets to the tenth or hundredth person,some energy is lost in the transfer from moleculeto molecule. Thus, if one end of the iron rod issitting in a fire and one end is surrounded by airat room temperature, it is unlikely that the end inthe air will ever get as hot as the end in the fire.

Incidentally, the qualities that make metallicsolids good conductors of heat also make themgood conductors of electricity. In the firstinstance, kinetic energy is being passed frommolecule to molecule, whereas in an electricalfield, electrons—freed from the atoms of whichthey are normally a part—are able to move alongthe line of molecules. Because plastic is much lessconductive than metal, an electrician will use a screwdriver with a plastic handle. Similarly,a metal pan typically has a handle of wood orplastic.

CONVECTION. There is a term, “con-vection oven,” that is actually a redundancy: allovens heat through convection, the principalmeans of transferring heat through a fluid. Inphysics, “fluid” refers both to liquids and gases—anything that tends to flow. Instead of simplymoving heat, as in conduction, convectioninvolves the movement of heated material—thatis, fluid. When air is heated, it displaces cold (thatis, unheated) air in its path, setting up a convec-tion current.

Convection takes place naturally, as forinstance when hot air rises from the land on awarm day. This heated air has a lower densitythan that of the less heated air in the atmosphereabove it, and, therefore, is buoyant. As it rises,however, it loses energy and cools. This cooledair, now more dense than the air around it, sinksagain, creating a repeating cycle.

The preceding example illustrates naturalconvection; the heat of an oven, on the otherhand, is an example of forced convection—a sit-uation in which some sort of pump or mecha-nism moves heated fluid. So, too, is the coolingwork of a refrigerator, though the refrigeratormoves heat in the opposite direction.

Forced convection can also take place withina natural system. The human heart is a pump,and blood carries excess heat generated by thebody to the skin. The heat passes through the



Thermo-dynamics

skin by means of conduction, and at the surfaceof the skin, it is removed from the body in anumber of ways, primarily by the cooling evapo-ration of moisture—that is, perspiration.

RADIATION. If the Sun is hot—hotenough to severely burn the skin of a person whospends too much time exposed to its rays—thenwhy is it cold in the upper atmosphere? After all,the upper atmosphere is closer to the Sun. Andwhy is it colder still in the empty space above theatmosphere, which is still closer to the Sun? Thereason is that in outer space there is no mediumfor convection, and in the upper atmosphere,where the air molecules are very far apart, thereis hardly any medium. How, then, does heatcome to the Earth from the Sun? By radiation,which is radically different from conduction orconvection. The other two involve ordinary ther-mal energy, but radiation involves electromag-netic energy.

A great deal of “stuff” travels through theelectromagnetic spectrum, discussed in anotheressay in this book: radio waves, microwaves fortelevision and radar, infrared light, visible light, xrays, gamma rays. Though the relatively narrowband of visible-light wavelengths is the only partof the spectrum of which people are aware ineveryday life, other parts—particularly theinfrared and ultraviolet bands—are involved inthe heat one feels from the Sun. (Ultraviolet rays,in fact, cause sunburns.)

Heat by means of radiation is not as “other-worldly” as it might seem: in fact, one does nothave to point to the Sun for examples of it. Anytime an object glows as a result of heat—as forexample, in the case of firelight—that is anexample of radiation. Some radiation is emittedin the form of visible light, but the heat compo-nent is in infrared rays. This also occurs in anincandescent light bulb. In an incandescent bulb,incidentally, much of the energy is lost to the heatof infrared rays, and the efficiency of a fluores-cent bulb lies in the fact that it converts whatwould otherwise be heat into usable light.

The Laws of Thermodynamics

Having explored the behavior of heat, both at themolecular level and at levels more easily per-ceived by the senses, it is possible to discuss thelaws of thermodynamics alluded to throughoutthis essay. These laws illustrate the relationshipsbetween heat and energy examined earlier, and

show, for instance, why a refrigerator or air con-ditioner must have an external source of energyto move heat in a direction opposite to its normalflow.

The story of how these laws came to be dis-covered is a saga unto itself, involving the contri-butions of numerous men in various places overa period of more than a century. In 1791, Swissphysicist Pierre Prevost (1751-1839) put forth histheory of exchanges, stating correctly that allbodies radiate heat. Hence, as noted earlier, thereis no such thing as “cold”: when one holds snowin one’s hand, cold does not flow from the snowinto the hand; rather, heat flows from the hand tothe snow.

Seven years later, an American-British physi-cist named Benjamin Thompson, Count Rum-ford (1753) was boring a cannon with a bluntdrill when he noticed that this action generated agreat deal of heat. This led him to question theprevailing wisdom, which maintained that heatwas a fluid form of matter; instead, Thompsonbegan to suspect that heat must arise from someform of motion.

CARNOT ’S ENGINE. The nextmajor contribution came from the French physi-cist and engineer Sadi Carnot (1796-1832).


BENJAMIN THOMPSON, COUNT RUMFORD. (Illustration by

H. Humphrey. UPI/Corbis-Bettmann. Reproduced by permission.)


Thermo-dynamics

Though he published only one scientific work,Reflections on the Motive Power of Fire (1824), thistreatise caused a great stir in the European scien-tific community. In it, Carnot made the firstattempt at a scientific definition of work,describing it as “weight lifted through a height.”Even more important was his proposal for ahighly efficient steam engine.

A steam engine, like a modern-day internalcombustion engine, is an example of a largerclass of machine called heat engine. A heatengine absorbs heat at a high temperature, per-forms mechanical work, and, as a result, gives offheat a lower temperature. (The reason why thattemperature must be lower is established in thesecond law of thermodynamics.)

For its era, the steam engine was what thecomputer is today: representing the cutting edgein technology, it was the central preoccupation ofthose interested in finding new ways to accom-plish old tasks. Carnot, too, was fascinated by thesteam engine, and was determined to help over-come its disgraceful inefficiency: in operation, asteam engine typically lost as much as 95% of itsheat energy.

In his Reflections, Carnot proposed that themaximum efficiency of any heat engine wasequal to (TH-TL)/TH, where TH is the highestoperating temperature of the machine, and TL

the lowest. In order to maximize this value, TL

has to be absolute zero, which is impossible toreach, as was later illustrated by the third law ofthermodynamics.

In attempting to devise a law for a perfectlyefficient machine, Carnot inadvertently provedthat such a machine is impossible. Yet his workinfluenced improvements in steam enginedesign, leading to levels of up to 80% efficiency.In addition, Carnot’s studies influenced Kelvin—who actually coined the term “thermodynam-ics”—and others.

THE FIRST LAW OF THERMO-

DYNAMICS. During the 1840s, JuliusRobert Mayer (1814-1878), a German physicist,published several papers in which he expoundedthe principles known today as the conservationof energy and the first law of thermodynamics.As discussed earlier, the conservation of energyshows that within a system isolated from all out-side factors, the total amount of energy remainsthe same, though transformations of energyfrom one form to another take place.

The first law of thermodynamics states thisfact in a somewhat different manner. As with theother laws, there is no definitive phrasing;instead, there are various versions, all of whichsay the same thing. One way to express the law isas follows: Because the amount of energy in asystem remains constant, it is impossible to per-form work that results in an energy outputgreater than the energy input. For a heat engine,this means that the work output of the engine,combined with its change in internal energy, isequal to its heat input. Most heat engines, how-ever, operate in a cycle, so there is no net changein internal energy.

Earlier, it was stated that a refrigeratorextracts two or three times as much heat from itsinner compartment as the amount of energyrequired to run it. On the surface, this seems tocontradict the first law: isn’t the refrigerator put-ting out more energy than it received? But theheat it extracts is only part of the picture, and notthe most important part from the perspective ofthe first law.

A regular heat engine, such as a steam orinternal-combustion engine, pulls heat from ahigh-temperature reservoir to a low-temperaturereservoir, and, in the process, work is accom-plished. Thus, the hot steam from the high-tem-perature reservoir makes possible the accom-plishment of work, and when the energy isextracted from the steam, it condenses in thelow-temperature reservoir as relatively coolwater.

A refrigerator, on the other hand, reversesthis process, taking heat from a low-temperaturereservoir (the evaporator inside the cooling com-partment) and pumping it to a high-temperaturereservoir outside the refrigerator. Instead of pro-ducing a work output, as a steam engine does, itrequires a work input—the energy supplied viathe wall outlet. Of course, a refrigerator does pro-duce an “output,” by cooling the food inside, butthe work it performs in doing so is equal to theenergy supplied for that purpose.

THE SECOND LAW OF THER-

MODYNAMICS. Just a few years afterMayer’s exposition of the first law, another Ger-man physicist, Rudolph Julius Emanuel Clausius(1822-1888) published an early version of thesecond law of thermodynamics. In an 1850paper, Clausius stated that “Heat cannot, of itself,pass from a colder to a hotter body.” He refined



Thermo-dynamics

this 15 years later, introducing the concept ofentropy—the tendency of natural systemstoward breakdown, and specifically, the tendencyfor the energy in a system to be dissipated.

The second law of thermodynamics beginsfrom the fact that the natural flow of heat isalways from a high-temperature reservoir to alow-temperature reservoir. As a result, no enginecan be constructed that simply takes heat from asource and performs an equivalent amount ofwork: some of the heat will always be lost. Inother words, it is impossible to build a perfectlyefficient engine.

Though its relation to the first law is obvi-ous, inasmuch as it further defines the limita-tions of machine output, the second law of ther-modynamics is not derived from the first. Else-where in this volume, the first law of thermody-namics—stated as the conservation of energylaw—is discussed in depth, and, in that context,it is in fact necessary to explain how the behaviorof machines in the real world does not contradictthe conservation law.

Even though they mean the same thing, thefirst law of thermodynamics and the conserva-tion of energy law are expressed in different ways.The first law of thermodynamics states that “theglass is half empty,” whereas the conservation ofenergy law shows that “the glass is half full.” Thethermodynamics law emphasizes the bad news:that one can never get more energy out of amachine than the energy put into it. Thus, allhopes of a perpetual motion machine weredashed. The conservation of energy, on the otherhand, stresses the good news: that energy is neverlost.

In this context, the second law of thermody-namics delivers another dose of bad news:though it is true that energy is never lost, theenergy available for work output will never be asgreat as the energy put into a system. A carengine, for instance, cannot transform all of itsenergy input into usable horsepower; some of theenergy will be used up in the form of heat andsound. Though energy is conserved, usable ener-gy is not.

Indeed, the concept of entropy goes farbeyond machines as people normally understandthem. Entropy explains why it is easier to breaksomething than to build it—and why, for eachperson, the machine called the human body will

inevitably break down and die, or cease to func-tion, someday.

THE THIRD LAW OF THERMO-

DYNAMICS. The subject of entropy leadsdirectly to the third law of thermodynamics, for-mulated by German chemist Hermann WalterNernst (1864-1941) in 1905. The third law statesthat at the temperature of absolute zero, entropyalso approaches zero. From this statement,Nernst deduced that absolute zero is thereforeimpossible to reach.

All matter is in motion at the molecularlevel, which helps define the three major phasesof matter found on Earth. At one extreme is agas, whose molecules exert little attractiontoward one another, and are therefore in constantmotion at a high rate of speed. At the other endof the phase continuum (with liquids somewherein the middle) are solids. Because they are closetogether, solid particles move very little, andinstead of moving in relation to one another,they merely vibrate in place. But they do move.

Absolute zero, or 0K on the Kelvin scale oftemperature, is the point at which all molecularmotion stops entirely—or at least, it virtuallystops. (In fact, absolute zero is defined as thetemperature at which the motion of the averageatom or molecule is zero.) As stated earlier,Carnot’s engine achieves perfect efficiency if itslowest temperature is the same as absolute zero;but the second law of thermodynamics showsthat a perfectly efficient machine is impossible.This means that absolute zero is an unreachableextreme, rather like matter exceeding the speedof light, also an impossibility.

This does not mean that scientists do notattempt to come as close as possible to absolutezero, and indeed they have come very close. In1993, physicists at the Helsinki University ofTechnology Low Temperature Laboratory in Fin-land used a nuclear demagnetization device toachieve a temperature of 2.8 • 10-10 K, or0.00000000028K. This means that a fragmentequal to only 28 parts in 100 billion separatedthis temperature from absolute zero—but it wasstill above 0K. Such extreme low-temperatureresearch has a number of applications, mostnotably with superconductors, materials thatexhibit virtually no resistance to electrical cur-rent at very low temperatures.



Thermo-dynamics




the motion of molecules in a solid virtual-

ly ceases. The third law of thermodynamics

establishes the impossibility of actually

reaching absolute zero.

BTU (BRITISH THERMAL UNIT): A

measure of energy or heat in the British

system, often used in reference to the

capacity of an air conditioner. A Btu is

equal to 778 foot-pounds, or 1,054 joules.

CALORIE: A measure of heat or energy

in the SI or metric system, equal to the heat

that must be added to or removed from 1

gram of water to change its temperature by

33.8°F (1°C). The dietary Calorie (capital

C) with which most people are familiar is

the same as the kilocalorie.

CONDUCTION: The transfer of heat

by successive molecular collisions. Con-

duction is the principal means of heat

transfer in solids, particularly metals.







The first law of thermodynamics is the

same as the conservation of energy.








CONVECTION: The transfer of heat

through the motion of hot fluid from one

place to another. In physics, a “fluid” can be

either a gas or a liquid, and convection is

the principal means of heat transfer, for

instance, in air and water.

ENERGY: The ability to accomplish

work.

ENTROPY: The tendency of natural

systems toward breakdown, and specifical-

ly, the tendency for the energy in a system

to be dissipated. Entropy is closely related

to the second law of thermodynamics.

FIRST LAW OF THERMODYNAMICS:

A law which states the amount of energy in

a system remains constant, and therefore it

is impossible to perform work that results

in an energy output greater than the ener-

gy input. This is the same as the conserva-

tion of energy.

FOOT-POUND: The principal unit of

energy—and thus of heat—in the British

or English system. The metric or SI unit is

the joule. A foot-pound (ft • lb) is equal to

1.356 J.



Heat is transferred by three methods con-

duction, convection, and radiation.

HEAT CAPACITY: The amount of heat

that must be added to, or removed from, a

unit of mass of a given substance to change

its temperature by 33.8°F (1°C). Heat

capacity is sometimes called specific heat

capacity or specific heat. A kilocalorie is

the heat capacity of 1 gram of water.

HEAT ENGINE: A machine that

absorbs heat at a high temperature, per-

forms mechanical work, and as a result

gives off heat at a lower temperature.



KEY TERMS


Thermo-dynamics


JOULE: The principal unit of energy—

and thus of heat—in the SI or metric sys-

tem, corresponding to 1 newton-meter (N

• m). A joule (J) is equal to 0.7376 foot-

pounds.








are directly related; hence Celsius tempera-

tures can be converted to Kelvins by adding

273.15.

KILOCALORIE: A measure of heat or

energy in the SI or metric system, equal to

the heat that must be added to or removed

from 1 kilogram of water to change its

temperature by 33.8°F (1°C). As its name

suggests, a kilocalorie is 1,000 calories. The

dietary Calorie (capital C) with which

most people are familiar is the same as the

kilocalorie.

MECHANICAL ENERGY: The sum of

potential energy and kinetic energy in a

given system.


that an object possesses due to its position.

RADIATION: The transfer of heat by

means of electromagnetic waves, which

require no physical medium (e.g., water or

air) for the transfer. Earth receives the Sun’s

heat by means of radiation.

SECOND LAW OF THERMODYNAM-

ICS: A law of thermodynamics which

states that no engine can be constructed

that simply takes heat from a source and

performs an equivalent amount of work.

Some of the heat will always be lost, and

therefore it is impossible to build a perfect-

ly efficient engine. This is a result of the

fact that the natural flow of heat is always

from a high-temperature reservoir to a

low-temperature reservoir—a fact

expressed in the concept of entropy. The

second law is sometimes referred to as “the

law of entropy.”







ronment.

TEMPERATURE: The direction of

internal energy flow between bodies when

heat is being transferred. Temperature

measures the average molecular kinetic

energy in transit between those bodies.








energy.

THIRD LAW OF THERMODYNAMICS:

A law of thermodynamics which states that

at the temperature of absolute zero,

entropy also approaches zero. Zero entropy

would contradict the second law of ther-

modynamics, meaning that absolute zero is

therefore impossible to reach.


given distance to displace or move an

object. Work is thus the product of force

and distance exerted in the same direction.



Thermo-dynamics

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-

Wesley, 1991.

Brown, Warren. Alternative Sources of Energy. Introduc-

tion by Russell E. Train. New York: Chelsea House,

1994.

Encyclopedia of Thermodynamics (Web site).

<http://therion.minpet.unibas.ch/minpet/groups/

thermodict/> (April 12, 2001).

Entropy and the Second Law of Thermodynamics

(Web site). <http://www.2ndlaw.com> (April 12,

2001).

Fleisher, Paul. Matter and Energy: Principles of Matterand Thermodynamics. Minneapolis, MN: Lerner Pub-lications, 2002.


Moran, Jeffrey B. How Do We Know the Laws of Thermo-dynamics? New York: Rosen Publishing Group, 2001.

Santrey, Laurence. Heat. Illustrated by Lloyd Birming-ham. Mahwah, N.J.: Troll Associates, 1985.


“Temperature and Thermodynamics” PhysLINK.com(Web site). <http://www.physlink.com/ae_thermo.cfm> (April 12, 2001).




HEATHeat

CONCEPTHeat is a form of energy—specifically, the energythat flows between two bodies because of differ-ences in temperature. Therefore, the scientificdefinition of heat is different from, and moreprecise than, the everyday meaning. Physicistsworking in the area of thermodynamics studyheat from a number of perspectives, includingspecific heat, or the amount of energy required tochange the temperature of a substance, andcalorimetry, the measurement of changes in heatas a result of physical or chemical changes. Ther-modynamics helps us to understand such phe-nomena as the operation of engines and thegradual breakdown of complexity in physical sys-tems—a phenomenon known as entropy.

HOW IT WORKS

Heat, Work, and Energy

Thermodynamics is the study of the relation-ships between heat, work, and energy. Work is theexertion of force over a given distance to displaceor move an object, and is, thus, the product offorce and distance exerted in the same direction.Energy, the ability to accomplish work, appearsin numerous manifestations—including thermalenergy, or the energy associated with heat.

Thermal and other types of energy, includ-ing electromagnetic, sound, chemical, andnuclear energy, can be described in terms of twoextremes: kinetic energy, or the energy associatedwith movement, and potential energy, or theenergy associated with position. If a spring ispulled back to its maximum point of tension, itspotential energy is also at a maximum; once it isreleased and begins springing through the air to

return to its original position, it begins gainingkinetic energy and losing potential energy.

All manifestations of energy appear in bothkinetic and potential forms, somewhat like theway football teams are organized to play bothoffense or defense. Just as a football team takes anoffensive role when it has the ball, and a defensiverole when the other team has it, a physical systemtypically undergoes regular transformationsbetween kinetic and potential energy, and mayhave more of one or the other, depending onwhat is taking place in the system.

What Heat Is and Is Not

Thermal energy is actually a form of kineticenergy generated by the movement of particles atthe atomic or molecular level: the greater themovement of these particles, the greater the ther-mal energy. Heat is internal thermal energy thatflows from one body of matter to another—or,more specifically, from a system at a higher tem-perature to one at a lower temperature. Thus,temperature, like heat, requires a scientific defi-nition quite different from its common meaning:temperature measures the average molecularkinetic energy of a system, and governs the direc-tion of internal energy flow between them.

Two systems at the same temperature aresaid to be in a state of thermal equilibrium.When this occurs, there is no exchange of heat.Though in common usage, “heat” is an expres-sion of relative warmth or coldness, in physicalterms, heat exists only in transfer between twosystems. What people really mean by “heat” is theinternal energy of a system—energy that is aproperty of that system rather than a property oftransferred internal energy.


Heat means, convection. In fact, there are three meth-ods heat is transferred: conduction, involvingsuccessive molecular collisions and the transferof heat between two bodies in contact; convec-tion, which requires the motion of fluid from oneplace to another; or radiation, which takes placethrough electromagnetic waves and requires nophysical medium, such as water or air, for thetransfer.

CONDUCTION. Solids, particularlymetals, whose molecules are packed relativelyclose together, are the best materials for conduc-tion. Molecules of liquid or non-metallic solidsvary in their ability to conduct heat, but gas is apoor conductor, because of the loose attractionsbetween its molecules.

The qualities that make metallic solids goodconductors of heat, as a matter of fact, also makethem good conductors of electricity. In the con-duction of heat, kinetic energy is passed frommolecule to molecule, like a long line of peoplestanding shoulder to shoulder, passing a secret.(And, just as the original phrasing of the secretbecomes garbled, some kinetic energy isinevitably lost in the series of transfers.)

As for electrical conduction, which takesplace in a field of electric potential, electrons arefreed from their atoms; as a result, they are ableto move along the line of molecules. Becauseplastic is much less conductive than metal, anelectrician uses a screwdriver with a plastic han-dle; similarly, a metal cooking pan typically has awooden or plastic handle.

CONVECTION. Wherever fluids areinvolved—and in physics, “fluid” refers both toliquids and gases—convection is a common formof heat transfer. Convection involves the move-ment of heated material—whether it is air, water,or some other fluid.

Convection is of two types: natural convec-tion and forced convection, in which a pump orother mechanism moves the heated fluid. Whenheated air rises, this is an example of natural con-vection. Hot air has a lower density than that ofthe cooler air in the atmosphere above it, and,therefore, is buoyant; as it rises, however, it losesenergy and cools. This cooled air, now denserthan the air around it, sinks again, creating arepeating cycle that generates wind.

Examples of forced convection include sometypes of ovens and even a refrigerator or air con-ditioner. These two machines both move warm


NO SUCH THING AS “COLD.”

Though the term “cold” has plenty of meaning inthe everyday world, in physics terminology, itdoes not. Cold and heat are analogous to dark-ness and light: again, darkness means somethingin our daily experience, but in physical terms,darkness is simply the absence of light. To speakof cold or darkness as entities unto themselves israther like saying, after spending 20 dollars, “Ihave 20 non-dollars in my pocket.”

If you grasp a snowball in your hand, ofcourse, your hand gets cold. The human mindperceives this as a transfer of cold from the snow-ball, but, in fact, exactly the opposite happens:heat moves from your hand to the snow, and ifenough heat enters the snowball, it will melt. Atthe same time, the departure of heat from yourhand results in a loss of internal energy near thesurface of your hand, which you experience as asensation of coldness.

Transfers of Heat

In holding the snowball, heat passes from thesurface of the hand by one means, conduction,then passes through the snowball by another

IF YOU HOLD A SNOWBALL IN YOUR HAND, AS VANNA

WHITE AND HER SON ARE DOING IN THIS PICTURE, HEAT

WILL MOVE FROM YOUR HAND TO THE SNOWBALL. YOUR

HAND EXPERIENCES THIS AS A SENSATION OF COLD-NESS. (Reuters NewMedia Inc./Corbis. Reproduced by permission.)


Heatair from an interior to an exterior place. Thus,the refrigerator pulls hot air from the compart-ment and expels it to the surrounding room,while an air conditioner pulls heat from a build-ing and releases it to the outside.

But forced convection does not necessarilyinvolve humanmade machines: the human heartis a pump, and blood carries excess heat generat-ed by the body to the skin. The heat passesthrough the skin by means of conduction, and atthe surface of the skin, it is removed from thebody in a number of ways, primarily by the cool-ing evaporation of perspiration.

RADIATION. Outer space, of course, iscold, yet the Sun’s rays warm the Earth, an appar-ent paradox. Because there is no atmosphere inspace, convection is impossible. In fact, heat fromthe Sun is not dependant on any fluid mediumfor its transfer: it comes to Earth by means ofradiation. This is a form of heat transfer signifi-cantly different from the other two, because itinvolves electromagnetic energy, instead of ordi-nary thermal energy generated by the action ofmolecules. Heat from the Sun comes through arelatively narrow area of the light spectrum,including infrared, visible light, and ultra-violet rays.

Every form of matter emits electromagneticwaves, though their presence may not be readilyperceived. Thus, when a metal rod is heated, itexperiences conduction, but part of its heat isradiated, manifested by its glow—visible light.Even when the heat in an object is not visible,however, it may be radiating electromagneticenergy, for instance, in the form of infrared light.And, of course, different types of matter radiatebetter than others: in general, the better an objectis at receiving radiation, the better it is at emit-ting it.

Measuring Heat

The measurement of temperature by degrees inthe Fahrenheit or Celsius scales is a part of every-day life, but measurements of heat are not asfamiliar to the average person. Because heat is aform of energy, and energy is the ability to per-form work, heat is, therefore, measured by thesame units as work.

The principal unit of work or energy in themetric system (known within the scientific com-munity as SI, or the SI system) is the joule.


Abbreviated “J,” a joule is equal to 1 newton-

meter (N • m). The newton is the SI unit of force,

and since work is equal to force multiplied by

distance, measures of work can also be separated

into these components. For instance, the British

measure of work brings together a unit of dis-

tance, the foot, and a unit of force, the pound. A

foot-pound (ft • lb) is equal to 1.356 J, and 1 joule

is equal to 0.7376 ft • lb.

In the British system, Btu, or British thermal

unit, is another measure of energy used for

machines such as air conditioners. One Btu is

equal to 778 ft • lb or 1,054 J. The kilocalorie in

addition to the joule, is an important SI measure

of heat. The amount of energy required to

change the temperature of 1 gram of water by

1°C is called a calorie, and a kilocalorie is equal to

1,000 calories. Somewhat confusing is the fact

that the dietary Calorie (capital C), with which

most people are familiar, is not the same as a

calorie (lowercase C)—rather, a dietary Calorie is

the equivalent of a kilocalorie.

A REFRIGERATOR IS A TYPE OF REVERSE HEAT ENGINE

THAT USES A COMPRESSOR, LIKE THE ONE SHOWN AT

THE BACK OF THIS REFRIGERATOR, TO COOL THE

REFRIGERATOR’S INTERIOR. (Ecoscene/Corbis. Reproduced by

permission.)


Heat REAL-L IFEAPPLICATIONS

Specific Heat

Specific heat is the amount of heat that must beadded to, or removed from, a unit of mass for agiven substance to change its temperature by1°C. Thus, a kilocalorie, because it measures theamount of heat necessary to effect that changeprecisely for a kilogram of water, is identical tothe specific heat for that particular substance inthat particular unit of mass.

The higher the specific heat, the more resist-ant the substance is to changes in temperature.Many metals, in fact, have a low specific heat,making them easy to heat up and cool down.This contributes to the tendency of metals toexpand when heated (a phenomenon also dis-cussed in the Thermal Expansion essay), and,thus, to their malleability.

MEASURING AND CALCULAT-

ING SPECIFIC HEAT. The specific heatof any object is a function of its mass, its compo-sition, and the desired change in temperature.The values of the initial and final temperature arenot important—only the difference betweenthem, which is the temperature change.

The components of specific heat are relatedto one another in the formula Q = mcδT. Here Qis the quantity of heat, measured in joules, whichmust be added. The mass of the object is desig-nated by m, and the specific heat of the particu-lar substance in question is represented with c.The Greek letter delta (δ) designates change, andδT stands for “change in temperature.”

Specific heat is measured in units of J/kg • °C(joules per kilogram-degree Centigrade), thoughfor the sake of convenience, this is usually ren-dered in terms of kilojoules (kJ), or 1,000joules—that is, kJ/kg • °C. The specific heat ofwater is easily derived from the value of a kilo-calorie: it is 4.185, the same number of joulesrequired to equal a kilocalorie.

Calorimetry

The measurement of heat gain or loss as a resultof physical or chemical change is called calorime-try (pronounced kal-IM-uh-tree). Like the word“calorie,” the term is derived from a Latin rootmeaning “heat.”

The foundations of calorimetry go back tothe mid-nineteenth century, but the field owesmuch to scientists’ work that took place over aperiod of about 75 years prior to that time. In1780, French chemist Antoine Lavoisier (1743-1794) and French astronomer and mathemati-cian Pierre Simon Laplace (1749-1827) had useda rudimentary ice calorimeter for measuring theheats in formations of compounds. Around thesame time, Scottish chemist Joseph Black (1728-1799) became the first scientist to make a cleardistinction between heat and temperature.

By the mid-1800s, a number of thinkers hadcome to the realization that—contrary to pre-vailing theories of the day—heat was a form ofenergy, not a type of material substance. Amongthese were American-British physicist BenjaminThompson, Count Rumford (1753-1814) andEnglish chemist James Joule (1818-1889)—forwhom, of course, the joule is named.

Calorimetry as a scientific field of studyactually had its beginnings with the work ofFrench chemist Pierre-Eugene Marcelin Berth-elot (1827-1907). During the mid-1860s, Berth-elot became intrigued with the idea of measuringheat, and by 1880, he had constructed the firstreal calorimeter.

CALORIMETERS. Essential tocalorimetry is the calorimeter, which can be anydevice for accurately measuring the temperatureof a substance before and after a change occurs. Acalorimeter can be as simple as a styrofoam cup.Its quality as an insulator, which makes styro-foam ideal for holding in the warmth of coffeeand protecting the hand from scalding as well,also makes styrofoam an excellent material forcalorimetric testing. With a styrofoam calorime-ter, the temperature of the substance inside thecup is measured, a reaction is allowed to takeplace, and afterward, the temperature is meas-ured a second time.

The most common type of calorimeter usedis the bomb calorimeter, designed to measure theheat of combustion. Typically, a bomb calorime-ter consists of a large container filled with water,into which is placed a smaller container, the com-bustion crucible. The crucible is made of metal,having thick walls with an opening throughwhich oxygen can be introduced. In addition, thecombustion crucible is designed to be connectedto a source of electricity.



HeatIn conducting a calorimetric test using abomb calorimeter, the substance or object to bestudied is placed inside the combustion crucibleand ignited. The resulting reaction usually occursso quickly that it resembles the explosion of abomb—hence, the name “bomb calorimeter.”Once the “bomb” goes off, the resulting transferof heat creates a temperature change in the water,which can be readily gauged with a thermometer.

To study heat changes at temperatures high-er than the boiling point of water (212°F or100°C), physicists use substances with higherboiling points. For experiments involvingextremely large temperature ranges, an aneroid(without liquid) calorimeter may be used. In thiscase, the lining of the combustion crucible mustbe of a metal, such as copper, with a high coeffi-cient or factor of thermal conductivity.

Heat Engines

The bomb calorimeter that Berthelot designed in1880 measured the caloric value of fuels, and wasapplied to determining the thermal efficiency ofa heat engine. A heat engine is a machine thatabsorbs heat at a high temperature, performsmechanical work, and as a result, gives off heat ata lower temperature.

The desire to create efficient heat enginesspurred scientists to a greater understanding ofthermodynamics, and this resulted in the laws ofthermodynamics, discussed at the conclusion ofthis essay. Their efforts were intimately connect-ed with one of the greatest heat engines ever cre-ated, a machine that literally powered the indus-trialized world during the nineteenth century:the steam engine.

HOW A STEAM ENGINE WORKS.

Like all heat engines (except reverse heat enginessuch as the refrigerator, discussed below), a steamengine pulls heat from a high-temperature reser-voir to a low-temperature reservoir, and in theprocess, work is accomplished. The hot steamfrom the high-temperature reservoir makes pos-sible the accomplishment of work, and when theenergy is extracted from the steam, the steamcondenses in the low-temperature reservoir,becoming relatively cool water.

A steam engine is an external-combustionengine, as opposed to the internal-combustionengine that took its place at the forefront ofindustrial technology at the beginning of thetwentieth century. Unlike an internal-combus-

tion engine, a steam engine burns its fuel outsidethe engine. That fuel may be simply firewood,which is used to heat water and create steam. Thethermal energy of the steam is then used topower a piston moving inside a cylinder, thus,converting thermal energy to mechanical energyfor purposes such as moving a train.

EVOLUTION OF STEAM POW-

ER. As with a number of advanced concepts inscience and technology, the historical roots of thesteam engine can be traced to the Greeks, who—just as they did with ideas such as the atom or theSun-centered model of the universe—thoughtabout it, but failed to develop it. The great inven-tor Hero of Alexandria (c. 65-125) actually creat-ed several steam-powered devices, but he per-ceived these as mere novelties, hardly worthy ofscientific attention. Though Europeans adoptedwater power, as, for instance, in waterwheels,during the late ancient and medieval periods,further progress in steam power did not occurfor some 1,500 years.

Following the work of French physicistDenis Papin (1647-1712), who invented the pres-sure cooker and conducted the first experimentswith the use of steam to move a piston, Englishengineer Thomas Savery (c. 1650-1715) built thefirst steam engine. Savery had abandoned the useof the piston in his machine, but another Englishengineer, Thomas Newcomen (1663-1729), rein-troduced the piston for his own steam-enginedesign.

Then in 1763, a young Scottish engineernamed James Watt (1736-1819) was repairing aNewcomen engine and became convinced hecould build a more efficient model. His steamengine, introduced in 1769, kept the heating andcooling processes separate, eliminating the needfor the engine to pause in order to reheat. Theseand other innovations that followed—includingthe introduction of a high-pressure steam engineby English inventor Richard Trevithick (1771-1833)—transformed the world.

CARNOT PROVIDES THEORET-

ICAL UNDERSTANDING. The menwho developed the steam engine were mostlypractical-minded figures who wanted only tobuild a better machine; they were not particular-ly concerned with the theoretical explanation forits workings. Then in 1824, a French physicistand engineer by the name of Sadi Carnot (1796-1832) published his sole work, the highly influ-



Heat ential Reflections on the Motive Power of Fire(1824), in which he discussed heat engines scien-tifically.

In Reflections, Carnot offered the first defini-tion of work in terms of physics, describing it as“weight lifted through a height.” Analyzing Watt’ssteam engine, he also conducted groundbreakingstudies in the nascent science of thermodynam-ics. Every heat engine, he explained, has a theo-retical limit of efficiency related to the tempera-ture difference in the engine: the greater the difference between the lowest and highest tem-perature, the more efficient the engine.

Carnot’s work influenced the developmentof more efficient steam engines, and also had animpact on the studies of other physicists investi-gating the relationship between work, heat, andenergy. Among these was William Thomson,Lord Kelvin (1824-1907). In addition to coiningthe term “thermodynamics,” Kelvin developedthe Kelvin scale of absolute temperature andestablished the value of absolute zero, equal to -273.15°C or -459.67°F.

According to Carnot’s theory, maximumeffectiveness was achieved by a machine thatcould reach absolute zero. However, later devel-opments in the understanding of thermodynam-ics, as discussed below, proved that both maxi-mum efficiency and absolute zero are impossibleto attain.

REVERSE HEAT ENGINES. It iseasy to understand that a steam engine is a heatengine: after all, it produces heat. But how is itthat a refrigerator, an air conditioner, and othercooling machines are also heat engines? More-over, given the fact that cold is the absence of heatand heat is energy, one might ask how a refriger-ator or air conditioner can possibly use energy toproduce cold, which is the same as the absence ofenergy. In fact, cooling machines simply reversethe usual process by which heat engines operate,and for this reason, they are called “reverse heatengines.” Furthermore, they use energy to extractheat.

A steam engine takes heat from a high-tem-perature reservoir—the place where the water isturned into steam—and uses that energy to pro-duce work. In the process, energy is lost and theheat moves to a low-temperature reservoir, whereit condenses to form relatively cool water. Arefrigerator, on the other hand, pulls heat from alow-temperature reservoir called the evaporator,

into which flows heat from the refrigerated com-partment—the place where food and other perishables are kept. The coolant from the evaporator take this heat to the condenser, ahigh-temperature reservoir at the back of therefrigerator, and in the process it becomes a gas.Heat is released into the surrounding air; this iswhy the back of a refrigerator is hot.

Instead of producing a work output, as asteam engine does, a refrigerator requires a workinput—the energy supplied via the wall outlet.The principles of thermodynamics show thatheat always flows from a high-temperature to alow-temperature reservoir, and reverse heatengines do not defy these laws. Rather, theyrequire an external power source in order toeffect the transfer of heat from a low-tempera-ture reservoir, through the gases in the evapora-tor, to a high-temperature reservoir.

The Laws of Thermodynamics

THE FIRST LAW OF THERMO-

DYNAMICS. There are three laws of ther-modynamics, which provide parameters as to theoperation of thermal systems in general, and heatengines in particular. The history behind the der-ivation of these laws is discussed in the essay onThermodynamics; here, the laws themselves willbe examined in brief form.

The physical law known as conservation ofenergy shows that within a system isolated fromall outside factors, the total amount of energyremains the same, though transformations ofenergy from one form to another take place. Thefirst law of thermodynamics states the same factin a somewhat different manner.

According to the first law of thermodynam-ics, because the amount of energy in a systemremains constant, it is impossible to performwork that results in an energy output greaterthan the energy input. Thus, it could be said thatthe conservation of energy law shows that “theglass is half full”: energy is never lost. On thehand, the first law of thermodynamics shows that“the glass is half empty”: no machine can everproduce more energy than was put into it. Hence,a perpetual motion machine is impossible,because in order to keep a machine running continually, there must be a continual input ofenergy.

THE SECOND LAW OF THER-

MODYNAMICS. The second law of ther-



Heat





ly ceases. The third law of thermodynamics

establishes the impossibility of actually

reaching absolute zero.

BTU (BRITISH THERMAL UNIT): A

measure of energy or heat in the British

system, often used in reference to the

capacity of an air conditioner. A Btu is

equal to 778 foot-pounds, or 1,054 joules.

CALORIE: A measure of heat or energy

in the SI or metric system, equal to the heat

that must be added to or removed from 1

gram of water to change its temperature by

1°C. The dietary Calorie (capital C) with

which most people are familiar is the same

as the kilocalorie.

CALORIMETRY: The measurement of

heat gain or loss as a result of physical or

chemical change.

CONDUCTION: The transfer of heat

by successive molecular collisions. Con-

duction is the principal means of heat

transfer in solids, particularly metals.


law of physics stating that within a system

isolated from all other outside factors, the

total amount of energy remains the same,

though transformations of energy from

one form to another take place. The first

law of thermodynamics is the same as the

conservation of energy.

CONVECTION: The transfer of heat

through the motion of hot fluid from one

place to another. In physics, a “fluid” can be

either a gas or a liquid, and convection is

the principal means of heat transfer, for

instance, in air and water.

ENERGY: The ability to accomplish

work.

ENTROPY: The tendency of natural

systems toward breakdown, and specifical-

ly, the tendency for the energy in a system

to be dissipated. Entropy is closely related

to the second law of thermodynamics.

FIRST LAW OF THERMODYNAMICS:

A law stating that the amount of energy in

a system remains constant, and therefore, it

is impossible to perform work that results

in an energy, output greater than the ener-

gy input. This is the same as the conserva-

tion of energy.

FOOT-POUND: The principal unit of

energy—and, thus, of heat—in the British

or English system. The metric or SI unit is

the joule. A foot-pound (ft • lb) is equal to

1.356 J.



Heat is transferred by three methods con-

duction, convection, and radiation.

HEAT ENGINE: A machine that

absorbs heat at a high temperature, per-

forms mechanical work, and, as a result,

gives off heat at a lower temperature.

JOULE: The principal unit of energy—

and, thus, of heat—in the SI or metric sys-

tem, corresponding to 1 newton-meter

(N • m). A joule (J) is equal to 0.7376 foot-

pounds.

KEY TERMS


Heat











adding 273.15.

KILOCALORIE: A measure of heat or

energy in the SI or metric system, equal to

the heat that must be added to or removed

from 1 kilogram of water to change its

temperature by 1°C. As its name suggests, a

kilocalorie is 1,000 calories. The dietary

Calorie (capital C) with which most people

are familiar, is the same as the kilocalorie.




that an object possesses due to its position.

RADIATION: The transfer of heat by


require no physical medium (for example,

water or air) for the transfer. Earth receives

the Sun’s heat by means of radiation.

SECOND LAW OF THERMODYNAM-

ICS: A law of thermodynamics stating

that no engine can be constructed that

simply takes heat from a source and per-

forms an equivalent amount of work.

Some of the heat will always be lost, and,

therefore, it is impossible to build a

perfectly efficient engine. This is a result of

the fact that the natural flow of heat is

always from a high-temperature reservoir

to a low-temperature reservoir—a fact

expressed in the concept of entropy. The

second law is sometimes referred to as “the

law of entropy.”


modynamics begins from the fact that the natu-

ral flow of heat is always from a high-tempera-

ture to a low-temperature reservoir. As a result,

no engine can be constructed that simply takes

heat from a source and performs an equivalent

amount of work: some of the heat will always be

lost. In other words, it is impossible to build a

perfectly efficient engine.

In effect, the second law of thermodynamics

compounds the “bad news” delivered by the first

law with some even worse news: though it is true

that energy is never lost, the energy available for

work output will never be as great as the energy

put into a system. Linked to the second law is the

concept of entropy, the tendency of natural sys-

tems toward breakdown, and specifically, the ten-

dency for the energy in a system to be dissipated.

“Dissipated” in this context means that the high-

and low-temperature reservoirs approach equal

temperatures, and as this occurs, entropyincreases.

THE THIRD LAW OF THERMO-

DYNAMICS. Entropy also plays a part in thethird law of thermodynamics, which states that atthe temperature of absolute zero, entropy alsoapproaches zero. This might seem to counteractthe “worse news” of the second law, but in fact,what the third law shows is that absolute zero isimpossible to reach.

As stated earlier, Carnot’s engine wouldachieve perfect efficiency if its lowest tempera-ture were the same as absolute zero; but the sec-ond law of thermodynamics shows that a per-fectly efficient machine is impossible. Relativitytheory (which first appeared in 1905, the sameyear as the third law of thermodynamics) showedthat matter can never exceed the speed of light.In the same way, the collective effect of the sec-ond and third laws is to prove that absolute


Heat


zero—the temperature at which molecularmotion in all forms of matter theoretically ceas-es—can never be reached.

WHERE TO LEARN MORE


Bonnet, Robert L and Dan Keen. Science Fair Projects:Physics. Illustrated by Frances Zweifel. New York:Sterling, 1999.

Encyclopedia of Thermodynamics (Web site). <http://therion.minpet.unibas.ch/minpet/groups/thermodict/> (April 12, 2001).

Friedhoffer, Robert. Physics Lab in the Home. Illustratedby Joe Hosking. New York: Franklin Watts, 1997.

Manning, Mick and Brita Granström. Science School.New York: Kingfisher, 1998.


Moran, Jeffrey B. How Do We Know the Laws of Thermo-dynamics? New York: Rosen Publishing Group, 2001.

Santrey, Laurence. Heat. Illustrated by Lloyd Birming-ham. Mahwah, NJ: Troll Associates, 1985.


“Temperature and Thermodynamics” PhysLINK.com(Web site). <http://www.physlink.com/ae_thermo.cfm> (April 12, 2001).

SPECIFIC HEAT: The amount of heat

that must be added to, or removed from, a

unit of mass of a given substance to change

its temperature by 1°C. A kilocalorie is the

specific heat of 1 gram of water.







ronment.

TEMPERATURE: The direction of

internal energy flow between two systems

when heat is being transferred. Tempera-

ture measures the average molecular kinet-

ic energy in transit between those systems.






THERMAL EQUILIBRIUM: The state

that exists when two systems have the same

temperature. As a result, there is no

exchange of heat between them.



energy.

THIRD LAW OF THERMODYNAMICS:

A law of thermodynamics which states that

at the temperature of absolute zero,

entropy also approaches zero. Zero entropy

would contradict the second law of ther-

modynamics, meaning that absolute zero

is, therefore, impossible to reach.


given distance to displace or move an

object. Work is, thus, the product of force

and distance exerted in the same direction.




T EMPER ATURETemperature

CONCEPTTemperature is one of those aspects of the every-day world that seems rather abstract whenviewed from the standpoint of physics. In scien-tific terms, it is not simply a measure of hot andcold, but an indicator of molecular motion andenergy flow. Thermometers measure tempera-ture by a number of means, including the expan-sion that takes place in a medium such as mercu-ry or alcohol. These measuring devices aregauged in several different ways, with scalesbased on the freezing and boiling points ofwater—as well as, in the case of the absolutetemperature scale, the point at which all molecu-lar motion virtually ceases.

HOW IT WORKS

Heat

Energy appears in many forms, including ther-mal energy, or the energy associated with heat.Heat is internal thermal energy that flows fromone body of matter to another—or, more specif-ically, from a system at a higher temperature toone at a lower temperature.

Two systems at the same temperature aresaid to be in a state of thermal equilibrium.When this occurs, there is no exchange of heat.Though people ordinarily speak of “heat” as anexpression of relative warmth or coldness, inphysical terms, heat only exists in transferbetween two systems. It is never somethinginherently part of a system; thus, unless there is atransfer of internal energy, there is no heat, sci-entifically speaking.

HEAT: ENERGY IN TRANSIT.

Thus, heat cannot be said to exist unless there isone system in contact with another system of dif-fering temperature. This can be illustrated by wayof the old philosophical question: “If a tree fallsin the woods when there is no one to hear it, doesit make a sound?” From a physicist’s point ofview, of course, sound waves are emitted whetheror not there is an ear to receive their vibrations;but, consider this same scenario in terms of heat.First, replace the falling tree with a hypotheticalobject possessing a certain amount of internalenergy; then replace sound waves with heat. Inthis case, if this object is not in contact withsomething else that has a different temperature,it “does not make a sound”—in other words, ittransfers no internal energy, and, thus, there is noheat from the standpoint of physics.

This could even be true of two incredibly“hot” objects placed next to one another inside avacuum—an area devoid of matter, including air.If both have the same temperature, there is noheat, only two objects with high levels of internalenergy. Note that a vacuum was specified: assum-ing there was air around them, and that the airwas of a lower temperature, both objects wouldthen be transferring heat to the air.

RELATIVE MOTION BETWEEN

MOLECULES. If heat is internal thermalenergy in transfer, from whence does this energyoriginate? From the movement of molecules.Every type of matter is composed of molecules,and those molecules are in motion relative to oneanother. The greater the amount of relativemotion between molecules, the greater the kinet-ic energy, or the energy of movement, which ismanifested as thermal energy. Thus, “heat”—to


Temperatureuse the everyday term for what physicistsdescribe as thermal energy—is really nothingmore than the result of relative molecularmotion. Thus, thermal energy is sometimes iden-tified as molecular translational energy.

Note that the molecules are in relativemotion, meaning that if one were “standing” ona molecule, one would see the other moleculesmoving. This is not the same as movement on thepart of a large object composed of molecules; inthis case, molecules themselves are not directlyinvolved in relative motion.

Put another way, the movement of Earththrough space is an entirely different type ofmovement from the relative motion of objects onEarth—people, animals, natural forms such asclouds, manmade forms of transportation, andso forth. In this example, Earth is analogous to a“large” item of matter, such as a baseball, astream of water, or a cloud of gas.

The smaller objects on Earth are analogousto molecules, and, in both cases, the motion ofthe larger object has little direct impact on themotion of smaller objects. Hence, as discussed inthe Frame of Reference essay, it is impossible toperceive with one’s senses the fact that Earth isactually hurling through space at incrediblespeeds.

MOLECULAR MOTION AND

PHASES OF MATTER. The relativemotion of molecules determines phase of mat-ter—that is, whether something is a solid, liquid,or gas. When molecules move quickly in relationto one another, they exert a small electromagnet-ic attraction toward one another, and the largermaterial of which they are a part is called a gas. Aliquid, on the other hand, is a type of matter inwhich molecules move at moderate speeds inrelation to one another, and therefore exert amoderate intermolecular attraction.

The kinetic theory of gases relates molecularmotion to energy in gaseous substances. It doesnot work as well in relation to liquids and solids;nonetheless, it is safe to say that—generallyspeaking—a gas has more energy than a liquid,and a liquid more energy than a solid. In a solid,the molecules undergo very little relative motion:instead of bumping into each other, like gas mol-ecules and (to a lesser extent) liquid molecules,solid molecules merely vibrate in place.


Understanding Temperature

As with heat, temperature requires a scientific

definition quite different from its common

meaning. Temperature may be defined as a meas-

ure of the average molecular translational energy

in a system—that is, in any material body.

Because it is an average, the mass or other

characteristics of the body do not matter. A large

quantity of one substance, because it has more

molecules, possesses more thermal energy than a

smaller quantity of that same substance. Since it

has more thermal energy, it transfers more heat

to any body or system with which it is in contact.

Yet, assuming that the substance is exactly the

same, the temperature, as a measure of average

energy, will be the same as well.

Temperature determines the direction of

internal energy flow between two systems when

heat is being transferred. This can be illustrated

through an experience familiar to everyone: hav-

ing one’s temperature taken with a thermometer.

If one has a fever, one’s mouth will be warmer

than the thermometer, and therefore heat will be

transferred to the thermometer from the mouth

until the two objects have the same temperature.

WILLIAM THOMSON, (BETTER KNOWN AS LORD KELVIN)ESTABLISHED WHAT IS NOW KNOWN AS THE KELVIN

SCALE.


Temperature The boiling water warms the tub of coolwater, and due to the high ratio of cool water toboiling water in the bathtub, the boiling waterexpends all its energy raising the temperature inthe bathtub as a whole. The greater the ratio ofvery hot water to cool water, on the other hand,the warmer the bathtub will be in the end. Buteven after the bath water is heated, it will contin-ue to lose heat, assuming the air in the room isnot warmer than the water in the tub. If the waterin the tub is warmer than the air, it immediatelybegins transferring thermal energy to the low-temperature air until their temperatures areequalized.

As for the coffee and the ice cube, what hap-pens is quite different from, indeed, opposite to,the common understanding of the process. Inother words, the ice does not “cool down” thecoffee: the coffee warms up the ice and presum-ably melts it. Once again, however, it expends atleast some of its thermal energy in doing so, andas a result, the coffee becomes cooler than it was.

If the coffee is placed inside a freezer, there isa large temperature difference between it and thesurrounding environment—so much so that if itis left for hours, the once-hot coffee will freeze.But again, the freezer does not cool down the cof-fee; the molecules in the coffee respond to thetemperature difference by working to warm upthe freezer. In this case, they have to “work over-time,” and since the freezer has a constant supplyof electrical energy, the heated molecules of thecoffee continue to expend themselves in a futileeffort to warm the freezer. Eventually, the coffeeloses so much energy that it is frozen solid;meanwhile, the heat from the coffee has beentransferred outside the freezer to the atmospherein the surrounding room.

THERMAL EXPANSION AND

EQUILIBRIUM. Temperature is related tothe concept of thermal equilibrium, and has aneffect on thermal expansion. As discussed below,as well as within the context of thermal expan-sion, a thermometer provides a gauge of temper-ature by measuring the level of thermal expan-sion experienced by a material (for example,mercury) within the thermometer.

In the examples used earlier—the ther-mometer in the mouth, the hot water in the coolbathtub, and the ice cube in the cup of coffee—the systems in question eventually reach thermalequilibrium. This is rather like averaging theirtemperatures, though, in fact, the equation


At that point of thermal equilibrium, a tempera-ture reading can be taken from the thermometer.

TEMPERATURE AND HEAT

FLOW. The principles of thermodynamics—the study of the relationships between heat,work, and energy, show that heat always flowsfrom an area of higher temperature to an area oflower temperature. The opposite simply cannothappen, because coldness, though it is very realin terms of sensory experience, is not an inde-pendent phenomenon. There is not, strictlyspeaking, such a thing as “cold”—only theabsence of heat, which produces the sensation ofcoldness.

One might pour a kettle of boiling waterinto a cold bathtub to heat it up; or put an icecube in a hot cup of coffee “to cool it down.”These seem like two very different events, butfrom the standpoint of thermodynamics, theyare exactly the same. In both cases, a body of hightemperature is placed in contact with a body oflow temperature, and in both cases, heat passesfrom the high-temperature body to the low-tem-perature one.

A THERMOMETER WORKS BY MEASURING THE LEVEL OF

THERMAL EXPANSION EXPERIENCED BY A MATERIAL

WITHIN THE THERMOMETER. MERCURY HAS BEEN A COM-MON THERMOMETER MATERIAL SINCE THE 1700S. (Pho-

tograph by Michael Prince/Corbis. Reproduced by permission.)


Temperatureinvolved is more complicated than a simplearithmetic average.

In the case of an ordinary mercury ther-mometer, the need to achieve thermal equilibri-um explains why one cannot get an instanta-neous temperature reading: first, the mouthtransfers heat to the thermometer, and once bothmouth and thermometer reach the same temper-ature, they are in thermal equilibrium. At thatpoint, it is possible to gauge the temperature ofthe mouth by reading the thermometer.


Development of the Ther-mometer

A thermometer can be defined scientifically as adevice that gauges temperature by measuring atemperature-dependent property, such as theexpansion of a liquid in a sealed tube. As withmany aspects of scientific or technologicalknowledge, the idea of the thermometerappeared in ancient times, but was never devel-oped. Again, like so many other intellectual phe-nomena, it lay dormant during the medievalperiod, only to be resurrected at the beginning ofthe modern era.

The Greco-Roman physician Galen (c. 129-216) was among the first thinkers to envision ascale for measuring temperature. Of course, whathe conceived of as “temperature” was closer tothe everyday meaning of that term, not its moreprecise scientific definition: the ideas of molecu-lar motion, heat, and temperature discussed inthis essay emerged only in the period beginningabout 1750. In any case, Galen proposed thatequal amounts of boiling water and ice be com-bined to establish a “neutral” temperature, withfour units of warmth above it and four degrees ofcold below.

THE THERMOSCOPE. The greatphysicist Galileo Galilei (1564-1642) is some-times credited with creating the first practicaltemperature measuring device, called a thermo-scope. Certainly Galileo—whether or not he wasthe first—did build a thermoscope, which con-sisted of a long glass tube planted in a containerof liquid. Prior to inserting the tube into the liq-uid—which was usually colored water, thoughGalileo’s thermoscope used wine—as much air as

possible was removed from the tube. This creat-ed a vacuum, and as a result of pressure differ-ences between the liquid and the interior of thethermoscope tube, some of the liquid went intothe tube.

But the liquid was not the thermometricmedium—that is, the substance whose tempera-ture-dependent property changes the thermo-scope measured. (Mercury, for instance, is thethermometric medium in most thermometerstoday.) Instead, the air was the medium whosechanges the thermoscope measured: when it waswarm, the air expanded, pushing down on theliquid; and when the air cooled, it contracted,allowing the liquid to rise.

It is interesting to note the similarity indesign between the thermoscope and the barom-eter, a device for measuring atmospheric pressureinvented by Italian physicist Evangelista Torricel-li (1608-1647) around the same time. Neitherwere sealed, but by the mid-seventeenth century,scientists had begun using sealed tubes contain-ing liquid instead of air. These were the first truethermometers.

EARLY THERMOMETERS. Ferdi-nand II, Grand Duke of Tuscany (1610-1670), iscredited with developing the first thermometerin 1641. Ferdinand’s thermometer used alcoholsealed in glass, which was marked with a temper-ature scale containing 50 units. It did not, how-ever, designate a value for zero.

English physicist Robert Hooke (1635-1703)created a thermometer using alcohol dyed red.Hooke’s scale was divided into units equal toabout 1/500 of the volume of the thermometricmedium, and for the zero point, he chose thetemperature at which water freezes. Thus, Hookeestablished a standard still used today; likewise,his thermometer itself set a standard. Built in1664, it remained in use by the Royal Society—the foremost organization for the advancementof science in England during the early modernperiod—until 1709.

Olaus Roemer (1644-1710), a Danishastronomer, introduced another important stan-dard. In 1702, he built a thermometer based noton one but two fixed points, which he designatedas the temperature of snow or crushed ice, andthe boiling point of water. As with Hooke’s use ofthe freezing point, Roemer’s idea of the freezingand boiling points of water as the two parameters



Temperature for temperature measurements has remained inuse ever since.

Temperature Scales

FAHRENHEIT. Not only did he devel-op the Fahrenheit scale, oldest of the temperaturescales still used in Western nations today, butGerman physicist Daniel Fahrenheit (1686-1736)also built the first thermometer to contain mer-cury as a thermometric medium. Alcohol has alow boiling point, whereas mercury remains fluidat a wide range of temperatures. In addition, itexpands and contracts at a very constant rate,and tends not to stick to glass. Furthermore, itssilvery color makes a mercury thermometer easyto read.

Fahrenheit also conceived the idea of using“degrees” to measure temperature in his ther-mometer, which he introduced in 1714. It is nomistake that the same word refers to portions ofa circle, or that exactly 180 degrees—half thenumber in a circle—separate the freezing andboiling points for water on Fahrenheit’s ther-mometer. Ancient astronomers attempting todenote movement in the skies used a circle with360 degrees as a close approximation of the ratiobetween days and years. The number 360 is alsouseful for computations, because it has a largequantity of divisors, as does 180—a total of 16whole-number divisors other than 1 and itself.

Though it might seem obvious that 0 shoulddenote the freezing point and 180 the boilingpoint on Fahrenheit’s scale, such an idea was farfrom obvious in the early eighteenth century.Fahrenheit considered the idea not only of a 0-to-180 scale, but also of a 180-to-360 scale. In theend, he chose neither—or rather, he chose not toequate the freezing point of water with zero onhis scale. For zero, he chose the coldest possibletemperature he could create in his laboratory,using what he described as “a mixture of salammoniac or sea salt, ice, and water.” Salt lowersthe melting point of ice (which is why it is usedin the northern United States to melt snow andice from the streets on cold winter days), and,thus, the mixture of salt and ice produced anextremely cold liquid water whose temperaturehe equated to zero.

With Fahrenheit’s scale, the ordinary freez-ing point of water was established at 32°, and theboiling point exactly 180° above it, at 212°. Just afew years after he introduced his scale, in 1730, a

French naturalist and physicist named ReneAntoine Ferchault de Reaumur (1683-1757) pre-sented a scale for which 0° represented the freez-ing point of water and 80° the boiling point.Although the Reaumur scale never caught on tothe same extent as Fahrenheit’s, it did include onevaluable addition: the specification that temper-ature values be determined at standard sea-levelatmospheric pressure.

CELSIUS. With its 32-degree freezingpoint and its 212-degree boiling point, theFahrenheit system is rather ungainly, lacking theneat orderliness of a decimal or base-10 scale.The latter quality became particularly importantwhen, 10 years after the French Revolution of1789, France adopted the metric system formeasuring length, mass, and other physical phe-nomena. The metric system eventually spread tovirtually the entire world, with the exception ofEnglish-speaking countries, where the morecumbersome British system still prevails. Buteven in the United States and Great Britain, sci-entists use the metric system. The metric temper-ature measure is the Celsius scale, created in 1742by Swedish astronomer Anders Celsius (1701-1744).

Like Fahrenheit, Celsius chose the freezingand boiling points of water as his two referencepoints, but he determined to set them 100, ratherthan 180, degrees apart. Interestingly, he plannedto equate 0° with the boiling point, and 100° withthe freezing point—proving that even the mostapparently obvious aspects of a temperature scalewere once open to question. Only in 1750 did fel-low Swedish physicist Martin Strömer change theorientation of the Celsius scale.

Celsius’s scale was based not simply on theboiling and freezing points of water, but, specifi-cally, those points at normal sea-level atmospher-ic pressure. The latter, itself a unit of measureknown as an atmosphere (atm), is equal to 14.7lb/in2, or 101,325 pascals in the metric system. ACelsius degree is equal to 1/100 of the differencebetween the freezing and boiling temperatures ofwater at 1 atm.

The Celsius scale is sometimes called thecentigrade scale, because it is divided into 100degrees, cent being a Latin root meaning “hun-dred.” By international convention, its valueswere refined in 1948, when the scale was rede-fined in terms of temperature change for an idealgas, as well as the triple point of water. (Triple



Temperaturepoint is the temperature and pressure at which asubstance is at once a solid, liquid, and vapor.) Asa result of these refinements, the boiling point ofwater on the Celsius scale is actually 99.975°. Thisrepresents a difference equal to about 1 part in4,000—hardly significant in daily life, though asignificant change from the standpoint ofthe precise measurements made in scientific laboratories.

KELVIN. In about 1787, French physicistand chemist J. A. C. Charles (1746-1823) madean interesting discovery: that at 0°C, the volumeof gas at constant pressure drops by 1/273 forevery Celsius degree drop in temperature. Thisseemed to suggest that the gas would simply dis-appear if cooled to -273°C, which, of course,made no sense. In any case, the gas would mostlikely become first a liquid, and then a solid, longbefore it reached that temperature.

The man who solved the quandary raised byCharles’s discovery was born a year afterCharles—who also formulated Charles’s law—died. He was William Thomson, Lord Kelvin(1824-1907), and in 1848, he put forward thesuggestion that it was molecular translationalenergy, and not volume, that would become zeroat -273°C. He went on to establish what came tobe known as the Kelvin scale.

Sometimes known as the absolute tempera-ture scale, the Kelvin scale is based not on thefreezing point of water, but on absolute zero—the temperature at which molecular motioncomes to a virtual stop. This is -273.15°C (-459.67°F), which in the Kelvin scale is designat-ed as 0K. (Kelvin measures do not use the term orsymbol for “degree.”)

Though scientists normally use metric or SImeasures, they prefer the Kelvin scale to Celsius,because the absolute temperature scale is directlyrelated to average molecular translational energy.Thus, if the Kelvin temperature of an object isdoubled, this means that its average moleculartranslational energy has doubled as well. Thesame cannot be said if the temperature were dou-bled from, say, 10°C to 20°C, or from 40°C to80°F, since neither the Celsius nor the Fahrenheitscale is based on absolute zero.

CONVERSIONS. The Kelvin scale is,however, closely related to the Celsius scale, inthat a difference of 1 degree measures the sameamount of temperature in both. Therefore, Cel-sius temperatures can be converted to Kelvins by

adding 273.15. There is also an absolute temper-ature scale that uses Fahrenheit degrees. This isthe Rankine scale, created by Scottish engineerWilliam Rankine (1820-1872), but it is seldomused today: scientists and others who desireabsolute temperature measures prefer the preci-sion and simplicity of the Celsius-based Kelvinscale.

Conversion between Celsius and Fahrenheitfigures is a bit more challenging. To convert atemperature from Celsius to Fahrenheit, multiplyby 9/5 and add 32. It is important to perform thesteps in that order, because reversing them willproduce a wrong answer. Thus, 100°C multipliedby 9/5 or 1.8 equals 180, which, when added to 32equals 212°F. Obviously, this is correct, since100°C and 212°F each represent the boiling pointof water. But, if one adds 32 to 100°, then multi-plies it by 9/5, the result is 237.6°F—an incorrectanswer.

For converting Fahrenheit temperatures toCelsius, there are also two steps, involving multi-plication and subtraction, but the order isreversed. Here, the subtraction step is performedbefore the multiplication step: thus, 32 is sub-tracted from the Fahrenheit temperature, thenthe result is multiplied by 5/9. Beginning with212°F, if 32 is subtracted, this equals 180. Multi-plied by 5/9, the result is 100°C—the correctanswer.

One reason the conversion formulae usefractions instead of decimal fractions (what mostpeople simply call “decimals”) is that 5/9 is arepeating decimal fraction (0.55555....) Further-more, the symmetry of 5/9 and 9/5 makes mem-orization easy. One way to remember the formu-la is that Fahrenheit is multiplied by a fraction—since 5/9 is a real fraction, whereas 9/5 is actuallya whole number plus a fraction.

Thermometers

As discussed earlier, with regard to the early his-tory of the thermometer, it is important that theglass tube be kept sealed; otherwise, atmosphericpressure contributes to inaccurate readings,because it influences the movement of the ther-mometric medium. Also important is the choiceof the thermometric medium itself.

Water quickly proved unreliable, due to itsunusual properties: it does not expand uniform-ly with a rise in temperature, or contract uni-formly with a lowered temperature. Rather, it



Temperature


reaches its maximum density at 39.2°F (4°C), andis less dense both above and below that tempera-ture. Therefore, alcohol, which responds in amuch more uniform fashion to changes in tem-perature, took its place.

MERCURY THERMOMETERS.

Alcohol is still used in thermometers today, butthe preferred thermometric medium is mercury.As noted earlier, its advantages include a muchhigher boiling point, a tendency not to stick toglass, and a silvery color that makes its levels easyto gauge visually. Like alcohol, mercury expandsat a uniform rate with an increase in tempera-ture: hence, the higher the temperature, the high-er the mercury stands in the thermometer.

In a typical mercury thermometer, mercuryis placed in a long, narrow sealed tube called acapillary. The capillary is inscribed with figures

for a calibrated scale, usually in such a way as toallow easy conversions between Fahrenheit andCelsius. A thermometer is calibrated by measur-ing the difference in height between mercury atthe freezing point of water, and mercury at theboiling point of water. The interval betweenthese two points is then divided into equal incre-ments—180, as we have seen, for the Fahrenheitscale, and 100 for the Celsius scale.

ELECTRIC THERMOMETERS.

Faster temperature measures can be obtained bythermometers using electricity. All matter dis-plays a certain resistance to electrical current, aresistance that changes with temperature. There-fore, a resistance thermometer uses a fine wirewrapped around an insulator, and when a changein temperature occurs, the resistance in the wirechanges as well. This makes possible much quick-




ly ceases.

CELSIUS SCALE: A scale of tempera-

ture, sometimes known as the centigrade

scale, created in 1742 by Swedish

astronomer Anders Celsius (1701-1744).

The Celsius scale establishes the freezing

and boiling points of water at 0° and 100°,

respectively. To convert a temperature from

the Celsius to the Fahrenheit scale, multi-

ply by 9/5 and add 32. The Celsius scale is

part of the metric system used by most

non-English speaking countries today.

Though the worldwide scientific commu-

nity uses the metric or SI system for most

measurements, scientists prefer the related

Kelvin scale.

FAHRENHEIT SCALE: The oldest of

the temperature scales still used in Western

nations today, created in 1714 by German

physicist Daniel Fahrenheit (1686-1736).

The Fahrenheit scale establishes the freez-

ing and boiling points of water at 32° and

212° respectively. To convert a temperature

from the Fahrenheit to the Celsius scale,

subtract 32 and multiply by 5/9. Most Eng-

lish-speaking countries use the Fahrenheit

scale.












adding 273.15. The Kelvin scale is used

almost exclusively by scientists.



KEY TERMS


Temperature


er temperature readings than those offered by athermometer containing a traditional thermo-metric medium.

Resistance thermometers are highly reliable,but expensive, and are used primarily for veryprecise measurements. More practical for every-day use is a thermistor, which also uses the prin-ciple of electric resistance, but is much simplerand less expensive. Thermistors are used for pro-viding measurements of the internal temperatureof food, for instance, and for measuring humanbody temperature.

Another electric temperature-measurementdevice is a thermocouple. When wires of two dif-ferent materials are connected, this creates asmall level of voltage that varies as a function oftemperature. A typical thermocouple uses twojunctions: a reference junction, kept at some con-

stant temperature, and a measurement junction.The measurement junction is applied to the itemwhose temperature is to be measured, and anytemperature difference between it and the refer-ence junction registers as a voltage change, whichis measured with a meter connected to the sys-tem.

OTHER TYPES OF THERMOME-

TER. A pyrometer also uses electromagneticproperties, but of a very different kind. Ratherthan responding to changes in current or voltage,the pyrometer is a gauge that responds to visibleand infrared radiation. Temperature and colorare closely related: thus, it is no accident thatgreens, blues, and purples, at one end of the visi-ble light spectrum, are associated with coolness,while reds, oranges, and yellows at the other endare associated with heat. As with the thermocou-

MOLECULAR TRANSLATIONAL EN-

ERGY: The kinetic energy in a system

produced by the movement of molecules

in relation to one another.



tions, or any material body, isolated from

the rest of the universe. Anything outside

of the system, including all factors and

forces irrelevant to a discussion of that sys-

tem, is known as the environment.












THERMAL EQUILIBRIUM: The state

that exists when two systems have the same

temperature. As a result, there is no

exchange of heat between them.



energy.

THERMOMETRIC MEDIUM: A sub-

stance whose properties change with tem-

perature. A mercury or alcohol thermome-

ter measures such changes.

THERMOMETER: A device that gauges

temperature by measuring a temperature-

dependent property, such as the expansion

of a liquid in a sealed tube, or resistance to

electric current.

TRIPLE POINT: The temperature and

pressure at which a substance is at once a

solid, liquid, and vapor.





Temperature ple, a pyrometer has both a reference element

and a measurement element, which compares

light readings between the reference filament and

the object whose temperature is being measured.

Still other thermometers, such as those in an

oven that tell the user its internal temperature,

are based on the expansion of metals with heat.

In fact, there are a wide variety of thermometers,

each suited to a specific purpose. A pyrometer,

for instance, is good for measuring the tempera-

ture of an object that the thermometer itself does

not touch.

WHERE TO LEARN MORE

About Temperature (Web site).<http://www.unidata.ucar.edu/staff/blynds/tmp.html> (April 18, 2001).

About Temperature Sensors (Web site). <http://www.tem-peratures.com> (April 18, 2001).

Gardner, Robert. Science Projects About Methods of Mea-suring. Berkeley Heights, N.J.: Enslow Publishers,2000.

Maestro, Betsy and Giulio Maestro. Temperature and You.New York: Macmillan/McGraw-Hill School Publish-ing, 1990.

Megaconverter (Web site).<http://www.megaconverter.com> (April 18, 2001).

NPL: National Physics Laboratory: Thermal Stuff: Begin-ners’ Guides (Web site).<http://www.npl.co.uk/npl/cbtm/thermal/stuff/guides.html> (April 18, 2001).

Royston, Angela. Hot and Cold. Chicago: HeinemannLibrary, 2001.

Santrey, Laurence. Heat. Illustrated by Lloyd Birming-ham. Mahwah, N.J.: Troll Associates, 1985.


Walpole, Brenda. Temperature. Illustrated by Chris Fair-clough and Dennis Tinkler. Milwaukee, WI: GarethStevens Publishing, 1995.




THERMAL EXPANS IONThermal Expansion

CONCEPTMost materials are subject to thermal expansion:a tendency to expand when heated, and to con-tract when cooled. For this reason, bridges arebuilt with metal expansion joints, so that theycan expand and contract without causing faultsin the overall structure of the bridge. Othermachines and structures likewise have built-inprotection against the hazards of thermal expan-sion. But thermal expansion can also be advanta-geous, making possible the workings of ther-mometers and thermostats.

HOW IT WORKS

Molecular TranslationalEnergy

In scientific terms, heat is internal energy thatflows from a system of relatively high tempera-ture to one at a relatively low temperature. Theinternal energy itself, identified as thermal ener-gy, is what people commonly mean when theysay “heat.” A form of kinetic energy due to themovement of molecules, thermal energy is some-times called molecular translational energy.

Temperature is defined as a measure of theaverage molecular translational energy in a sys-tem, and the greater the temperature change formost materials, as we shall see, the greater theamount of thermal expansion. Thus, all theseaspects of “heat”—heat itself (in the scientificsense), as well as thermal energy, temperature,and thermal expansion—are ultimately affectedby the motion of molecules in relation to oneanother.

MOLECULAR MOTION AND

NEWTONIAN PHYSICS. In general, thekinetic energy created by molecular motion canbe understood within the framework of classicalphysics—that is, the paradigm associated withSir Isaac Newton (1642-1727) and his laws ofmotion. Newton was the first to understand thephysical force known as gravity, and he explainedthe behavior of objects within the context ofgravitational force. Among the concepts essentialto an understanding of Newtonian physics arethe mass of an object, its rate of motion (whetherin terms of velocity or acceleration), and the dis-tance between objects. These, in turn, are allcomponents central to an understanding of howmolecules in relative motion generate thermalenergy.

The greater the momentum of an object—that is, the product of its mass multiplied by itsrate of velocity—the greater the impact it has onanother object with which it collides. Thegreater, also, is its kinetic energy, which is equalto one-half its mass multiplied by the square ofits velocity. The mass of a molecule, of course, isvery small, yet if all the molecules within anobject are in relative motion—many of them col-liding and, thus, transferring kinetic energy—this is bound to lead to a relatively large amountof thermal energy on the part of the larger object.

MOLECULAR ATTRACTION AND

PHASES OF MATTER. Yet, preciselybecause molecular mass is so small, gravitationalforce alone cannot explain the attractionbetween molecules. That attraction instead mustbe understood in terms of a second type offorce—electromagnetism—discovered by Scot-tish physicist James Clerk Maxwell (1831-1879).The details of electromagnetic force are not


ThermalExpansion


important here; it is necessary only to know thatall molecules possess some component of electri-cal charge. Since like charges repel and oppositecharges attract, there is constant electromagneticinteraction between molecules, and this pro-duces differing degrees of attraction.

The greater the relative motion betweenmolecules, generally speaking, the less theirattraction toward one another. Indeed, these twoaspects of a material—relative attraction andmotion at the molecular level—determinewhether that material can be classified as a solid,liquid, or gas. When molecules move slowly inrelation to one another, they exert a strongattraction, and the material of which they are a

part is usually classified as a solid. Molecules ofliquid, on the other hand, move at moderatespeeds, and therefore exert a moderate attrac-tion. When molecules move at high speeds, theyexert little or no attraction, and the material isknown as a gas.

Predicting Thermal Expansion

COEFFICIENT OF LINEAR EX-

PANSION. A coefficient is a number thatserves as a measure for some characteristic orproperty. It may also be a factor against whichother values are multiplied to provide a desiredresult. For any type of material, it is possible to

BECAUSE STEEL HAS A RELATIVELY HIGH COEFFICIENT OF THERMAL EXPANSION, STANDARD RAILROAD TRACKS ARE

CONSTRUCTED SO THAT THEY CAN SAFELY EXPAND ON A HOT DAY WITHOUT DERAILING THE TRAINS TRAVELING OVER

THEM. (Milepost 92 1/2/Corbis. Reproduced by permission.)


ThermalExpansion


calculate the degree to which that material willexpand or contract when exposed to changes intemperature. This is known, in general terms, asits coefficient of expansion, though, in fact, thereare two varieties of expansion coefficient.

The coefficient of linear expansion is a con-stant that governs the degree to which the lengthof a solid will change as a result of an alterationin temperature For any given substance, the coef-ficient of linear expansion is typically a numberexpressed in terms of 10-5/°C. In other words, thevalue of a particular solid’s linear expansioncoefficient is multiplied by 0.00001 per °C. (The°C in the denominator, shown in the equationbelow, simply “drops out” when the coefficient of

linear expansion is multiplied by the change intemperature.)

For quartz, the coefficient of linear expan-sion is 0.05. By contrast, iron, with a coefficientof 1.2, is 24 times more likely to expand or con-tract as a result of changes in temperature. (Steelhas the same value as iron.) The coefficient foraluminum is 2.4, twice that of iron or steel. Thismeans that an equal temperature change willproduce twice as much change in the length of abar of aluminum as for a bar of iron. Lead isamong the most expansive solid materials, with acoefficient equal to 3.0.

CALCULATING LINEAR EX-

PANSION. The linear expansion of a given

A MAN ICE FISHING IN MONTANA. BECAUSE OF THE UNIQUE THERMAL EXPANSION PROPERTIES OF WATER, ICE FORMS

AT THE TOP OF A LAKE RATHER THAN THE BOTTOM, THUS ALLOWING MARINE LIFE TO CONTINUE LIVING BELOW ITS

SURFACE DURING THE WINTER. (Corbis. Reproduced by permission.)


ThermalExpansion

solid can be calculated according to the formulaδL = aLO∆T. The Greek letter delta (d) means “achange in”; hence, the first figure representschange in length, while the last figure in theequation stands for change in temperature. Theletter a is the coefficient of linear expansion, andLO is the original length.

Suppose a bar of lead 5 meters long experi-ences a temperature change of 10°C; what will itschange in length be? To answer this, a (3.0 • 10-5/°C) must be multiplied by LO (5 m) and δT(10°C). The answer should be 150 & 10-5 m, or1.5 mm. Note that this is simply a change inlength related to a change in temperature: if thetemperature is raised, the length will increase,and if the temperature is lowered by 10°C, thelength will decrease by 1.5 mm.

VOLUME EXPANSION. Obviously,linear equations can only be applied to solids.Liquids and gases, classified together as fluids,conform to the shape of their container; hence,the “length” of any given fluid sample is the sameas that of the solid that contains it. Fluids are,however, subject to volume expansion—that is, achange in volume as a result of a change in tem-perature.

To calculate change in volume, the formulais very much the same as for change in length;only a few particulars are different. In the formu-la δV = bVOδT, the last term, again, meanschange in temperature, while δV means changein volume and VO is the original volume. The let-ter b refers to the coefficient of volume expan-sion. The latter is expressed in terms of 10-4/°C,or 0.0001 per °C.

Glass has a very low coefficient of volumeexpansion, 0.2, and that of Pyrex glass isextremely low—only 0.09. For this reason, itemsmade of Pyrex are ideally suited for cooking. Sig-nificantly higher is the coefficient of volumeexpansion for glycerin, an oily substance associ-ated with soap, which expands proportionally toa factor of 5.1. Even higher is ethyl alcohol, witha volume expansion coefficient of 7.5.


Liquids

Most liquids follow a fairly predictable pattern ofgradual volume increase, as a response to an

increase in temperature, and volume decrease, inresponse to a decrease in temperature. Indeed,the coefficient of volume expansion for a liquidgenerally tends to be higher than for a solid,and—with one notable exception discussedbelow— a liquid will contract when frozen.

The behavior of gasoline pumped on a hotday provides an example of liquid thermalexpansion in response to an increase in tempera-ture. When it comes from its underground tankat the gas station, the gasoline is relatively cool,but it will warm when sitting in the tank of analready warm car. If the car’s tank is filled and thevehicle left to sit in the sun—in other words, ifthe car is not driven after the tank is filled—thegasoline might very well expand in volume fas-ter than the fuel tank, overflowing onto the pavement.

ENGINE COOLANT. Another exam-ple of thermal expansion on the part of a liquidcan be found inside the car’s radiator. If the radi-ator is “topped off” with coolant on a cold day, anincrease in temperature could very well cause thecoolant to expand until it overflows. In the past,this produced a problem for car owners, becausecar engines released the excess volume of coolantonto the ground, requiring periodic replacementof the fluid.

Later-model cars, however, have an overflowcontainer to collect fluid released as a result ofvolume expansion. As the engine cools downagain, the container returns the excess fluid to theradiator, thus, “recycling” it. This means thatnewer cars are much less prone to overheating asolder cars. Combined with improvements inradiator fluid mixtures, which act as antifreeze incold weather and coolant in hot, the “recycling”process has led to a significant decrease in break-downs related to thermal expansion.

WATER. One good reason not to use purewater in one’s radiator is that water has a farhigher coefficient of volume expansion than atypical engine coolant. This can be particularlyhazardous in cold weather, because frozen waterin a radiator could expand enough to crack theengine block.

In general, water—whose volume expansioncoefficient in the liquid state is 2.1, and 0.5 in thesolid state—exhibits a number of interestingcharacteristics where thermal expansion is con-cerned. If water is reduced from its boilingpoint—212°F (100°C) to 39.2°F (4°C) it will



ThermalExpansion

steadily contract, like any other substanceresponding to a drop in temperature. Normally,however, a substance continues to become denseras it turns from liquid to solid; but this does notoccur with water.

At 32.9°F, water reaches it maximum densi-ty, meaning that its volume, for a given unit ofmass, is at a minimum. Below that temperature,it “should” (if it were like most types of matter)continue to decrease in volume per unit of mass,but, in fact, it steadily begins to expand. Thus, itis less dense, with a greater volume per unit ofmass, when it reaches the freezing point. It is forthis reason that when pipes freeze in winter, theyoften burst—explaining why a radiator filledwith water could be a serious problem in verycold weather.

In addition, this unusual behavior withregard to thermal expansion and contractionexplains why ice floats: solid water is less densethan the liquid water below it. As a result, frozenwater stays at the top of a lake in winter; since iceis a poor conductor of heat, energy cannot escapefrom the water below it in sufficient amounts tofreeze the rest of the lake water. Thus, the waterbelow the ice stays liquid, preserving plant andanimal life.

Gases

THE GAS LAWS. As discussed, liq-uids expand by larger factors than solids do.Given the increasing amount of molecular kinet-ic energy for a liquid as compared to a solid, andfor a gas as compared to a liquid, it should not besurprising, then, to learn that gases respond tochanges in temperature with a volume changeeven greater than that of liquids. Of course,where a gas is concerned, “volume” is more diffi-cult to measure, because a gas simply expands tofill its container. In order for the term to have anymeaning, pressure and temperature must bespecified as well.

A number of the gas laws describe the threeparameters for gases: volume, temperature, andpressure. Boyle’s law, for example, holds that inconditions of constant temperature, an inverserelationship exists between the volume and pres-sure of a gas: the greater the pressure, the less thevolume, and vice versa. Even more relevant to thesubject of thermal expansion is Charles’s law.

Charles’s law states that when pressure iskept constant, there is a direct relationship

between volume and temperature. As a gas heatsup, its volume increases, and when it cools down,its volume reduces accordingly. Thus, if an airmattress is filled in an air-conditioned room, andthe mattress is then taken to the beach on a hotday, the air inside will expand. Depending onhow much its volume increases, the expansion ofthe hot air could cause the mattress to “pop.”

VOLUME GAS THERMOME-

TERS. Whereas liquids and solids vary signif-icantly with regard to their expansion coeffi-cients, most gases follow more or less the samepattern of expansion in response to increases intemperature. The predictable behavior of gases inthese situations led to the development of theconstant gas thermometer, a highly reliableinstrument against which other thermometers—including those containing mercury (seebelow)—are often gauged.

In a volume gas thermometer, an emptycontainer is attached to a glass tube containingmercury. As gas is released into the empty con-tainer, this causes the column of mercury tomove upward. The difference between the formerposition of the mercury and its position after theintroduction of the gas shows the differencebetween normal atmospheric pressure and thepressure of the gas in the container. It is, then,possible to use the changes in volume on the partof the gas as a measure of temperature. Theresponse of most gases, under conditions of lowpressure, to changes in temperature is so uniformthat volume gas thermometers are often used tocalibrate other types of thermometers.

Solids

Many solids are made up of crystals, regularshapes composed of molecules joined to oneanother as though on springs. A spring that ispulled back, just before it is released, is an exam-ple of potential energy, or the energy that anobject possesses by virtue of its position. For acrystalline solid at room temperature, potentialenergy and spacing between molecules are rela-tively low. But as temperature increases and thesolid expands, the space between moleculesincreases—as does the potential energy in thesolid.

In fact, the responses of solids to changes intemperature tend to be more dramatic, at leastwhen they are seen in daily life, than are thebehaviors of liquids or gases under conditions of



ThermalExpansion

thermal expansion. Of course, solids actuallyrespond less to changes in temperature than flu-ids do; but since they are solids, people expecttheir contours to be immovable. Thus, when thevolume of a solid changes as a result of anincrease in thermal energy, the outcome is morenoteworthy.

JAR LIDS AND POWER LINES.

An everyday example of thermal expansion canbe seen in the kitchen. Almost everyone has hadthe experience of trying unsuccessfully to budgea tight metal lid on a glass container, and afterrunning hot water over the lid, finding that itgives way and opens at last. The reason for this isthat the high-temperature water causes the metallid to expand. On the other hand, glass—as notedearlier—has a low coefficient of expansion. Oth-erwise, it would expand with the lid, whichwould defeat the purpose of running hot waterover it. If glass jars had a high coefficient ofexpansion, they would deform when exposed torelatively low levels of heat.

Another example of thermal expansion in asolid is the sagging of electrical power lines on ahot day. This happens because heat causes themto expand, and, thus, there is a greater length ofpower line extending from pole to pole thanunder lower temperature conditions. It is highlyunlikely, of course, that the heat of summercould be so great as to pose a danger of powerlines breaking; on the other hand, heat can createa serious threat with regard to larger structures.

EXPANSION JOINTS. Most largebridges include expansion joints, which lookrather like two metal combs facing one another,their teeth interlocking. When heat causes thebridge to expand during the sunlight hours of ahot day, the two sides of the expansion jointmove toward one another; then, as the bridgecools down after dark, they begin gradually toretract. Thus the bridge has a built-in safety zone;otherwise, it would have no room for expansionor contraction in response to temperaturechanges. As for the use of the comb shape, thisstaggers the gap between the two sides of theexpansion joint, thus minimizing the bumpmotorists experience as they drive over it.

Expansion joints of a different design canalso be found in highways, and on “highways” ofrail. Thermal expansion is a particularly seriousproblem where railroad tracks are concerned,since the tracks on which the trains run are made

of steel. Steel, as noted earlier, expands by a fac-tor of 12 parts in 1 million for every Celsiusdegree change in temperature, and while thismay not seem like much, it can create a seriousproblem under conditions of high temperature.

Most tracks are built from pieces of steelsupported by wooden ties, and laid with a gapbetween the ends. This gap provides a buffer forthermal expansion, but there is another matter toconsider: the tracks are bolted to the wooden ties,and if the steel expands too much, it could pullout these bolts. Hence, instead of being placed ina hole the same size as the bolt, the bolts are fit-ted in slots, so that there is room for the track toslide in place slowly when the temperature rises.

Such an arrangement works agreeably fortrains that run at ordinary speeds: their wheelsmerely make a noise as they pass over the gaps,which are rarely wider than 0.5 in (0.013 m). Ahigh-speed train, however, cannot travel overirregular track; therefore, tracks for high-speedtrains are laid under conditions of relatively hightension. Hydraulic equipment is used to pull sec-tions of the track taut; then, once the track issecured in place along the cross ties, the tensionis distributed down the length of the track.

Thermometers and Thermostats

MERCURY IN THERMOMETERS.

A thermometer gauges temperature by measur-ing a temperature-dependent property. A ther-mostat, by contrast, is a device for adjusting thetemperature of a heating or cooling system. Bothuse the principle of thermal expansion in theiroperation. As noted in the example of the metallid and glass jar above, glass expands little withchanges in temperature; therefore, it makes anideal container for the mercury in a thermome-ter. As for mercury, it is an ideal thermometricmedium—that is, a material used to gauge tem-perature—for several reasons. Among these is ahigh boiling point, and a highly predictable, uni-form response to changes in temperature.

In a typical mercury thermometer, mercuryis placed in a long, narrow sealed tube called acapillary. Because it expands at a much faster ratethan the glass capillary, mercury rises and fallswith the temperature. A thermometer is calibrat-ed by measuring the difference in height betweenmercury at the freezing point of water, and mer-cury at the boiling point of water. The interval



ThermalExpansion


between these two points is then divided intoequal increments in accordance with one of thewell-known temperature scales.

THE BIMETALLIC STRIP IN

THERMOSTATS. In a thermostat, the cen-tral component is a bimetallic strip, consisting ofthin strips of two different metals placed back toback. One of these metals is of a kind that pos-sesses a high coefficient of linear expansion,while the other metal has a low coefficient. Atemperature increase will cause the side with ahigher coefficient to expand more than the side

that is less responsive to temperature changes. Asa result, the bimetallic strip will bend to one side.

When the strip bends far enough, it willclose an electrical circuit, and, thus, direct the airconditioner to go into action. By adjusting thethermostat, one varies the distance that thebimetallic strip must be bent in order to close thecircuit. Once the air in the room reaches thedesired temperature, the high-coefficient metalwill begin to contract, and the bimetallic stripwill straighten. This will cause an opening of theelectrical circuit, disengaging the air conditioner.

COEFFICIENT: A number that serves

as a measure for some characteristic or

property. A coefficient may also be a factor

against which other values are multiplied

to provide a desired result.

COEFFICIENT OF LINEAR EXPAN-

SION: A figure, constant for any partic-

ular type of solid, used in calculating the

amount by which the length of that solid

will change as a result of temperature

change. For any given substance, the coeffi-

cient of linear expansion is typically a

number expressed in terms of 10-5/°C.

COEFFICIENT OF VOLUME EXPAN-

SION: A figure, constant for any partic-

ular type of material, used in calculating

the amount by which the volume of that

material will change as a result of tempera-

ture change. For any given substance, the

coefficient of volume expansion is typical-

ly a number expressed in terms of 10-4/°C.





MOLECULAR TRANSLATIONAL EN-

ERGY: The kinetic energy in a system

produced by the movement of molecules

in relation to one another.



position.



tions, or any material body, isolated from

the rest of the universe. Anything outside

of the system, including all factors and

forces irrelevant to a discussion of that sys-

tem, is known as the environment.












THERMAL EXPANSION: A property

in all types of matter that display a tenden-

cy to expand when heated, and to contract

when cooled.

KEY TERMS


ThermalExpansion

In cold weather, when the temperature-con-trol system is geared toward heating rather thancooling, the bimetallic strip acts in much thesame way—only this time, the high-coefficientmetal contracts with cold, engaging the heater.Another type of thermostat uses the expansion ofa vapor rather than a solid. In this case, heating ofthe vapor causes it to expand, pushing on a set ofbrass bellows and closing the circuit, thus, engag-ing the air conditioner.

WHERE TO LEARN MORE


“Comparison of Materials: Coefficient of Thermal Expan-sion” (Web site). <http://www.handyharmancanada.com/TheBrazingBook/comparis.html> (April 21,2001).

Encyclopedia of Thermodynamics (Web site). <http://the-rion.minpet.unibas.ch/minpet/groups/thermodict/>(April 12, 2001).

Fleisher, Paul. Matter and Energy: Principles of Matter

and Thermodynamics. Minneapolis, MN: Lerner Pub-

lications, 2002.

NPL: National Physics Laboratory: Thermal Stuff: Begin-

ners’ Guides (Web site). <http://www.npl.co.uk/

npl/cbtm/thermal/stuff/guides.html> (April 18,

2001).

Royston, Angela. Hot and Cold. Chicago: Heinemann

Library, 2001.



“Thermal Expansion Measurement” (Web site).

<http://www.measurementsgroup.com/guide/tn/

tn513/513intro.html> (April 21, 2001).

“Thermal Expansion of Solids and Liquids” (Web site).

<http://www.physics.mun.ca/~gquirion/P2053/

html19b/> (April 21, 2001).

Walpole, Brenda. Temperature. Illustrated by Chris Fair-

clough and Dennis Tinkler. Milwaukee, WI: Gareth

Stevens Publishing, 1995.



253


WAVE MOT ION AND OSC I LL AT ION

WAVE MOT ION AND OSC I LL AT ION

WAVE MOT ION

OSC I LLAT ION

FREQUENCY

RESONANCE

INTERFERENCE

D I FFRACT ION

DOPPLER EFFECT



WAVE MOT IONWave Motion

CONCEPTWave motion is activity that carries energy fromone place to another without actually movingany matter. Studies of wave motion are mostcommonly associated with sound or radio trans-missions, and, indeed, these are among the mostcommon forms of wave activity experienced indaily life. Then, of course, there are waves on theocean or the waves produced by an object fallinginto a pool of still water—two very visual exam-ples of a phenomenon that takes place every-where in the world around us.

HOW IT WORKS

Related Forms of Motion

In wave motion, energy—the ability to performwork, or to exert force over distance—is trans-mitted from one place to another without actual-ly moving any matter along the wave. In sometypes of waves, such as those on the ocean, itmight seem as though matter itself has been dis-placed; that is, it appears that the water has actu-ally moved from its original position. In fact, thisis not the case: molecules of water in an oceanwave move up and down, but they do not actual-ly travel with the wave itself. Only the energy ismoved.

A wave is an example of a larger class of reg-ular, repeated, and/or back-and-forth types ofmotion. As with wave motion, these varieties ofmovement may or may not involve matter, but,in any case, the key component is not matter, butenergy. Broadest among these is periodic motion,or motion that is repeated at regular intervalscalled periods. A period might be the amount of

time that it takes an object orbiting another (as,for instance, a satellite going around Earth) tocomplete one cycle of orbit. With wave motion, aperiod is the amount of time required to com-plete one full cycle of the wave, from trough tocrest and back to trough.

HARMONIC MOTION. Harmonicmotion is the repeated movement of a particleabout a position of equilibrium, or balance. Inharmonic motion—or, more specifically, simpleharmonic motion—the object moves back andforth under the influence of a force directedtoward the position of equilibrium, or the placewhere the object stops if it ceases to be in motion.A familiar example of harmonic motion, to any-one who has seen an old movie with a clichéddepiction of a hypnotist, is the back-and-forthmovement of the hypnotist’s watch, as he tries tocontrol the mind of his patient.

One variety of harmonic motion is vibra-tion, which wave motion resembles in somerespects. Both wave motion and vibration areperiodic, involving the regular repetition of a cer-tain form of movement. In both, there is a con-tinual conversion and reconversion betweenpotential energy (the energy of an object due toits position, as for instance with a sled at the topof a hill) and kinetic energy (the energy of anobject due to its motion, as with the sled whensliding down the hill.) The principal differencebetween vibration and wave motion is that, inthe first instance, the energy remains in place,whereas waves actually transport energy fromone place to another.

OSCILLATION. Oscillation is a type ofharmonic motion, typically periodic, in one ormore dimensions. Suppose a spring is fixed in


Wave Motion first spring is once again disturbed: the energywill pass through the rubber bands, from springto spring, causing the entire row to oscillate. Thisis similar to what happens in the motion of awave.

Types and Properties ofWaves

There are some types of waves that do not followregular, repeated patterns; these are discussedbelow, in the illustration concerning a string, inwhich a pulse is created and reflected. Of princi-pal concern here, however, is the periodic wave, aseries of wave motions, following one after theother in regular succession. Examples of period-ic waves include waves on the ocean, soundwaves, and electromagnetic waves. The last ofthese include visible light and radio, among others.

Electromagnetic waves involve only energy;on the other hand, a mechanical wave involvesmatter as well. Ocean waves are mechanicalwaves; so, too, are sound waves, as well as thewaves produced by pulling a string. It is impor-tant to note, again, that the matter itself is notmoved from place to place, though it may movein place without leaving its position. For exam-ple, water molecules in the crest of an ocean waverotate in the same direction as the wave, whilethose in the trough of the wave rotate in a direc-tion opposite to that of the wave, yet there is nonet motion of the water: only energy is transmit-ted along the wave.

FIVE PROPERTIES OF WAVES.

There are three notable interrelated characteris-tics of periodic waves. One of these is wave speed,symbolized by v and typically calculated inmeters per second. Another is wavelength, repre-sented as λ (the Greek letter lambda), which isthe distance between a crest and the adjacentcrest, or a trough and the adjacent trough. Thethird is frequency, abbreviated as f, which is thenumber of waves passing through a given pointduring the interval of 1 second.

Frequency is measured in terms of cycles persecond, or Hertz (Hz), named in honor of nine-teenth-century German physicist HeinrichRudolf Hertz (1857-1894). If a wave has a fre-quency of 100 Hz, this means that 100 waves arepassing through a given point during the intervalof 1 second. Higher frequencies are expressed interms of kilohertz (kHz; 103 or 1,000 cycles per


place to a ceiling, such that it hangs downward.At this point, the spring is in a position of equi-librium. Now, consider what happens if thespring is grasped at a certain point and lifted,then let go. It will, of course, fall downward withthe force of gravity until it comes to a stop—butit will not stop at the earlier position of equilib-rium. Instead, it will continue downward to apoint of maximum tension, where it possessesmaximum potential energy as well. Then, it willspring upward again, and as it moves, its kineticenergy increases, while potential energy decreas-es. At the high point of this period of oscillation,the spring will not be as high as it was before itwas originally released, but it will be higher thanthe position of equilibrium.

Once it falls, the spring will again go lowerthan the position of equilibrium, but not as lowas before—and so on. This is an example of oscil-lation. Now, imagine what happens if anotherspring is placed beside the first one, and they areconnected by a rubber band. If just the firstspring is disturbed, as before, the second springwill still move, because the energy created by themovement of the first spring will be transmittedto the second one via the rubber band. The samewill happen if a row of springs, all side-by-side,are attached by multiple rubber bands, and the

HEINRICH HERTZ. (Hulton-Deutsch Collection/Corbis. Reproduced

by permission.)

Wave Motion


Wave Motion


second) or megahertz (MHz; 106 or 1 millioncycles per second.)

Frequency is clearly related to wave speed,and there is also a relationship—though it is notso immediately grasped—between wavelengthand speed. Over the interval of 1 second, a givennumber of waves pass a certain point (frequen-cy), and each wave occupies a certain distance(wavelength). Multiplied by one another, thesetwo properties equal the speed of the wave. Thiscan be stated as a formula: v = fλ.

Earlier, the term “period” was defined interms of wave motion as the amount of timerequired to complete one full cycle of the wave.Period, symbolized by T, can be expressed interms of frequency, and, thus, can also be relatedto the other two properties identified above. It isthe inverse of frequency, meaning that T = 1/f.Furthermore, period is equal to the ratio ofwavelength to wave speed; in other words,T = λ/v.

A fifth property of waves—one not mathe-matically related to wavelength, wave speed, fre-quency, or period, is amplitude. Amplitude canbe defined as the maximum displacement ofoscillating particles from their normal position.For an ocean wave, amplitude is the distance

from either the crest or the trough to the levelthat the ocean would maintain if it were per-fectly still.

WAVE SHAPES. When most peoplethink of waves, naturally, one of the first imagesthat comes to mind is that of waves on the ocean.These are an example of a transverse wave, or onein which the vibration or motion is perpendicu-lar to the direction the wave is moving. (Actually,ocean waves are simply perceived as transversewaves; in fact, as discussed below, their behavioris rather more complicated.) In a longitudinalwave, on the other hand, the movement of vibra-tion is in the same direction as the wave itself.

Transverse waves are easier to visualize, par-ticularly with regard to the aspects of wavemotion—for example, frequency and ampli-tude—discussed above. Yet, longitudinal wavescan be understood in terms of a common exam-ple. Sound waves, for instance, are longitudinal:thus, when a stereo is turned up to a high vol-ume, the speakers vibrate in the same direction asthe sound itself.

A longitudinal wave may be understood as aseries of fluctuations in density. If one were totake a coiled spring (such as the toy known as the“Slinky”) and release one end while holding the

TRANSVERSE WAVES PRODUCED BY A WATER DROPLET PENETRATING THE SURFACE OF A BODY OF LIQUID. (Photograph

by Martin Dohrn/Science Photo Library, National Audubon Society Collection/Photo Researchers, Inc. Reproduced with permission.)


Wave Motion other, the motion of the springs would producelongitudinal waves. As these waves pass throughthe spring, they cause some portions of it to becompressed and others extended. The distancebetween each point of compression is the wave-length.

Now, to return to the qualified statementmade above: that ocean waves are an example oftransverse waves. We perceive them as transversewaves, but, in fact, they are also longitudinal. Infact, all types of waves on the surface of a liquidare a combination of longitudinal and transverse,and are known as surface waves. Thus, if onedrops a stone into a body of still water, wavesradiate outward (longitudinal), but these wavesalso have a component that is perpendicular tothe surface of the water, meaning that they arealso transverse.


Pulses on a String

There is another variety of wave, though it isdefined in terms of behavior rather than thedirection of disturbance. (In terms of direction,it is simply a variety of transverse wave.) This is astanding wave, produced by causing vibrationson a string or other piece of material whose endsare fixed in place. Standing waves are really aseries of pulses that travel down the string andare reflected back to the point of the original dis-turbance.

Suppose you hold a string in one hand, withthe other end attached to a wall. If you give thestring a shake, this causes a pulse—an isolated,non-periodic disturbance—to move down it. Apulse is a single wave, and the behavior of thislone wave helps us to understand what happenswithin the larger framework of wave motion. Aswith wave motion in general, the movement ofthe pulse involves both kinetic and potentialenergy. The tension of the string itself createspotential energy; then, as the movement of thepulse causes the string to oscillate upward anddownward, this generates a certain amount ofkinetic energy.

TENSION AND REFLECTION.

The speed of the pulse is a function of the stringand its properties, not of the way that the pulse

was originally delivered. The tighter the string,and the less its mass per unit of length, the fasterthe pulse travels down it. The greater the massper unit of length, however, the greater the iner-tia resisting the movement of the pulse. Further-more, the more loosely you hold the string, theless it will respond to the movement of the pulse.

In accordance with the third law of motion,there should be an equal and opposite reactiononce the pulse comes into contact with the wall.Assuming that you are holding the string tightly,this reaction will be manifested in the form of aninverted wave, or one that is upside-down in rela-tion to the original pulse. In this case, the tensionon the end attached to the support is equal andopposite to the tension exerted by your hand. Asa result, the pulse comes back in the same shapeas before, but inverted.

If, on the other hand, you hold the other endof the string loosely; instead, once it reaches thewall, its kinetic energy will be converted intopotential energy, which will cause the end of thestring closest to the wall to move downward. Thiswill result in sending back a pulse that is reversedin horizontal direction, but the same in verticaldirection.

In both cases, the energy in the string isreflected backward to its source—that is, to theplace from which the pulse was originally pro-duced by the action of your hand. If, however,you hold the string so that its level of tension isexactly between perfect rigidity and perfectlooseness, then the pulse will not be reflected. Inother words, there will be no reflected wave.

TRANSMISSION AND REFLEC-

TION. If two strings are joined end-to-end,and a pulse is produced at one end, the pulsewould, of course, be transmitted to the secondstring. If, however, the second string has a greatermass per unit of length than the first one, theresult would be two pulses: a transmitted pulsemoving in the “right” direction, and a reflected,inverted pulse, moving toward the originalsource of energy. If, on the other hand, the firststring has a greater mass per unit of length thanthe second one, the reflected pulse would be erect(right side up), not inverted.

For simplicity’s sake, this illustration hasbeen presented in terms of a string attached to awall, but, in fact, transmission and reflectionoccur in a number of varieties of wave motion—



Wave Motionnot just those involving pulses or standing waves.A striking example occurs when light hits anordinary window. The majority of the light, ofcourse, is transmitted through the window pane,but a portion is reflected. Thus, as one looksthrough the window, one also sees one’s re-flection.

Similarly, sound waves are reflected depend-ing on the medium with which they are in con-tact. A canyon wall, for instance, will reflect agreat deal of sound, and, thus, it is easy to pro-duce an echo in such a situation. On the otherhand, there are many instances in which thedesire is to “absorb” sound by transmitting it tosome other form of material. Thus, for example,the lobby of an upscale hotel will include a num-ber of plants, as well as tapestries and variouswall hangings. In addition to adding beauty,these provide a medium into which the sound ofvoices and other noises can be transmitted and,thus, absorbed.

Sound Waves

PRODUCTION. The experience ofsound involves production, or the generation ofsound waves; transmission, or the movement ofthose waves from their source; and reception, theprincipal example of which is hearing. Sounditself is discussed in detail elsewhere. Of primaryconcern here is the transmission, and to a lesserextent, the production of sound waves.

In terms of production, sound waves are, asnoted, longitudinal waves: changes in pressure,or alternations between condensation and rar-efaction. Vibration is integral to the generation ofsound. When the diaphragm of a loudspeakerpushes outward, it forces nearby air moleculescloser together, creating a high-pressure regionall around the loudspeaker. The loudspeaker’sdiaphragm is pushed backward in response, thusfreeing up a volume of space for the air mole-cules. These, then, rush toward the diaphragm,creating a low-pressure region behind the high-pressure one. As a result, the loudspeaker sendsout alternating waves of high pressure (conden-sation) and low pressure (rarefaction).

FREQUENCY AND WAVE-

LENGTH. As sound waves pass through amedium such as air, they create fluctuationsbetween condensation and rarefaction. Theseresult in pressure changes that cause the listener’seardrum to vibrate with the same frequency as

the sound wave, a vibration that the ear’s innermechanisms translate and pass on to the brain.The range of audibility for the human ear is from20 Hz to 20 kHz. The lowest note of the eighty-eight keys on a piano is 27 Hz and the highest4.186 kHz. This places the middle and upper reg-ister of the piano well within the optimal rangefor audibility, which is between 3 and 4 kHz.

Sound travels at a speed of about 1,088 ft(331 m) per second through air at sea level, andthe range of sound audible to human earsincludes wavelengths as large as 11 ft (3.3 m) andas small as 1.3 in (3.3 cm). Unlike light waves,which are very small, the wavelengths of audiblesound are comparable to the sizes of ordinaryobjects. This creates an interesting contrastbetween the behaviors of sound and light whenconfronted with an obstacle to their trans-mission.

It is fairly easy to block out light by simplyholding up a hand in front of one’s eyes. Whenthis happens, the Sun casts a shadow on the otherside of one’s hand. The same action does notwork with one’s ears and the source of a sound,however, because the wavelengths of sound arelarge enough to go right past a relatively smallobject such as a hand. However, if one were toput up a tall, wide cement wall between oneselfand the source of a sound—as is often done inareas where an interstate highway passes right bya residential community—the object would besufficiently large to block out much of the sound.

Radio Waves

Radio waves, like visible light waves, are part ofthe electromagnetic spectrum. They are charac-terized by relatively long wavelengths and lowfrequencies—low, that is, in contrast to the muchhigher frequencies of both visible and invisiblelight waves. The frequency range of radio isbetween 10 KHz and about 2,000 MHz—in otherwords, from 10,000 Hz to as much as 2 billionHz—an impressively wide range.

AM radio broadcasts are found between 0.6and 1.6 MHz, and FM broadcasts between 88 and108 MHz. Thus, FM is at a much, much higherfrequency than AM, with the lowest frequency onthe FM dial 55 times as great as the highest on theAM dial. There are other ranges of frequencyassigned by the FCC (Federal CommunicationsCommission) to other varieties of radio trans-



Wave Motion


mission: for instance, citizens’ band (CB) radios

are in a region between AM and FM, ranging

from 26.985 MHz to 27.405 MHz.

Frequency does not indicate power. The

power of a radio station is a function of the

wattage available to its transmitter: hence, radio

stations often promote themselves with

announcements such as “operating with 100,000

watts of power....” Thus, an AM station, though it

has a much lower frequency than an FM station,

may possess more power, depending on the

wattage of the transmitter. Indeed, as we shall see,

it is precisely because of its high frequency that

an FM station lacks the broadcast range of an

AM station.

AMPLITUDE AND FREQUENCY

MODULATIONS. What is the differencebetween AM and FM? Or to put it another way,why is it that an AM station may be heardhalfway across the country, yet its sound on a carradio fades out when the car goes under an over-pass? The difference relates to how the variousradio signals are modulated.

A radio signal is simply a carrier: it maycarry Morse code, or it may carry complexsounds, but in order to transmit voices andmusic, its signal must be modulated. This can bedone, for instance, by varying the instantaneousamplitude of the radio wave, which is a functionof the radio station’s power. These variations inamplitude are called amplitude modulation, or

AMPLITUDE: The maximum displace-

ment of particles in oscillation from their

normal position. For an ocean wave,

amplitude is the distance from either the

crest or the trough to the level that the

ocean would maintain if it were per-

fectly still.

ENERGY: The ability to perform work,

which is the exertion of force over a given

distance. Work is the product of force and

distance, where force and distance are

exerted in the same direction.

FREQUENCY: The number of waves

passing through a given point during the

interval of one second. The higher the fre-

quency, the shorter the wavelength. Fre-

quency can also be mathematically related

to wave speed and period.

HARMONIC MOTION: The repeated

movement of a particle about a position of

equilibrium, or balance.

HERTZ: A unit for measuring frequen-

cy, equal to one cycle per second. If a sound

wave has a frequency of 20,000 Hz, this

means that 20,000 waves are passing

through a given point during the interval

of one second. Higher frequencies are

expressed in terms of kilohertz (kHz; 103

or 1,000 cycles per second) or megahertz

(MHz; 106 or 1 million cycles per second).


an object possesses due to its motion, as

with a sled when sliding down a hill. This is

contrasted with potential energy.

LONGITUDINAL WAVE: A wave in

which the movement of vibration is in the

same direction as the wave itself. This is

contrasted to a transverse wave.




energy.

MECHANICAL WAVE: A type of wave

that involves matter. Ocean waves are

mechanical waves; so, too, are the waves

produced by pulling a string. The matter

itself may move in place, but, as with all

KEY TERMS


Wave Motion


AM, and this was the first type of commercialradio to appear. Developed in the period beforeWorld War I, AM made its debut as a popularphenomenon shortly after the war.

Ironically, FM (frequency modulation) wasdeveloped not long after AM, but it did notbecome commercially viable until well afterWorld War II. As its name suggests, frequencymodulation involves variation in the signal’s fre-quency. The amplitude stays the same, and this—combined with the high frequency—produces anice, even sound for FM radio.

But the high frequency also means that FMsignals do not travel as far. If a person is listeningto an FM station while moving away from the

station’s signal, eventually the station will be

below the horizon relative to the car, and the car

radio will no longer be able to receive the signal.

In contrast to the direct, or line-of-sight, trans-

missions of FM stations, AM signals (with their

longer wavelengths) are reflected off of layers in

Earth’s ionosphere. As a result, a nighttime signal

from a “clear channel station” may be heard

across much of the continental United States.

WHERE TO LEARN MORE

Ardley, Neil. Sound Waves to Music. New York: Glouces-ter Press, 1990.

Berger, Melvin and Gilda Berger. What Makes an OceanWave?: Questions and Answers About Oceans andOcean Life. New York: Scholastic, 2001.

types of wave motion, there is no net

movement of matter—only of energy.

OSCILLATION: A type of harmonic

motion, typically periodic, in one or more

dimensions.

PERIOD: For wave motion, a period is

the amount of time required to complete

one full cycle of the wave, from trough to

crest and back to trough. Period can be

mathematically related to frequency, wave-

length, and wave speed.

PERIODIC MOTION: Motion that is

repeated at regular intervals. These inter-

vals are known as periods.

PERIODIC WAVE: A wave in which a

uniform series of crests and troughs follow

one after the other in regular succession.

By contrast, the wave produced by apply-

ing a pulse to a stretched string does not

follow regular, repeated patterns.


that an object possesses due to its position,

as for instance with a sled at the top of a

hill. This is contrasted with kinetic energy.

PULSE: An isolated, non-periodic dis-

turbance that takes place in wave motion of

a type other than that of a periodic wave.

STANDING WAVE: A type of trans-

verse wave produced by causing vibrations

on a string or other piece of material whose

ends are fixed in place.

SURFACE WAVE: A wave that exhibits

the behavior of both a transverse wave and

a longitudinal wave.

TRANSVERSE WAVE: A wave in

which the vibration or motion is perpendi-

cular to the direction in which the wave is

moving. This is contrasted to a longitudi-

nal wave.

WAVELENGTH: The distance between

a crest and the adjacent crest, or the trough

and an adjacent trough, of a wave. Wave-

length, abbreviated λ (the Greek letter

lambda) is mathematically related to wave

speed, period, and frequency.

WAVE MOTION: Activity that carries

energy from one place to another without

actually moving any matter.



Wave Motion Catherall, Ed. Exploring Sound. Austin, TX: Steck-

Vaughn Library, 1990.

Glover, David. Sound and Light. New York: Kingfisher

Books, 1993.

“Longitudinal and Transverse Wave Motion” (Web site).

<http://www.kettering.edu/~drussell/Demos/waves/

wavemotion.html> (April 22, 2001).

“Multimedia Activities: Wave Motion.” ExploreScience.com

(Web site). <http://www.explorescience.com/

activities/activity_list.cfm?catego ryID=3> (April 22,

2001).

Ruchlis, Hyman. Bathtub Physics. Edited by Donald Barr;illustrated by Ray Skibinski. New York: Harcourt,Brace, and World, 1967.

“Wave Motion” (Web site).<http://www.media.uwe.ac.uk/masoud/projects/water/wave.html> (April 22, 2001).

“Wave Motion and Sound.” The Physics Web (Web site).<http://www.hcrhs.hunterdon.k12.nj.us/disk2/Physics/wave.html> (April 22, 2001).

“Wave Motion Menu.”Carson City-Crystal High SchoolPhysics and Chemistry Departments (Web site).<http://members.aol.com/cepeirce/b2.html> (April22, 2001).




OSC I LL AT IONOscillation

CONCEPTWhen a particle experiences repeated movementabout a position of stable equilibrium, or bal-ance, it is said to be in harmonic motion, and ifthis motion is repeated at regular intervals, it iscalled periodic motion. Oscillation is a type ofharmonic motion, typically periodic, in one ormore dimensions. Among the examples of oscil-lation in the physical world are the motion of aspring, a pendulum, or even the steady back-and-forth movement of a child on a swing.

HOW IT WORKS

Stable and Unstable Equilib-rium

When a state of equilibrium exists, the vectorsum of the forces on an object is equal to zero.There are three varieties of equilibrium: stable,unstable, and neutral. Neutral equilibrium, dis-cussed in the essay on Statics and Equilibriumelsewhere in this book, does not play a significantrole in oscillation; on the other hand, stable andunstable equilibrium do.

In the example of a playground swing, whenthe swing is simply hanging downward—eitherempty or occupied—it is in a position of stableequilibrium. The vector sums are balanced,because the swing hangs downward with a force(its weight) equal to the force of the bars on theswing set that hold it up. If it were disturbedfrom this position, as, for instance, by someonepushing the swing, it would tend to return to itsoriginal position.

If, on the other hand, the swing were raisedto a certain height—if, say, a child were swinging

and an adult caught the child at the point ofmaximum displacement—this would be anexample of unstable equilibrium. The swing is inequilibrium because the forces on it are balanced:it is being held upward with a force equal to itsweight. Yet, this equilibrium is unstable, becausea disturbance (for instance, if the adult lets go ofthe swing) will cause it to move. Since the swingtends to oscillate, it will move back and forthacross the position of stable equilibrium beforefinally coming to a rest in the stable position.

Properties of Oscillation

There are two basic models of oscillation to con-sider, and these can be related to the motion oftwo well-known everyday objects: a spring and aswing. As noted below, objects not commonlyconsidered “springs,” such as rubber bands, dis-play spring-like behavior; likewise one couldsubstitute “pendulum” for swing. In any case, it iseasy enough to envision the motion of these twovarieties of oscillation: a spring generally oscil-lates along a straight line, whereas a swingdescribes an arc.

Either case involves properties common toall objects experiencing oscillation. There isalways a position of stable equilibrium, and thereis always a cycle of oscillation. In a single cycle,the oscillating particle moves from a certainpoint in a certain direction, then reverses direc-tion and returns to the original point. Theamount of time it takes to complete one cycle iscalled a period, and the number of cycles thattake place during one second is the frequency ofthe oscillation. Frequency is measured in Hertz(Hz), with 1 Hz—the term is both singular andplural—equal to one cycle per second.


Oscillation


It is easiest to think of a cycle as the move-ment from a position of stable equilibrium toone of maximum displacement, or the furthestpossible point from stable equilibrium. Becausestable equilibrium is directly in the middle of acycle, there are two points of maximum displace-ment. For a swing or pendulum, maximum dis-placement occurs when the object is at its highestpoint on either side of the stable equilibriumposition. For example, maximum displacementin a spring occurs when the spring reaches thefurthest point of being either stretched or com-pressed.

The amplitude of a cycle is the maximumdisplacement of particles during a single periodof oscillation, and the greater the amplitude, thegreater the energy of the oscillation. When anobject reaches maximum displacement, it revers-es direction, and, therefore, it comes to a stop foran instant of time. Thus, the speed of movementis slowest at that position, and fastest as it passesback through the position of stable equilibrium.An increase in amplitude brings with it anincrease in speed, but this does not lead to achange in the period: the greater the ampli-tude, the further the oscillating object has tomove, and, therefore, it takes just as long to com-plete a cycle.

Restoring Force

Imagine a spring hanging vertically from a ceil-ing, one end attached to the ceiling for supportand the other free to hang. It would thus be in aposition of stable equilibrium: the spring hangsdownward with a force equal to its weight, andthe ceiling pulls it upward with an equal andopposite force. Suppose, now, that the spring ispulled downward.

A spring is highly elastic, meaning that it canexperience a temporary stress and still reboundto its original position; by contrast, some objects(for instance, a piece of clay) respond to defor-mation with plastic behavior, permanentlyassuming the shape into which they weredeformed. The force that directs the spring backto a position of stable equilibrium—the force, inother words, which must be overcome when thespring is pulled downward—is called a restoringforce.

The more the spring is stretched, the greaterthe amount of restoring force that must be over-come. The same is true if the spring is com-pressed: once again, the spring is removed from aposition of equilibrium, and, once again, therestoring force tends to pull it outward to its“natural” position. Here, the example is a spring,

THE BOUNCE PROVIDED BY A TRAMPOLINE IS DUE TO ELASTIC POTENTIAL ENERGY. (Photograph by Kevin Fleming/Corbis.



Oscillation


but restoring force can be understood just as eas-ily in terms of a swing: once again, it is the forcethat tends to return the swing to a position of sta-ble equilibrium. There is, however, one signifi-cant difference: the restoring force on a swing isgravity, whereas, in the spring, it is related to theproperties of the spring itself.

Elastic Potential Energy

For any solid that has not exceeded the elasticlimit—the maximum stress it can endure with-out experiencing permanent deformation—there is a proportional relationship between forceand the distance it can be stretched. This isexpressed in the formula F = ks, where s is thedistance and k is a constant related to the size andcomposition of the material in question.

The amount of force required to stretch thespring is the same as the force that acts to bring itback to equilibrium— that is, the restoring force.Using the value of force, thus derived, it is possi-ble, by a series of steps, to establish a formula forelastic potential energy. The latter, sometimescalled strain potential energy, is the potentialenergy that a spring or a spring-like object pos-sesses by virtue of its deformation from the stateof equilibrium. It is equal to 1⁄2ks2.

POTENTIAL AND KINETIC EN-

ERGY. Potential energy, as its name suggests,involves the potential of something to moveacross a given interval of space—for example,when a sled is perched at the top of a hill. As itbegins moving through that interval, the objectwill gain kinetic energy. Hence, the elastic poten-tial energy of the spring, when the spring is heldat a position of the greatest possible displace-ment from equilibrium, is at a maximum. Onceit is released, and the restoring force begins tomove it toward the equilibrium position, poten-tial energy drops and kinetic energy increases.But the spring will not just return to equilibriumand stop: its kinetic energy will cause it to keepgoing.

In the case of the “swing” model of oscilla-tion, elastic potential energy is not a factor.(Unless, of course, the swing itself were suspend-ed on some sort of spring, in which case theobject will oscillate in two directions at once.)Nonetheless, all systems of motion involvepotential and kinetic energy. When the swing isat a position of maximum displacement, its

potential energy is at a maximum as well. Then,as it moves toward the position of stable equilib-rium, it loses potential energy and gains kineticenergy. Upon passing through the stable equilib-

A BUNGEE JUMPER HELPS ILLUSTRATE A REAL-WORLD

EXAMPLE OF OSCILLATION. (Eye Ubiquitous/Corbis. Reproduced

by permission.)


Oscillation rium position, kinetic energy again decreases,while potential energy increases. The sum of thetwo forms of energy is always the same, but thegreater the amplitude, the greater the value ofthis sum.


Springs and Damping

Elastic potential energy relates primarily tosprings, but springs are a major part of everydaylife. They can be found in everything from theshock-absorber assembly of a motor vehicle tothe supports of a trampoline fabric, and in bothcases, springs blunt the force of impact.

If one were to jump on a piece of trampolinefabric stretched across an ordinary table—onewith no springs—the experience would not bemuch fun, because there would be little bounce.On the other hand, the elastic potential energy ofthe trampoline’s springs ensures that anyone ofnormal weight who jumps on the trampoline isliable to bounce some distance into the air. As aperson’s body comes down onto the trampolinefabric, this stretches the fabric (itself highly elas-tic) and, hence, the springs. Pulled from a posi-tion of equilibrium, the springs acquire elasticpotential energy, and this energy makes possiblethe upward bounce.

As a car goes over a bump, the spring in itsshock-absorber assembly is compressed, but theelastic potential energy of the spring immediate-ly forces it back to a position of equilibrium, thusensuring that the bump is not felt throughout theentire vehicle. However, springs alone wouldmake for a bouncy ride; hence, a modern vehiclealso has shock absorbers. The shock absorber, acylinder in which a piston pushes down on aquantity of oil, acts as a damper—that is, aninhibitor of the springs’ oscillation.

SIMPLE HARMONIC MOTION

AND DAMPING. Simple harmonic motionoccurs when a particle or object moves back andforth within a stable equilibrium position underthe influence of a restoring force proportional toits displacement. In an ideal situation, where fric-tion played no part, an object would continue tooscillate indefinitely.

Of course, objects in the real world do notexperience perpetual oscillation; instead, mostoscillating particles are subject to damping, orthe dissipation of energy, primarily as a result offriction. In the earlier illustration of the springsuspended from a ceiling, if the string is pulled toa position of maximum displacement and thenreleased, it will, of course, behave dramatically atfirst. Over time, however, its movements willbecome slower and slower, because of the damp-ing effect of frictional forces.

HOW DAMPING WORKS. Whenthe spring is first released, most likely it will flyupward with so much kinetic energy that it will,quite literally, bounce off the ceiling. But witheach transit within the position of equilibrium,the friction produced by contact between themetal spring and the air, and by contact betweenmolecules within the spring itself, will graduallyreduce the energy that gives it movement. Intime, it will come to a stop.

If the damping effect is small, the amplitudewill gradually decrease, as the object continues tooscillate, until eventually oscillation ceases. Onthe other hand, the object may be “overdamped,”such that it completes only a few cycles beforeceasing to oscillate altogether. In the spring illus-tration, overdamping would occur if one were tograb the spring on a downward cycle, then slow-ly let it go, such that it no longer bounced.

There is a type of damping less forceful thanoverdamping, but not so gradual as the slow dis-sipation of energy due to frictional forces alone.This is called critical damping. In a criticallydamped oscillator, the oscillating material ismade to return to equilibrium as quickly as pos-sible without oscillating. An example of a criti-cally damped oscillator is the shock-absorberassembly described earlier.

Even without its shock absorbers, thesprings in a car would be subject to some degreeof damping that would eventually bring a halt totheir oscillation; but because this damping is of avery gradual nature, their tendency is to contin-ue oscillating more or less evenly. Over time, ofcourse, the friction in the springs would weardown their energy and bring an end to theiroscillation, but by then, the car would most like-ly have hit another bump. Therefore, it makessense to apply critical damping to the oscillationof the springs by using shock absorbers.



OscillationBungee Cords and RubberBands

Many objects in daily life oscillate in a spring-likeway, yet people do not commonly associate themwith springs. For example, a rubber band, whichbehaves very much like a spring, possesses highelastic potential energy. It will oscillate whenstretched from a position of stable equilibrium.

Rubber is composed of long, thin moleculescalled polymers, which are arranged side by side.The chemical bonds between the atoms in apolymer are flexible and tend to rotate, produc-ing kinks and loops along the length of the mol-ecule. The super-elastic polymers in rubber arecalled elastomers, and when a piece of rubber ispulled, the kinks and loops in the elastomersstraighten.

The structure of rubber gives it a high degreeof elastic potential energy, and in order to stretchrubber to maximum displacement, there is apowerful restoring force that must be overcome.This can be illustrated if a rubber band isattached to a ceiling, like the spring in the earlierexample, and allowed to hang downward. If it ispulled down and released, it will behave much asthe spring did.

The oscillation of a rubber band will be evenmore appreciable if a weight is attached to the“free” end—that is, the end hanging downward.This is equivalent, on a small scale, to a bungeejumper attached to a cord. The type of cord usedfor bungee jumping is highly elastic; otherwise,the sport would be even more dangerous than italready is. Because of the cord’s elasticity, whenthe bungee jumper “reaches the end of his rope,”he bounces back up. At a certain point, he beginsto fall again, then bounces back up, and so on,oscillating until he reaches the point of stableequilibrium.

The Pendulum

As noted earlier, a pendulum operates in muchthe same way as a swing; the difference betweenthem is primarily one of purpose. A swing existsto give pleasure to a child, or a certain bittersweetpleasure to an adult reliving a childhood experi-ence. A pendulum, on the other hand, is not forplay; it performs the function of providing areading, or measurement.

One type of pendulum is a metronome,which registers the tempo or speed of music.Housed in a hollow box shaped like a pyramid, ametronome consists of a pendulum attached to asliding weight, with a fixed weight attached to thebottom end of the pendulum. It includes a num-ber scale indicating the number of oscillationsper minute, and by moving the upper weight,one can change the beat to be indicated.

ZHANG HENG’S SEISMO-

SCOPE. Metronomes were developed in theearly nineteenth century, but, by then, the con-cept of a pendulum was already old. In the sec-ond century A.D., Chinese mathematician andastronomer Zhang Heng (78-139) used a pendu-lum to develop the world’s first seismoscope, aninstrument for measuring motion on Earth’s sur-face as a result of earthquakes.

Zhang Heng’s seismoscope, which heunveiled in 132 A.D., consisted of a cylinder sur-rounded by bronze dragons with frogs (alsomade of bronze) beneath. When the earth shook,a ball would drop from a dragon’s mouth intothat of a frog, making a noise. The number ofballs released, and the direction in which theyfell, indicated the magnitude and location of theseismic disruption.

CLOCKS, SCIENTIFIC INSTRU-

MENTS, AND “FAX MACHINE”. In718 A.D., during a period of intellectual floweringthat attended the early T’ang Dynasty (618-907),a Buddhist monk named I-hsing and a militaryengineer named Liang Ling-tsan built an astro-nomical clock using a pendulum. Many clockstoday—for example, the stately and imposing“grandfather clock” found in some homes—like-wise, use a pendulum to mark time.

Physicists of the early modern era used pen-dula (the plural of pendulum) for a number ofinteresting purposes, including calculationsregarding gravitational force. Experiments withpendula by Galileo Galilei (1564-1642) led to thecreation of the mechanical pendulum clock—thegrandfather clock, that is—by distinguishedDutch physicist and astronomer Christiaan Huy-gens (1629-1695).

In the nineteenth century, A Scottish inven-tor named Alexander Bain (1810-1877) evenused a pendulum to create the first “faxmachine.” Using matching pendulum transmit-ters and receivers that sent and received electrical



Oscillation


impulses, he created a crude device that, at the

time, seemed to have little practical purpose. In

fact, Bain’s “fax machine,” invented in 1840, was

more than a century ahead of its time.

THE FOUCAULT PENDULUM.

By far the most important experiments with pen-

dula during the nineteenth century, however,

were those of the French physicist Jean Bernard

Leon Foucault (1819-1868). Swinging a heavy

iron ball from a wire more than 200 ft (61 m) in

length, he was able to demonstrate that Earth

rotates on its axis.

Foucault conducted his famous demonstra-

tion in the Panthéon, a large domed building in

Paris named after the ancient Pantheon of Rome.

He arranged to have sand placed on the floor of

the Panthéon, and placed a pin on the bottom of

the iron ball, so that it would mark the sand as

the pendulum moved. A pendulum in oscillation

maintains its orientation, yet the Foucault pen-


ment of particles from their normal posi-

tion during a single period of oscillation.

CYCLE: One full repetition of oscilla-

tion. In a single cycle, the oscillating parti-

cle moves from a certain point in a certain

direction, then switches direction and

moves back to the original point. Typically,

this is from the position of stable equilibri-

um to maximum displacement and back

again to the stable equilibrium position.

DAMPING: The dissipation of energy

during oscillation, which prevents an

object from continuing in simple harmon-

ic motion and will eventually force it to

stop oscillating altogether. Damping is

usually caused by friction.

ELASTIC POTENTIAL ENERGY:

The potential energy that a spring or a

spring-like object possesses by virtue of its

deformation from the state of equilibrium.

Sometimes called strain potential energy, it

is equal to 1⁄2KS2, WHERE S is the distance

stretched and k is a figure related to the

size and composition of the material in

question.

EQUILIBRIUM: A state in which the

vector sum for all lines of force on an

object is equal to zero.

FREQUENCY: For a particle experi-

encing oscillation, frequency is the number

of cycles that take place during one second.

Frequency is measured in Hertz.




another.


movement of a particle within a position of



cy. The number of Hertz is the number of

cycles per second.



with a sled, when sliding down a hill. This

is contrasted with potential energy.

MAXIMUM DISPLACEMENT: For an

object in oscillation, maximum displace-

ment is the furthest point from stable equi-

librium. Since stable equilibrium is in the

middle of a cycle, there are two points of

maximum displacement. For a swing or

pendulum, this occurs when the object is at

its highest point on either side of the stable

equilibrium position. Maximum displace-

KEY TERMS


Oscillation


dulum (as it came to be called) seemed to be

shifting continually toward the right, as indicated

by the marks in the sand.

The confusion related to reference point:

since Earth’s rotation is not something that can

be perceived with the senses, it was natural to

assume that the pendulum itself was changing

orientation—or rather, that only the pendulum

was moving. In fact, the path of Foucault’s pen-

dulum did not vary nearly as much as it seemed.

Earth itself was moving beneath the pendulum,providing an additional force which caused thependulum’s plane of oscillation to rotate.

WHERE TO LEARN MORE

Brynie, Faith Hickman. Six-Minute Science Experiments.Illustrated by Kim Whittingham. New York: SterlingPublishing Company, 1996.

Ehrlich, Robert. Turning the World Inside Out, and 174Other Simple Physics Demonstrations. Princeton, N.J.:Princeton University Press, 1990.

ment in a spring occurs when the spring is

either stretched or compressed as far as it

will go.



dimensions.

PERIOD: The amount of time required

for one cycle in oscillating motion—for

instance, from a position of maximum dis-

placement to one of stable equilib-

rium, and, once again, to maximum dis-

placement.






as for instance, with a sled at the top of a


RESTORING FORCE: A force that

directs an object back to a position of sta-

ble equilibrium. An example is the resist-

ance of a spring, when it is extended.

SIMPLE HARMONIC MOTION: Har-

monic motion, in which a particle moves

back and forth about a stable equilibrium

position under the influence of a restoring

force proportional to its displacement.

Simple harmonic motion is, in fact, an

ideal situation; most types of oscillation

are subject to some form of damping.

STABLE EQUILIBRIUM: A type of

equilibrium in which, if an object were dis-

turbed, it would tend to return to its origi-

nal position. For an object in oscillation,

stable equilibrium is in the middle of a

cycle, between two points of maximum

displacement.


both magnitude and direction.

VECTOR SUM: A calculation that

yields the net result of all the vectors

applied in a particular situation. Because

direction is involved, it is necessary when

calculating the vector sum of forces on an

object (as, for instance, when determining

whether or not it is in a state of equilibri-

um), to assign a positive value to forces in

one direction, and a negative value to

forces in the opposite direction. If the

object is in equilibrium, these forces will

cancel one another out.



Oscillation “Foucault Pendulum” Smithsonian Institution FAQs (Web

site). <http://www.si.edu/resource/faq/nmah/pendu-

lum.html> (April 23, 2001).

Kruszelnicki, Karl S. The Foucault Pendulum (Web site).

<http://www.abc.net.au/surf/pendulum/pendulum.

html> (April 23, 2001).

Schaefer, Lola M. Back and Forth. Edited by Gail Saun-

ders-Smith; P. W. Hammer, consultant. Mankato,

MN: Pebble Books, 2000.

Shirley, Jean. Galileo. Illustrated by Raymond Renard. St.Louis: McGraw-Hill, 1967.


Topp, Patricia. This Strange Quantum World and You.Nevada City, CA: Blue Dolphin, 1999.

Zubrowski, Bernie. Making Waves: Finding Out AboutRhythmic Motion. Illustrated by Roy Doty. New York:Morrow Junior Books, 1994.




F REQUENC YFrequency

CONCEPTEverywhere in daily life, there are frequencies ofsound and electromagnetic waves, constantlychanging and creating the features of the visibleand audible world familiar to everyone. Someaspects of frequency can only be perceived indi-rectly, yet people are conscious of them withouteven thinking about it: a favorite radio station,for instance, may have a frequency of 99.7 MHz,and fans of that station knows that every timethey turn the FM dial to that position, the sta-tion’s signal will be there. Of course, people can-not “hear” radio and television frequencies—part of the electromagnetic spectrum—but theevidence for them is everywhere. Similarly, peo-ple are not conscious, in any direct sense, of fre-quencies in sound and light—yet without differ-ences in frequency, there could be no speech ormusic, nor would there be any variations ofcolor.

HOW IT WORKS

Harmonic Motion and Energy

In order to understand frequency, it is first neces-sary to comprehend two related varieties ofmovement: oscillation and wave motion. Bothare examples of a broader category, periodicmotion: movement that is repeated at regularintervals called periods. Oscillation and wavemotion are also examples of harmonic motion,or the repeated movement of a particle about aposition of equilibrium, or balance.

KINETIC AND POTENTIAL EN-

ERGY. In harmonic motion, and in sometypes of periodic motion, there is a continual

conversion of energy from one form to another.On the one hand is potential energy, or the ener-gy of an object due to its position and, hence, itspotential for movement. On the other hand,there is kinetic energy, the energy of movementitself.

Potential-kinetic conversions take place con-stantly in daily life: any time an object is at a dis-tance from a position of stable equilibrium, andsome force (for instance, gravity) is capable ofmoving it to that position, it possesses potentialenergy. Once it begins to move toward that equi-librium position, it loses potential energy andgains kinetic energy. Likewise, a wave at its cresthas potential energy, and gains kinetic energy asit moves toward its trough. Similarly, an oscillat-ing object that is as far as possible from the sta-ble-equilibrium position has enormous potentialenergy, which dissipates as it begins to movetoward stable equilibrium.

VIBRATION. Though many examplesof periodic and harmonic motion can be foundin daily life, the terms themselves are certainlynot part of everyday experience. On the otherhand, everyone knows what “vibration” means:to move back and forth in place. Oscillation, dis-cussed in more detail below, is simply a more sci-entific term for vibration; and while waves arenot themselves merely vibrations, they involve—and may produce—vibrations. This, in fact, ishow the human ear hears: by interpreting vibra-tions resulting from sound waves.

Indeed, the entire world is in a state of vibra-tion, though people seldom perceive this move-ment—except, perhaps, in dramatic situationssuch as earthquakes, when the vibrations ofplates beneath Earth’s surface become too force-


Frequency In oscillation, whether the oscillator bespring-like or swing-like, there is always a cycle inwhich the oscillating particle moves from a cer-tain point in a certain direction, then reversesdirection and returns to the original point. Usu-ally a cycle is viewed as the movement from aposition of stable equilibrium to one of maxi-mum displacement, or the furthest possiblepoint from stable equilibrium. Because stableequilibrium is directly in the middle of a cycle,there are two points of maximum displacement:on a swing, this occurs when the object is at itshighest point on either side of the stable equilib-rium position, and on a spring, maximum dis-placement occurs when the spring is eitherstretched or compressed as far as it will go.

Wave Motion

Wave motion is a type of harmonic motion thatcarries energy from one place to another withoutactually moving any matter. While oscillationinvolves the movement of “an object,” whether itbe a pendulum, a stretched rubber band, or someother type of matter, a wave may or may notinvolve matter. Example of a wave made out ofmatter—that is, a mechanical wave—is a wave onthe ocean, or a sound wave, in which energyvibrates through a medium such as air. Even inthe case of the mechanical wave, however, thematter does not experience any net displacementfrom its original position. (Water molecules dorotate as a result of wave motion, but they end upwhere they began.)

There are waves that do not follow regular,repeated patterns; however, within the context offrequency, our principal concern is with periodicwaves, or waves that follow one another in regu-lar succession. Examples of periodic wavesinclude ocean waves, sound waves, and electro-magnetic waves.

Periodic waves may be further divided intotransverse and longitudinal waves. A transversewave is the shape that most people imagine whenthey think of waves: a regular up-and-down pat-tern (called “sinusoidal” in mathematical terms)in which the vibration or motion is perpendicu-lar to the direction the wave is moving.

A longitudinal wave is one in which themovement of vibration is in the same directionas the wave itself. Though these are a little hard-er to picture, longitudinal waves can be visual-ized as a series of concentric circles emanating


ful to ignore. All matter vibrates at the molecular

level, and every object possesses what is called a

natural frequency, which depends on its size,

shape, and composition. This explains how a

singer can shatter a glass by hitting a certain note,

which does not happen because the singer’s voice

has reached a particularly high pitch; rather, it is

a matter of attaining the natural frequency of the

glass. As a result, all the energy in the sound of

the singer’s voice is transferred to the glass, and it

shatters.

Oscillation

Oscillation is a type of harmonic motion, typi-

cally periodic, in one or more dimensions. There

are two basic types of oscillation: that of a swing

or pendulum and that of a spring. In each case,

an object is disturbed from a position of stable

equilibrium, and, as a result, it continues to move

back and forth around that stable equilibrium

position. If a spring is pulled from stable equilib-

rium, it will generally oscillate along a straight

path; a swing, on the other hand, will oscillate

along an arc.

GRANDFATHER CLOCKS ARE ONE OF THE BEST-KNOWN

VARIETIES OF A PENDULUM. (Photograph by Peter

Harholdt/Corbis. Reproduced by permission.)


Frequency


man physicist Heinrich Rudolf Hertz (1857-

1894), who greatly advanced understanding of

electromagnetic wave behavior during his short

career.

If something has a frequency of 100 Hz, this

means that 100 waves are passing through a given

point during the interval of one second, or that

an oscillator is completing 100 cycles in a second.

Higher frequencies are expressed in terms of

kilohertz (kHz; 103 or 1,000 cycles per second);

megahertz (MHz; 106 or 1 million cycles per sec-

ond); and gigahertz (GHz; 109 or 1 billion cycles

per second.).

A clear mathematical relationship exists

between period, symbolized by T, and frequency

(f): each is the inverse of the other. Hence,

,

and

.=f 1

T

=T 1f

MIDDLE C—WHICH IS AT THE MIDDLE OF A PIANO KEY-BOARD—IS THE STARTING POINT OF A BASIC MUSICAL

SCALE. IT IS CALLED THE FUNDAMENTAL FREQUENCY,OR THE FIRST HARMONIC. (Photograph by Francoise

Gervais/Corbis. Reproduced by permission.)

from a single point. Sound waves are longitudi-nal: thus when someone speaks, waves of soundvibrations radiate out in all directions.

Amplitude

There are certain properties of waves, such aswavelength, or the distance between waves, thatare not properties of oscillation. However, bothtypes of motion can be described in terms ofamplitude, period, and frequency. The first ofthese is not related to frequency in any mathe-matical sense; nonetheless, where sound wavesare concerned, both amplitude and frequencyplay a significant role in what people hear.

Though waves and oscillators share theproperties of amplitude, period, and frequency,the definitions of these differ slightly dependingon whether one is discussing wave motion oroscillation. Amplitude, generally speaking, is thevalue of maximum displacement from an aver-age value or position—or, in simpler terms,amplitude is “size.” For an object experiencingoscillation, it is the value of the object’s maxi-mum displacement from a position of stableequilibrium during a single period. It is thus the“size” of the oscillation.

In the case of wave motion, amplitude is alsothe “size” of a wave, but the precise definitionvaries, depending on whether the wave in ques-tion is transverse or longitudinal. In the firstinstance, amplitude is the distance from eitherthe crest or the trough to the average positionbetween them. For a sound wave, which is longi-tudinal, amplitude is the maximum value of thepressure change between waves.

Period and Frequency

Unlike amplitude, period is directly related tofrequency. For a transverse wave, a period is theamount of time required to complete one fullcycle of the wave, from trough to crest and backto trough. In a longitudinal wave, a period is theinterval between waves. With an oscillator, a peri-od is the amount of time it takes to complete onecycle. The value of a period is usually expressedin seconds.

Frequency in oscillation is the number ofcycles per second, and in wave motion, it is thenumber of waves that pass through a given pointper second. These cycles per second are calledHertz (Hz) in honor of nineteenth-century Ger-


Frequency If an object in harmonic motion has a fre-quency of 50 Hz, its period is 1/50 of a second(0.02 sec). Or, if it has a period of 1/20,000 of asecond (0.00005 sec), that means it has a fre-quency of 20,000 Hz.


Grandfather Clocks andMetronomes

One of the best-known varieties of pendulum(plural, pendula) is a grandfather clock. Itsinvention was an indirect result of experimentswith pendula by Galileo Galilei (1564-1642),work that influenced Dutch physicist andastronomer Christiaan Huygens (1629-1695) inthe creation of the mechanical pendulumclock—or grandfather clock, as it is commonlyknown.

The frequency of a pendulum, a swing-likeoscillator, is the number of “swings” per minute.Its frequency is proportional to the square root ofthe downward acceleration due to gravity (32 ftor 9.8 m/sec2) divided by the length of the pen-dulum. This means that by adjusting the lengthof the pendulum on the clock, one can change itsfrequency: if the pendulum length is shortened,the clock will run faster, and if it is lengthened,the clock will run more slowly.

Another variety of pendulum, this one dat-ing to the early nineteenth century, is ametronome, an instrument that registers thetempo or speed of music. Consisting of a pendu-lum attached to a sliding weight, with a fixedweight attached to the bottom end of the pendu-lum, a metronome includes a number scale indi-cating the frequency—that is, the number ofoscillations per minute. By moving the upperweight, one can speed up or slow down the beat.

Harmonics

As noted earlier, the volume of any sound isrelated to the amplitude of the sound waves. Fre-quency, on the other hand, determines the pitchor tone. Though there is no direct correlationbetween intensity and frequency, in order for aperson to hear a very low-frequency sound, itmust be above a certain decibel level.

The range of audibility for the human ear isfrom 20 Hz to 20,000 Hz. The optimal range forhearing, however, is between 3,000 and 4,000 Hz.

This places the piano, whose 88 keys range from27 Hz to 4,186 Hz, well within the range ofhuman audibility. Many animals have a muchwider range: bats, whales, and dolphins can hearsounds at a frequency up to 150,000 Hz. Buthumans have something that few animals canappreciate: music, a realm in which frequencychanges are essential.

Each note has its own frequency: middle C,for instance, is 264 Hz. But in order to producewhat people understand as music—that is, pleas-ing combinations of notes—it is necessary toemploy principles of harmonics, which expressthe relationships between notes. These mathe-matical relations between musical notes areamong the most intriguing aspects of the con-nection between art and science.

It is no wonder, perhaps, that the great Greekmathematician Pythagoras (c. 580-500 B.C.)believed that there was something spiritual ormystical in the connection between mathematicsand music. Pythagoras had no concept of fre-quency, of course, but he did recognize that therewere certain numerical relationships between thelengths of strings, and that the production ofharmonious music depended on these ratios.

RATIOS OF FREQUENCY AND

PLEASING TONES. Middle C—located,,appropriately enough, in the middle of a pianokeyboard—is the starting point of a basic musi-cal scale. It is called the fundamental frequency,or the first harmonic. The second harmonic, oneoctave above middle C, has a frequency of 528Hz, exactly twice that of the first harmonic; andthe third harmonic (two octaves above middle C)has a frequency of 792 cycles, or three times thatof middle C. So it goes, up the scale.

As it turns out, the groups of notes that peo-ple consider harmonious just happen to involvespecific whole-number ratios. In one of thosecurious interrelations of music and math thatwould have delighted Pythagoras, the smaller thenumbers involved in the ratios, the more pleasingthe tone to the human psyche.

An example of a pleasing interval within anoctave is a fifth, so named because it spans fivenotes that are a whole step apart. The C Majorscale is easiest to comprehend in this regard,because it does not require reference to the “blackkeys,” which are a half-step above or below the“white keys.” Thus, the major fifth in the C-Major scale is C, D, E, F, G. It so happens that the




AMPLITUDE: For an object oscillation,

amplitude is the value of the object’s max-

imum displacement from a position of sta-

ble equilibrium during a single period. In a

transverse wave, amplitude is the distance

from either the crest or the trough to the

average position between them. For a

sound wave, the best-known example of a

longitudinal wave, amplitude is the maxi-

mum value of the pressure change between

waves.

CYCLE: In oscillation, a cycle occurs

when the oscillating particle moves from a

certain point in a certain direction, then

switches direction and moves back to the

original point. Typically, this is from the

position of stable equilibrium to maxi-

mum displacement and back again to the

stable equilibrium position.




In wave motion, frequency is the number

of waves passing through a given point

during the interval of one second. In either

case, frequency is measured in Hertz.

Period (T) is the mathematical inverse of

frequency (f) hence f=1/T.




HERTZ: A unit for measuring fre-

quency, named after nineteenth-century

German physicist Heinrich Rudolf Hertz

(1857-1894). Higher frequencies are


or 1,000 cycles per second); megahertz

(MHz; 106 or 1 million cycles per second);

and gigahertz (GHz; 109 or 1 billion cycles

per second.)











ment is the farthest point from stable equi-

librium.



dimensions.

PERIOD: In oscillation, a period is the

amount of time required for one cycle. For

a transverse wave, a period is the amount

of time required to complete one full cycle

of the wave, from trough to crest and back

to trough. In a longitudinal wave, a period

is the interval between waves. Frequency is

the mathematical inverse of period (T):

hence, T=1/f.




KEY TERMSFrequency


Frequency




as, for instance, with a sled at the top of

a hill. This is contrasted with kinetic

energy.

STABLE EQUILIBRIUM: A position

in which, if an object were disturbed, it

would tend to return to its original posi-

tion. For an object in oscillation, stable

equilibrium is in the middle of a cycle,

between two points of maximum dis-

placement.




moving. This is contrasted to a longi-

tudinal wave.

WAVE MOTION: A type of harmonic

motion that carries energy from one place

to another without actually moving any

matter.


ratio in frequency between middle C and G (396Hz) is 2:3.

Less melodious, but still certainly tolerable,is an interval known as a third. Three steps upfrom middle C is E, with a frequency of 330 Hz,yielding a ratio involving higher numbers thanthat of a fifth—4:5. Again, the higher the num-bers involved in the ratio, the less appealing thesound is to the human ear: the combination E-F,with a ratio of 15:16, sounds positively grating.

The Electromagnetic Spectrum

Everyone who has vision is aware of sunlight,but, in fact, the portion of the electromagneticspectrum that people perceive is only a small partof it. The frequency range of visible light is from4.3 • 1014 Hz to 7.5 • 1014 Hz—in other words,from 430 to 750 trillion Hertz. Two things shouldbe obvious about these numbers: that both therange and the frequencies are extremely high. Yet,the values for visible light are small compared tothe higher reaches of the spectrum, and the rangeis also comparatively small.

Each of the colors has a frequency, and thevalue grows higher from red to orange, and so onthrough yellow, green, blue, indigo, and violet.Beyond violet is ultraviolet light, which humaneyes cannot see. At an even higher frequency arex rays, which occupy a broad band extendingalmost to 1020 Hz—in other words, 1 followed by20 zeroes. Higher still is the very broad range

of gamma rays, reaching to frequencies as high as 1025. The latter value is equal to 10 trilliontrillion.

Obviously, these ultra-ultra high-frequencywaves must be very small, and they are: the high-er gamma rays have a wavelength of around 10-15

meters (0.000000000000001 m). For frequencieslower than those of visible light, the wavelengthsget larger, but for a wide range of the electro-magnetic spectrum, the wavelengths are stillmuch too small to be seen, even if they were vis-ible. Such is the case with infrared light, or therelatively lower-frequency millimeter waves.

Only at the low end of the spectrum, withfrequencies below about 1010 Hz—still an incred-ibly large number—do wavelengths become thesize of everyday objects. The center of themicrowave range within the spectrum, forinstance, has a wavelength of about 3.28 ft (1 m).At this end of the spectrum—which includes television and radar (both examples ofmicrowaves), short-wave radio, and long-waveradio—there are numerous segments devoted tovarious types of communication.

RADIO AND MICROWAVE FRE-

QUENCIES. The divisions of these sectionsof the electromagnetic spectrum are arbitraryand manmade, but in the United States—wherethey are administered by the Federal Communi-cations Commission (FCC)—they have the forceof law. When AM (amplitude modulation) radiofirst came into widespread use in the early


1920s—Congress assigned AM stations the fre-quency range that they now occupy: 535 kHz to1.7 MHz.

A few decades after the establishment of theFCC in 1927, new forms of electronic communi-cation came into being, and these too wereassigned frequencies—sometimes in ways thatwere apparently haphazard. Today, television sta-tions 2-6 are in the 54-88 MHz range, while sta-tions 7-13 occupy the region from 174-220 MHz.In between is the 88 to 108 MHz band, assignedto FM radio. Likewise, short-wave radio (5.9 to26.1 MHz) and citizens’ band or CB radio (26.96to 27.41 MHz) occupy positions between AMand FM.

In fact, there are a huge variety of frequencyranges accorded to all manner of other commu-nication technologies. Garage-door openers andalarm systems have their place at around 40MHz. Much, much higher than these—higher, infact, than TV broadcasts—is the band allotted todeep-space radio communications: 2,290 to2,300 MHz. Cell phones have their own realm, ofcourse, as do cordless phones; but so too do radiocontrolled cars (75 MHz) and even baby moni-tors (49 MHz).

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA:Addison-Wesley, 1991.

Allocation of Radio Spectrum in the United States (Website). <http://members.aol.com/jneuhaus/fccindex/spectrum.html> (April 25, 2001).

DiSpezio, Michael and Catherine Leary. Awesome Experi-ments in Light and Sound. New York: Sterling Juve-nile, 2001.

Electromagnetic Spectrum (Web site). <http://www.jsc.mil/images/speccht.jpg> (April 25, 2001).

“How the Radio Spectrum Works.” How Stuff Works (Website). <http://www.howstuffworks.com/radio~spec-trum.html> (April 25, 2001).

Internet Resources for Sound and Light (Web site).<http://electro.sau.edu/SLResources.html> (April 25,2001).

“NIST Time and Frequency Division.” NIST: NationalInstitute of Standards and Technology (Web site).<http://www.boulder.nist.gov/timefreq/> (April 25,2001).

Parker, Steve. Light and Sound. Austin, TX: RaintreeSteck-Vaughn, 2000.

Physics Tutorial System: Sound Waves Modules (Web site).<http://csgrad.cs.vt.edu/~chin/chin_sound.html>(April 25, 2001).

“Radio Electronics Pages” ePanorama.net (Web site).<http://www.epanorama.net/radio.html> (April 25,2001).


Frequency



R ESONANCEResonance

CONCEPTThough people seldom witness it directly, theentire world is in a state of motion, and wheresolid objects are concerned, this motion is mani-fested as vibration. When the vibrations pro-duced by one object come into alignment withthose of another, this is called resonance. Thepower of resonance can be as gentle as an adultpushing a child on a swing, or as ferocious as theforce that toppled what was once the world’sthird-longest suspension bridge. Resonancehelps to explain all manner of familiar events,from the feedback produced by an electric guitarto the cooking of food in a microwave oven.

HOW IT WORKS

Vibration of Molecules

The possibility of resonance always exists wher-ever there is periodic motion, movement that isrepeated at regular intervals called periods,and/or harmonic motion, the repeated move-ment of a particle about a position of equilibri-um or balance. Many examples of resonanceinvolve large objects: a glass, a child on a swing, abridge. But resonance also takes place at a levelinvisible to the human eye using even the mostpowerful optical microscope.

All molecules exert a certain electromagnet-ic attraction toward each other, and generallyspeaking, the less the attraction between mole-cules, the greater their motion relative to oneanother. This, in turn, helps define the object inrelation to its particular phase of matter.

A substance in which molecules move athigh speeds, and therefore hardly attract one

another at all, is called a gas. Liquids are materi-als in which the rate of motion, and hence ofintermolecular attraction, is moderate. In a solid,on the other hand, there is little relative motion,and therefore molecules exert enormous attrac-tive forces. Instead of moving in relation to oneanother, the molecules that make up a solid tendto vibrate in place.

Due to the high rate of motion in gas mole-cules, gases possess enormous internal kineticenergy. The internal energy of solids and liquidsis much less than in gases, yet, as we shall see, theuse of resonance to transfer energy to theseobjects can yield powerful results.

Oscillation

In colloquial terms, oscillation is the same asvibration, but, in more scientific terms, oscilla-tion can be identified as a type of harmonicmotion, typically periodic, in one or moredimensions. All things that oscillate do so eitheralong a more or less straight path, like that of aspring pulled from a position of stable equilibri-um; or they oscillate along an arc, like a swing orpendulum.

In the case of the swing or pendulum, stableequilibrium is the point at which the object ishanging straight downward—that is, the posi-tion to which gravitation force would take it if noother net forces were acting on the object. For aspring, stable equilibrium lies somewherebetween the point at which the spring isstretched to its maximum length and the point atwhich it is subjected to maximum compressionwithout permanent deformation.


ResonanceCYCLES AND FREQUENCY. Acycle of oscillation involves movement from acertain point in a certain direction, then a rever-sal of direction and a return to the original point.It is simplest to treat a cycle as the movementfrom a position of stable equilibrium to one ofmaximum displacement, or the furthest possiblepoint from stable equilibrium.

The amount of time it takes to complete onecycle is called a period, and the number of cyclesin one second is the frequency of the oscillation.Frequency is measured in Hertz. Named afternineteenth-century German physicist HeinrichRudolf Hertz (1857-1894), a single Hertz (Hz)—the term is both singular and plural—is equal toone cycle per second.

AMPLITUDE AND ENERGY. Theamplitude of a cycle is the maximum displace-ment of particles during a single period of oscil-lation. When an oscillator is at maximum dis-placement, its potential energy is at a maximumas well. From there, it begins moving toward theposition of stable equilibrium, and as it does so,it loses potential energy and gains kinetic energy.Once it reaches the stable equilibrium position,kinetic energy is at a maximum and potentialenergy at a minimum.

As the oscillating object passes through theposition of stable equilibrium, kinetic energybegins to decrease and potential energy increases.By the time it has reached maximum displace-ment again—this time on the other side of thestable equilibrium position—potential energy isonce again at a maximum.

OSCILLATION IN WAVE MO-

TION. The particles in a mechanical wave (awave that moves through a material medium)have potential energy at the crest and trough, andgain kinetic energy as they move between thesepoints. This is just one of many ways in whichwave motion can be compared to oscillation.There is one critical difference between oscilla-tion and wave motion: whereas oscillationinvolves no net movement, but merely move-ment in place, the harmonic motion of wavescarries energy from one place to another.Nonetheless, the analogies than can be madebetween waves and oscillations are many, andunderstandably so: oscillation, after all, is anaspect of wave motion.

A periodic wave is one in which a uniformseries of crests and troughs follow one after the


other in regular succession. Two basic types of

periodic waves exist, and these are defined by the

relationship between the direction of oscillation

and the direction of the wave itself. A transverse

wave forms a regular up-and-down pattern, in

which the oscillation is perpendicular to the

direction in which the wave is moving. On the

other hand, in a longitudinal wave (of which a

sound wave is the best example), oscillation is in

the same direction as the wave itself.

Again, the wave itself experiences net move-

ment, but within the wave—one of its defining

characteristics, as a matter of fact—are oscilla-

tions, which (also by definition) experience no

net movement. In a transverse wave, which is

usually easier to visualize than a longitudinal

wave, the oscillation is from the crest to the

trough and back again. At the crest or trough,

potential energy is at a maximum, while kinetic

energy reaches a maximum at the point of equi-

librium between crest and trough. In a longitudi-

nal wave, oscillation is a matter of density fluctu-

ations: the greater the value of these fluctuations,

the greater the energy in the wave.

A COMMON EXAMPLE OF RESONANCE: A PARENT PUSH-ES HER CHILD ON A SWING. (Photograph by Annie Griffiths

Belt/Corbis. Reproduced by permission.)


Resonance


Parameters for DescribingHarmonic Motion

The maximum value of the pressure changebetween waves is the amplitude of a longitudinalwave. In fact, waves can be described according tomany of the same parameters used for oscilla-tion—frequency, period, amplitude, and so on.The definitions of these terms vary somewhat,depending on whether one is discussing oscilla-tion or wave motion; or, where wave motion isconcerned, on whether the subject is a transversewave or a longitudinal wave.

For the present purposes, however, it is nec-essary to focus on just a few specifics of harmon-ic motion. First of all, the type of motion with

which we will be concerned is oscillation, andthough wave motion will be mentioned, ourprincipal concern is the oscillations within thewaves, not the waves themselves. Second, the twoparameters of importance in understanding res-onance are amplitude and frequency.

Resonance and EnergyTransfer

Resonance can be defined as the condition inwhich force is applied to an oscillator at the pointof maximum amplitude. In this way, the motionof the outside force is perfectly matched to thatof the oscillator, making possible a transfer ofenergy.

THE POWER OF RESONANCE CAN DESTROY A BRIDGE. ON NOVEMBER 7, 1940, THE ACCLAIMED TACOMA NARROWS

BRIDGE COLLAPSED DUE TO OVERWHELMING RESONANCE. (UPI/Corbis-Bettmann. Reproduced by permission.)


ResonanceAs its name suggests, resonance is a matter ofone object or force “getting in tune with” anoth-er object. One literal example of this involvesshattering a wine glass by hitting a musical notethat is on the same frequency as the natural fre-quency of the glass. (Natural frequency dependson the size, shape, and composition of the objectin question.) Because the frequencies resonate, orare in sync with one another, maximum energytransfer is possible.

The same can be true of soldiers walkingacross a bridge, or of winds striking the bridge ata resonant frequency—that is, a frequency thatmatches that of the bridge. In such situations, alarge structure may collapse under a force thatwould not normally destroy it, but the effects ofresonance are not always so dramatic. Sometimesresonance can be a simple matter, like pushing achild in a swing in such a way as to ensure thatthe child gets maximum enjoyment for the effortexpended.


A Child on a Swing and aPendulum in a Museum

Suppose a father is pushing his daughter on aswing, so that she glides back and forth throughthe air. A swing, as noted earlier, is a classic exam-ple of an oscillator. When the child gets in theseat, the swing is in a position of stable equilibri-um, but as the father pulls her back before releas-ing her, she is at maximum displacement.

He releases her, and quickly, potential ener-gy becomes kinetic energy as she swings towardthe position of stable equilibrium, then up againon the other side. Now the half-cycle is repeated,only in reverse, as she swings backward towardher father. As she reaches the position fromwhich he first pushed her, he again gives her a lit-tle push. This push is essential, if she is to keepgoing. Without friction, she could keep onswinging forever at the same rate at which shebegun. But in the real world, the wearing of theswing’s chain against the support along the barabove the swing will eventually bring the swingitself to a halt.

TIMING THE PUSH. Therefore, thefather pushes her—but in order for his push tobe effective, he must apply force at just the right

moment. That right moment is the point ofgreatest amplitude—the point, that is, at whichthe father’s pushing motion and the motion ofthe swing are in perfect resonance.

If the father waits until she is already on thedownswing before he pushes her, not all theenergy of his push will actually be applied tokeeping her moving. He will have failed to effi-ciently add energy to his daughter’s movementon the swing. On the other hand, if he pushes hertoo soon—that is, while she is on the upswing—he will actually take energy away from her movement.

If his purpose were to bring the swing to astop, then it would make good sense to push heron the upswing, because this would produce acycle of smaller amplitude and hence less energy.But if the father’s purpose is to help his daughterkeep swinging, then the time to apply energy is atthe position of maximum displacement.

It so happens that this is also the position atwhich the swing’s speed is the slowest. Once itreaches maximum displacement, the swing isabout to reverse direction, and, therefore, it stopsfor a split-second. Once it starts moving again,now in a new direction, both kinetic energy andspeed increase until the swing passes through theposition of stable equilibrium, where it reachesits highest rate.

THE FOUCAULT PENDULUM.

Hanging from a ceiling in Washington, D.C.’sSmithsonian Institution is a pendulum 52 ft(15.85 m) long, at the end of which is an iron ballweighing 240 lb (109 kg). Back and forth itswings, and if one sits and watches it longenough, the pendulum appears to move gradual-ly toward the right. Over the course of 24 hours,in fact, it seems to complete a full circuit, movingback to its original orientation.

There is just one thing wrong with this pic-ture: though the pendulum is shifting direction,this does not nearly account for the total changein orientation. At the same time the pendulum ismoving, Earth is rotating beneath it, and it is theviewer’s frame of reference that creates the mis-taken impression that only the pendulum isrotating. In fact it is oscillating, swinging backand forth from the Smithsonian ceiling, butthough it shifts orientation somewhat, thegreater component of this shift comes from themovement of the Earth itself.



Resonance This particular type of oscillator is known asa Foucault pendulum, after French physicist JeanBernard Leon Foucault (1819-1868), who in1851 used just such an instrument to prove thatEarth is rotating. Visitors to the Smithsonian,after they get over their initial bewilderment atthe fact that the pendulum is not actually rotat-ing, may well have another question: how exactlydoes the pendulum keep moving?

As indicated earlier, in an ideal situation, apendulum continues oscillating. But situationson Earth are not ideal: with each swing, the Fou-cault pendulum loses energy, due to friction fromthe air through which it moves. In addition, thecable suspending it from the ceiling is also oscil-lating slightly, and this, too, contributes to ener-gy loss. Therefore, it is necessary to add energy tothe pendulum’s swing.

Surrounding the cable where it attaches tothe ceiling is an electromagnet shaped like adonut, and on either side, near the top of thecable, are two iron collars. An electronic devicesenses when the pendulum reaches maximumamplitude, switching on the electromagnet,which causes the appropriate collar to give thecable a slight jolt. Because the jolt is delivered atthe right moment, the resonance is perfect, andenergy is restored to the pendulum.

Resonance in Electricity andElectromagnetic Waves

Resonance is a factor in electromagnetism, and inelectromagnetic waves, such as those of light orradio. Though much about electricity tends to berather abstract, the idea of current is fairly easy tounderstand, because it is more or less analogousto a water current: hence, the less impedance toflow, the stronger the current. Minimal imped-ance is achieved when the impressed voltage hasa certain resonant frequency.

NUCLEAR MAGNETIC RESO-

NANCE. The term “nuclear magnetic reso-nance” (NMR) is hardly a household world, butthanks to its usefulness in medicine, MRI—shortfor magnetic resonance imagining—is certainly awell-known term. In fact, MRI is simply themedical application of NMR. The latter is aprocess in which a rotating magnetic field is pro-duced, causing the nuclei of certain atoms toabsorb energy from the field. It is used in a rangeof areas, from making nuclear measurements to

medical imaging, or MRI. In the NMR process,the nucleus of an atom is forced to wobble like atop, and this speed of wobbling is increased byapplying a magnetic force that resonates with thefrequency of the wobble.

The principles of NMR were first developedin the late 1930s, and by the early 1970s they hadbeen applied to medicine. Thanks to MRI, physi-cians can make diagnoses without the patienthaving to undergo either surgery or x rays. Whena patient undergoes MRI, he or she is made to liedown inside a large tube-like chamber. A techni-cian then activates a powerful magnetic fieldthat, depending on its position, resonates withthe frequencies of specific body tissues. It is thuspossible to isolate specific cells and analyze themindependently, a process that would be virtuallyimpossible otherwise without employing highlyinvasive procedures.

LIGHT AND RADIO WAVES. Oneexample of resonance involving visible and invis-ible light in the electromagnetic spectrum is res-onance fluorescence. Fluorescence itself is aprocess whereby a material absorbs electromag-netic radiation from one source, then re-emitsthat radiation on a wavelength longer than thatof the illuminating radiation. Among its manyapplications are the fluorescent lights found inmany homes and public buildings. Sometimesthe emitted radiation has the same wavelength asthe absorbed radiation, and this is called reso-nance fluorescence. Resonance fluorescence isused in laboratories for analyzing phenomenasuch as the flow of gases in a wind tunnel.

Though most people do not realize thatradio waves are part of the electromagnetic spec-trum, radio itself is certainly a part of daily life,and, here again, resonance plays a part. Radiowaves are relatively large compared to visiblelight waves, and still larger in comparison tohigher-frequency waves, such as those in ultravi-olet light or x rays. Because the wavelength of aradio signal is as large as objects in ordinaryexperience, there can sometimes be conflict if thesize of an antenna does not match properly witha radio wave. When the sizes are compatible, this,too, is an example of resonance.

MICROWAVES. Microwaves occupy apart of the electromagnetic spectrum with high-er frequencies than those of radio waves. Exam-ples of microwaves include television signals,radar—and of course the microwave oven, which



Resonancecooks food without applying external heat.Like many other useful products, the microwaveoven ultimately arose from military-industrialresearch, in this case, during World War II. Intro-duced for home use in 1955, its popularity grewslowly for the first few decades, but in the 1970sand 1980s, microwave use increased dramatical-ly. Today, most American homes have micro-waves ovens.

Of course there will always be types of foodthat cook better in a conventional oven, but thebeauty of a microwave is that it makes possiblethe quick heating and cooking of foods—allwithout the drying effect of conventional baking.The basis for the microwave oven is the fact thatthe molecules in all forms of matter are vibrat-ing. By achieving resonant frequency, the ovenadds energy—heat—to food. The oven is notequipped in such a way as to detect the frequen-cy of molecular vibration in all possible sub-stances, however; instead, the microwaves reso-nant with the frequency of a single item found innearly all types of food: water.

Emitted from a small antenna, the micro-waves are directed into the cooking compart-ment of the oven, and, as they enter, they pass aset of turning metal fan blades. This is the stirrer,which disperses the microwaves uniformly overthe surface of the food to be heated. As amicrowave strikes a water molecule, resonancecauses the molecule to align with the direction ofthe wave. An oscillating magnetron, a tube thatgenerates radio waves, causes the microwaves tooscillate as well, and this, in turn, compels thewater molecules to do the same. Thus, the watermolecules are shifting in position several milliontimes a second, and this vibration generates ener-gy that heats the water.

Microwave ovens do not heat food from theinside out: like a conventional oven, they canonly cook from the outside in. But so much ener-gy is transferred to the water molecules that con-duction does the rest, ensuring relatively uniformheating of the food. Incidentally, the resonancebetween microwaves and water moleculesexplains why many materials used in cookingdishes—materials that do not contain water—can be placed in a microwave oven without beingmelted or burned. Yet metal, though it also con-tains no water, is unsafe.

Metals have free electrons, which makesthem good electrical conductors, and the pres-

ence of these free electrons means that themicrowaves produce electric currents in the sur-faces of metal objects placed in the oven.Depending on the shape of the object, these cur-rents can jump, or arc, between points on thesurface, thus producing sparks. On the otherhand, the interior of the microwave oven itself isin fact metal, and this is so precisely becausemicrowaves do bounce back and forth off ofmetal. Because the walls are flat and painted,however, currents do not arc between them.

Resonance of Sound Waves

A highly trained singer can hit a note that causesa wine glass to shatter, but what causes this tohappen is not the frequency of the note, per se. Inother words, the shattering is not necessarilybecause of the fact that the note is extremelyhigh; rather, it is due to the phenomenon of res-onance. The natural, or resonant, frequency inthe wine glass, as with all objects, is determinedby its shape and composition. If the singer’s voice(or a note from an instrument) hits the resonantfrequency, there will be a transfer of energy, aswith the father pushing his daughter on theswing. In this case, however, a full transfer ofenergy from the voice or musical instrument canoverload the glass, causing it to shatter.

Another example of resonance and soundwaves is feedback, popularized in the 1960s byrock guitarists such as Jimi Hendrix and PeteTownsend of the Who. When a musician strikesa note on an electric guitar string, the stringoscillates, and an electromagnetic device in theguitar converts this oscillation into an electricalpulse that it sends to an amplifier. The amplifierpasses this oscillation on to the speaker, but ifthe frequency of the speaker is the same as thatof the vibrations in the guitar, the result is feedback.

Both in scientific terms and in the view of amusic fan, feedback adds energy. The feedbackfrom the speaker adds energy to the guitar body,which, in turn, increases the energy in the vibra-tion of the guitar strings and, ultimately, thepower of the electrical signal is passed on to theamp. The result is increasing volume, and thefeedback thus creates a loop that continues torepeat until the volume drowns out all othernotes.



Resonance



ment of particles from their normal posi-

tion during a single period of oscillation.

CYCLE: One full repetition of oscil-

lation.




Frequency is measured in Hertz.





cy, named after nineteenth-century Ger-

man physicist Heinrich Rudolf Hertz

(1857-1894). Higher frequencies are



(MHz; 106 or 1 million cycles per second.)












librium.



dimensions.

PERIOD: The amount of time required

for one cycle in oscillating motion.









as, for instance, with a sled at the top of a


RESONANCE: The condition in which

force is applied to an object in oscillation at

the point of maximum amplitude.

RESONANT FREQUENCY: A fre-

quency that matches that of an oscillating

object.






between two points of maximum displace-

ment.





nal wave.




matter.

KEY TERMS


ResonanceHow Resonance Can Break a Bridge

The power of resonance goes beyond shattering aglass or torturing eardrums with feedback; it canactually destroy large structures. There is an oldfolk saying that a cat can destroy a bridge if itwalks across it in a certain way. This may or maynot be true, but it is certainly conceivable that agroup of soldiers marching across a bridge cancause it to crumble, even though it is capable ofholding much more than their weight, if therhythm of their synchronized footsteps resonateswith the natural frequency of the bridge. For thisreason, officers or sergeants typically order theirtroops to do something very unmilitary—tomarch out of step—when crossing a bridge.

The resonance between vibrations producedby wind and those of the structure itself broughtdown a powerful bridge in 1940, a highly dra-matic illustration of physics in action that wascaptured on both still photographs and film.Located on Puget Sound near Seattle, Washing-ton, the Tacoma Narrows Bridge was, at 2,800 ft(853 m) in length, the third-longest suspensionbridge in the world. But on November 7, 1940, itgave way before winds of 42 mi (68 km) perhour.

It was not just the speed of these winds, butthe fact that they produced oscillations of reso-nant frequency, that caused the bridge to twistand, ultimately, to crumble. In those few secondsof battle with the forces of nature, the bridgewrithed and buckled until a large segment col-

lapsed into the waters of Puget Sound. Fortu-nately, no one was killed, and a new, more stablebridge was later built in place of the one that hadcome to be known as “Galloping Gertie.” Theincident led to increased research and progress inunderstanding of aerodynamics, harmonicmotion, and resonance.

WHERE TO LEARN MORE


Berger, Melvin. The Science of Music. Illustrated byYvonne Buchanan. New York: Crowell, 1989.

“Bridges and Resonance” (Web site). <http://instruction.ferris.edu/loub/media/BRIDGE/Bridge.html> (April23, 2001).

“Resonance” (Web site). <http://hyperphysics.phyastr.gsu.edu/hbase/sound/reson.html> (April 26, 2001).

“Resonance” (Web site). <http://www.exploratorium.edu/xref/phenomena/resonance.html> (April 23,2001).

“Resonance.” The Physics Classroom (Web site).<http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l5a.html> (April 26, 2001).

“Resonance Experiment” (Web site). <http://131.123.17.138/> (April 26, 2001).

“Resonance, Frequency, and Wavelength” (Web site).<http://www.cpo.com/CPOCatalog/SW/sw_b1.html> (April 26, 2001).


“Tacoma Narrows Bridge Disaster” (Web site).<http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html> (April 23, 2001).




I N TERFERENCEInterference

CONCEPTWhen two or more waves interact and combine,they interfere with one another. But interferenceis not necessarily bad: waves may interfere con-structively, resulting in a wave larger than theoriginal waves. Or, they may interfere destruc-tively, combining in such a way that they form awave smaller than the original ones. Even so,destructive interference may have positive effects:without the application of destructive interfer-ence to the muffler on an automobile exhaustsystem, for instance, noise pollution from carswould be far worse than it is. Other examples ofinterference, both constructive and destructive,can be found wherever there are waves: in water,in sound, in light.

HOW IT WORKS

Waves

Whenever energy ripples through space, there isa wave. In fact, wave motion can be defined as atype of harmonic motion (repeated movementof a particle about a position of equilibrium, orbalance) that carries energy from one place toanother without actually moving any matter. Awave on the ocean is an example of a mechanicalwave, or one that involves matter; but though thematter moves in place, it is only the energy in thewave that experiences net movement.

Wave motion is related to oscillation, a typeof harmonic motion in one or more dimensions.There is one critical difference, however: oscilla-tion involves no net movement, only movementin place, whereas the harmonic motion of wavescarries energy from one place to another. Yet,

individual waves themselves are oscillating evenas the overall wave pattern moves.

A transverse wave forms a regular up-and-down pattern in which the oscillation is perpen-dicular to the direction the wave is moving.Ocean waves are transverse, though they alsohave properties of longitudinal waves. In a longi-tudinal wave, of which a sound wave is the bestexample, oscillation occurs in the same directionas the wave itself.

PARAMETERS OF WAVE MO-

TION. Some waves, composed of pulses, donot follow regular patterns. However, the wavesof principal concern in the present context areperiodic waves, ones in which a uniform series ofcrests and troughs follow each other in regularsuccession. Periodic motion is movement repeat-ed at regular intervals called periods. In the caseof wave motion, a period (represented by thesymbol T) is the amount of time required tocomplete one full cycle of the wave, from troughto crest and back to trough.

Period can be mathematically related to sev-eral other aspects of wave motion, includingwave speed, frequency, and wavelength. Frequen-cy (abbreviated f) is the number of waves passingthrough a given point during the interval of onesecond. It is measured in Hertz (Hz), named afternineteenth-century German physicist HeinrichRudolf Hertz (1857-1894), and a Hertz is equalto one cycle of oscillation per second. Higher fre-quencies are expressed in terms of kilohertz(kHz; 103 or 1,000 cycles per second) or mega-hertz (MHz; 106 or 1 million cycles per second.)Wavelength (represented by the symbol abbrevi-ated λ, the Greek letter lambda) is the distancebetween a crest and the adjacent crest, or a


Interference


trough and an adjacent trough, of a wave. Thehigher the frequency, the shorter the wavelength.

Another parameter for describing wavemotion—one that is mathematically independ-ent from the quantities so far described—isamplitude, or the maximum displacement ofparticles from a position of stable equilibrium.For an ocean wave, amplitude is the distancefrom either the crest or the trough to the levelthat the ocean would maintain if it were perfect-ly still.

Superposition and Inter-ference

SUPERPOSITION. The principle ofsuperposition holds that when several individualbut similar physical events occur in close prox-imity, the resulting effect is the sum of the mag-nitude of the separate events. This is akin to thepopular expression, “The whole is greater thanthe sum of the parts,” and it has numerous appli-cations in physics.

Where the strength of a gravitational field isbeing measured, for instance, superposition dic-tates that the strength of that field at any givenpoint is the sum of the mass of the individualparticles in that field. In the realm of electromag-

netic force, the same statement applies, thoughthe units being added are electrical charges ormagnetic poles, rather than quantities of mass.Likewise, in an electrical circuit, the total currentor voltage is the sum of the individual currentsand voltages in that circuit.

Superposition applies only in equations forlinear events—that is, phenomena that involvemovement along a straight line. Waves are linearphenomena, and, thus, the principle describesthe behavior of all waves when they come intocontact with one another. If two or more wavesenter the same region of space at the same time,then, at any instant, the total disturbance pro-duced by the waves at any point is equal to thesum of the disturbances produced by the indi-vidual waves.

INTERFERENCE. The principle ofsuperposition does not require that waves actual-ly combine; rather, the net effect is as though theywere combined. The actual combination or join-ing of two or more waves at a given point in spaceis called interference, and, as a result, the wavesproduce a single wave whose properties aredetermined by the properties of the individualwaves.

If two waves of the same wavelength occupythe same space in such a way that their crests and

A PIANO TUNER, USING A TUNING FORK SUCH AS THE ONES SHOWN ABOVE, UTILIZES INTERFERENCE TO TUNE THE

INSTRUMENT. (Bettmann/Corbis. Reproduced by permission.)


Interference


troughs align, the wave they produce will have anamplitude greater than that possessed by eitherwave initially. This is known as constructiveinterference. The more closely the waves are inphase—that is, perfectly aligned—the more con-structive the interference.

It is also possible that two or more waves cancome together such that the trough of one meetsthe crest of the other, or vice versa. In this case,what happens is destructive interference, and the resulting amplitude is the difference be-tween the values for the individual waves. If thewaves are perfectly unaligned—in other words, ifthe trough of one exactly meets the crest of theother—their amplitudes cancel out, and theresult is no wave at all.

Resonance

It is easy to confuse interference with resonance,and, therefore, a word should be said about thelatter phenomenon. The term resonancedescribes a situation in which force is applied toan oscillator at the point of maximum ampli-tude. In this way, the motion of the outside forceis perfectly matched to that of the oscillator,making possible a transfer of energy. As withinterference, resonance implies alignment

between two physical entities; however, there areseveral important differences.

Resonance can involve waves, as, forinstance, when sound waves resonate with thevibrations of an oscillator, causing a transfer ofenergy that sometimes produces dramaticresults. (See essay on Resonance.) But in thesecases, a wave is interacting with an oscillator, nota wave with a wave, as in situations of interfer-ence. Furthermore, whereas resonance entails atransfer of energy, interference involves a combi-nation of energy.

TRANSFER VS. COMBINATION.

The importance of this distinction is easy to seeif one substitutes money for energy, and peoplefor objects. If one passes on a sum of money toanother person, a business, or an institution—asa loan, repayment of a loan, a purchase, or agift—this is an example of a transfer. On theother hand, when married spouses each earnpaychecks, their cash is combined.

Transfer thus indicates that the originalholder of the cash (or energy) no longer has it.Yet, if the holder of the cash combines funds withthose of another, both share rights to an amountof money greater than the amount each original-ly owned. This is analogous to constructive inter-ference.

IF THIS BOAT’S WAKE WERE TO CROSS THE WAKE OF ANOTHER BOAT, THE RESULT WOULD BE BOTH CONSTRUCTIVE

AND DESTRUCTIVE INTERFERENCE. (Photograph by Roger Ressmeyer/Corbis. Reproduced by permission.)


InterferenceOn the other hand, a husband and wife (orany other group of people who pool their cash)also share liabilities, and, thus, a married personmay be subject to debt incurred by his or herspouse. If one spouse creates debt so great thatthe other spouse cannot earn enough to maintainthe payments, this painful situation is analogousto destructive interference.


Mechanical Waves

One of the easiest ways to observe interference isby watching the behavior of mechanical waves.Drop a stone into a still pond, and watch how itswaves ripple: this, as with most waveforms inwater, is an example of a surface wave, or one thatdisplays aspects of both transverse and longitudi-nal wave motion. Thus, as the concentric circlesof a longitudinal wave ripple outward in onedimension, there are also transverse movementsalong a plane perpendicular to that of the longi-tudinal wave.

While the first wave is still rippling acrossthe water, drop another stone close to the placewhere the first one was dropped. Now, there aretwo surface waves, crests and troughs collidingand interfering. In some places, they will inter-fere constructively, producing a wave—or rather,a portion of a wave—that is greater in amplitudethan either of the original waves. At other places,there will be destructive interference, with somewaves so perfectly out of phase that at one instantin time, a given spot on the water may look asthough it had not been disturbed at all.

One of the interesting aspects of this inter-action is the lack of uniformity in the instances ofinterference. As suggested in the preceding para-graph, it is usually not entire waves, but merelyportions of waves, that interfere constructively ordestructively. The result is that a seemingly sim-ple event—dropping two stones into a stillpond—produces a dazzling array of colliding cir-cles, broken by outwardly undisturbed areas ofdestructive interference.

A similar phenomenon, though manifestedby the interaction of geometric lines rather thanconcentric circles, occurs when two power boatspass each other on a lake. The first boat chops upthe water, creating a wake that widens behind it:

when seen from the air, the boat appears to be atthe apex of a triangle whose sides are formed byrippling eddies of water.

Now, another boat passes through the wakeof the first, only it is going in the opposite direc-tion and producing its own ever-widening wakeas it goes. As the waves from the two boats meet,some are in phase, but, more often than not, theyare only partly in phase, or they possess differingwavelengths. Therefore, the waves at least partial-ly cancel out one another in places, and in otherplaces, reinforce one another. The result is aninteresting patchwork of patterns when seenfrom the air.

Sound Waves

IN TUNE AND OUT OF TUNE.

The relationships between musical notes can beintriguing, and though tastes in music vary, mostpeople know when music is harmonious andwhen it is discordant. As discussed in the essay onfrequency, this harmony or discord can be equat-ed to the mathematical relationships between thefrequencies of specific notes: the lower the num-bers involved in the ratio, the more pleasing thesound.

The ratio between the frequency of middle Cand that of its first harmonic—that is, the C noteexactly one octave above it—is a nice, clean 1:2. Ifone were to play a song in the key of C-which, ona piano, involves only the “white notes” C-D-E-F-G-A-B—everything should be perfectly harmo-nious and (presumably) pleasant to the ear. Butwhat if the piano itself is out of tune? Or what ifone key is out of tune with the others?

The result, for anyone who is not tone-deaf,produces an overall impression of unpleasant-ness: it might be a bit hard to identify the sourceof this discomfort, but it is clear that somethingis amiss. At best, an out-of-tune piano mightsound like something that belonged in a saloonfrom an old Western; at worst, the sound of notesthat do not match their accustomed frequenciescan be positively grating.

HOW A TUNING FORK WORKS.

To rectify the situation, a professional pianotuner uses a tuning fork, an instrument that pro-duces a single frequency—say, 264 Hz, which isthe frequency of middle C. The piano tunerstrikes the tuning fork, and at the same timestrikes the appropriate key on the piano. If theirfrequencies are perfectly aligned, so is the sound



Interference of both; but, more likely, there will be interfer-ence, both constructive and destructive.

As time passes—measured in seconds oreven fractions of seconds—the sounds of thetuning fork and that of the piano key will alter-nate between constructive and destructive inter-ference. In the case of constructive interference,their combined sound will become louder thanthe individual sounds of either; and when theinterference is destructive, the sound of bothtogether will be softer than that produced byeither the fork or the key.

The piano tuner listens for these fluctuationsof loudness, which are called beats, and adjuststhe tension in the appropriate piano string untilthe beats disappear completely. As long as thereare beats, the piano string and the tuning forkwill produce together a frequency that is theaverage of the two: if, for instance, the out-of-tune middle C string vibrates at 262 Hz, theresulting frequency will be 263 Hz.

DIFFERENCE TONES. Anotherinteresting aspect of the interaction betweennotes is the “difference tone,” created by discord,which the human ear perceives as a third tone.Though E and F are both part of the C scale,when struck together, the sound is highly discor-dant. In light of what was said above about ratiosbetween frequencies, this dissonance is fitting,as the ratio here involves relatively high num-bers—15:16.

When two notes are struck together, theyproduce a combination tone, perceived by thehuman ear as a third tone. If the two notes areharmonious, the “third tone” is known as a sum-mation tone, and is equal to the combined fre-quencies of the two notes. But if the combinationis dissonant, as in the case of E and F, the thirdtone is known as a difference tone, equal to thedifference in frequencies. Since an E note vibratesat 330 Hz, and an F note at 352 Hz, the resultingdifference tone is equal to 22 Hz.

DESTRUCTIVE INTERFERENCE

IN SOUND WAVES. When music isplayed in a concert hall, it reverberates off thewalls of the auditorium. Assuming the place iswell designed acoustically, these bouncing soundwaves will interfere constructively, and the audi-torium comes alive with the sound of the music.In other situations, however, the sound wavesmay interfere destructively, and the result is a cer-tain muffled deadness to the sound.

Clearly, in a music hall, destructive interfer-ence is a problem; but there are cases in which itcan be a benefit—situations, that is, in which thepurpose, indeed, is to deaden the sound. Oneexample is an automobile muffler. A car’s exhaustsystem makes a great deal of noise, and, thus, if acar does not have a proper muffler, it creates agreat deal of noise pollution. A muffler counter-acts this by producing a sound wave out of phasewith that of the exhaust system; hence, it cancelsout most of the noise.

Destructive interference can also be used toreduce sound in a room. Once again, a machineis calibrated to generate sound waves that areperfectly out of phase with the offending noise—say, the hum of another machine. The resultingeffect conveys the impression that there is nonoise in the room, though, in fact, the soundwaves are still there; they have merely canceledeach other out.

Electromagnetic Waves

In 1801, English physicist Thomas Young (1773-1829), known for Young’s modulus of elasticitybecame the first scientist to identify interferencein light waves. Challenging the corpuscular theo-ry of light put forward by Sir Isaac Newton(1642-1727), Young set up an experiment inwhich a beam of light passed through two close-ly spaced pinholes onto a screen. If light was trulymade of particles, he said, the beams would proj-ect two distinct points onto the screen. Instead,what he saw was a pattern of interference.

In fact, Newton was partly right, but Young’sdiscovery helped advance the view of light as awave, which is also partly right. (According toquantum theory, developed in the twentieth cen-tury, light behaves both as waves and as parti-cles.) The interference in the visible spectrumthat Young witnessed was manifested as brightand dark bands. These bands are known asfringes—variations in intensity not unlike thebeats created in some instances of sound inter-ference, described above.

OILY FILMS AND RAINBOWS.

Many people have noticed the strangely beautifulpattern of colors generated when light interactswith an oily substance, as when light reflected ona soap bubble produces an astonishing array ofshades. Sometimes, this can happen in situationsnot otherwise aesthetically pleasing: an oily filmin a parking lot, left there by a car’s leaky



Interference



ment of particles in oscillation from a posi-

tion of stable equilibrium. For an ocean

wave, amplitude is the distance from either

the crest or the trough to the level that the

ocean would maintain if it were perfectly

still.

CONSTRUCTIVE INTERFERENCE:

A type of interference that occurs when

two or more waves combine in such a way

that they produce a wave whose amplitude

is greater than that of the original waves. If

waves are perfectly in phase—in other

words, if the crest and trough of one exact-

ly meets the crest and trough of the

other—then the resulting amplitude is the

sum of the individual amplitudes of the

separate waves.

CYCLE: In oscillation, a cycle occurs

when the oscillating particle moves from a

certain point in a certain direction, then

switches direction and moves back to the

original point. Typically, this is from the

position of stable equilibrium to maxi-

mum displacement and back again to the

stable equilibrium position. In a wave, a

cycle is equivalent to the movement from

trough to crest and back to trough.

DESTRUCTIVE INTERFERENCE: A

type of interference that occurs when two

or more waves combine to produce a wave

whose amplitude is less than that of the

original waves. If waves are perfectly out of

phase—in other words, if the trough of

one exactly meets the crest of the other,

and vice versa—their amplitudes cancel

out, and the result is no wave at all.

FREQUENCY: In wave motion, fre-

quency is the number of waves passing


of one second. The higher the frequency,

the shorter the wavelength. Frequency is

mathematically related to wave speed and

period.







(1857-1894). High frequencies are




INTERFERENCE: The combination of

two or more waves at a given point in space

to produce a wave whose properties are

determined by the properties of the indi-

vidual waves. This accords with the princi-

ple of superposition.








librium.

MECHANICAL WAVE: A type of

wave—for example, a wave on the ocean—

that involves matter. The matter itself may

move in place, but as with all types of wave

motion, there is no net movement of mat-

ter—only of energy.



dimensions.

KEY TERMS


Interference


crankcase, can produce a rainbow of colors if thesunlight hits it just right.

This happens because the thickness of theoil causes a delay in reflection of the light beam.Some colors pass through the film, becomingdelayed and, thus, getting out of phase with thereflected light on the surface of the film. Theseshades destructively interfere to such an extentthat the waves are cancelled, rendering theminvisible. Other colors reflect off the surface sothat they are perfectly in phase with the lighttraveling through the film, and appear as anattractive swirl of color on the surface of the oil.

The phenomenon of light-wave interferencewith oily or filmy surfaces has the effect of filter-ing light, and, thus, has a number of applicationsin areas relating to optics: sunglasses, lenses forbinoculars or cameras, and even visors for astro-nauts. In each case, unfiltered light could beharmful or, at least, inconvenient for the user,and the destructive interference eliminates cer-tain colors and unwanted reflections.

RADIO WAVES. Visible light is only asmall part of the electromagnetic spectrum,whose broad range of wave phenomena are, like-wise, subject to constructive or destructive inter-



one full cycle. Period is mathematically

related to frequency, wavelength, and wave

speed.







PHASE: When two waves of the same

frequency and amplitude are perfectly

aligned, they are said to be in phase.

PRINCIPLE OF SUPERPOSITION:

A physical principle stating that when sev-

eral individual, but similar, physical events

occur in close proximity to one another,

the resulting effect is the sum of the mag-

nitude of the separate events. Interference

is an example of superposition.

PULSE: An isolated, non-periodic dis-

turbance that takes place in wave motion of

a type other than that of a periodic wave.

RESONANCE: The condition in which

force is applied to an object in oscillation at

the point of maximum amplitude.






between two points of maximum dis-

placement.

SURFACE WAVE: A wave that exhibits

the behavior of both a transverse wave and

a longitudinal wave.





nal wave.




length, abbreviated λ (the Greek letter





to another, without actually moving any

matter.



Interferenceference. After visible light, the area of the spec-trum most people experience during an averageday is the realm of relatively low-frequency, long-wavelength radio waves and microwaves, the lat-ter including television broadcast signals.

People who rely on an antenna for their TVreception are likely to experience interference atsome point. However, an increasing number ofAmericans use either cable or satellite systems topick up TV programs. These are much less sus-ceptible to interference, due to the technology ofcoaxial cable, on the one hand, and digital com-pression, on the other. Thus, interference in television reception is a gradually diminishingproblem.

Interference among radio signals continuesto be a challenge, since most people still hear theradio via old-fashioned means rather thanthrough new technology, such as the Internet. Anumber of interference problems are created byactivity on the Sun, which has an enormouslypowerful electromagnetic field. Obviously, suchinterference is beyond the control of most radiolisteners, but according to a Web page set up byWHKY Radio in Hickory, North Carolina, thereare a number of things listeners can do todecrease interference in their own households.

Among the suggestions offered at theWHKY Web site is this: “Nine times out of ten, ifyour radio is near a computer, it will interferewith your radio. Computers send out all kinds ofsignals that your radio ‘thinks’ is a real radio sig-nal. Try to locate your radio away from comput-

ers... especially the monitor.” The Web site listeda number of other household appliances, as wellas outside phenomena such as power lines orthunderstorms, that can contribute to radiointerference.

WHERE TO LEARN MORE


Bloomfield, Louis A. “How Things Work: Radio.” HowThings Work (Web site). <http://rabi.phys.virginia.edu/HTW//radio.html> (April 27, 2001).

Harrison, David. “Sound” (Web site). <http://www.newi.ac.uk/buckley/sound.html> (April 27, 2001).

Interference Handbook/Federal Communications Commis-sion (Web site). <http://www.fcc.gov/cib/Publica-tions/tvibook.html> (April 27, 2001).


“Light—A-to-Z Science.” DiscoverySchool.com (Web site).<http://school.discovery.com/homeworkhelp/worldbook/atozscience/l/323260.html> (April 27,2001).

Oxlade, Chris. Light and Sound. Des Plaines, IL: Heine-mann Library, 2000.

“Sound Wave—Constructive and Destructive Interference”(Web site). <http://csgrad.cs.vt.edu/~chin/interference.html> (April 27, 2001).

Topp, Patricia. This Strange Quantum World and You.Nevada City, CA: Blue Dolphin, 1999.

WHKY Radio and TV (Web site).<http://www.whky.com/antenna.html> (April 27,2001).




D I F FR ACT IONDiffraction

CONCEPTDiffraction is the bending of waves aroundobstacles, or the spreading of waves by passingthem through an aperture, or opening. Any typeof energy that travels in a wave is capable of dif-fraction, and the diffraction of sound and lightwaves produces a number of effects. (Becausesound waves are much larger than light waves,however, diffraction of sound is a part of dailylife that most people take for granted.) Diffrac-tion of light waves, on the other hand, is muchmore complicated, and has a number of applica-tions in science and technology, including the use of diffraction gratings in the production ofholograms.

HOW IT WORKS

Comparing Sound and LightDiffraction

Imagine going to a concert hall to hear a band,and to your chagrin, you discover that your seatis directly behind a wide post. You cannot see theband, of course, because the light waves from thestage are blocked. But you have little troublehearing the music, since sound waves simply dif-fract around the pillar. Light waves diffractslightly in such a situation, but not enough tomake a difference with regard to your enjoymentof the concert: if you looked closely while sittingbehind the post, you would be able to observe thediffraction of the light waves glowing slightly, asthey widened around the post.

Suppose, now, that you had failed to obtaina ticket, but a friend who worked at the concertvenue arranged to let you stand outside an open

door and hear the band. The sound qualitywould be far from perfect, of course, but youwould still be able to hear the music well enough.And if you stood right in front of the doorway,you would be able to see light from inside theconcert hall. But, if you moved away from thedoor and stood with your back to the building,you would see little light, whereas the soundwould still be easily audible.

WAVELENGTH AND DIFFRAC-

TION. The reason for the difference—that is,why sound diffraction is more pronounced thanlight diffraction—is that sound waves are much,much larger than light waves. Sound travels bylongitudinal waves, or waves in which the move-ment of vibration is in the same direction as thewave itself. Longitudinal waves radiate outwardin concentric circles, rather like the rings of abull’s-eye.

The waves by which sound is transmitted arelarger, or comparable in size to, the column orthe door—which is an example of an aperture—and, hence, they pass easily through aperturesand around obstacles. Light waves, on the otherhand, have a wavelength, typically measured innanometers (nm), which are equal to one-mil-lionth of a millimeter. Wavelengths for visiblelight range from 400 (violet) to 700 nm (red):hence, it would be possible to fit about 5,000 ofeven the longest visible-light wavelengths on thehead of a pin!

Whereas differing wavelengths in light aremanifested as differing colors, a change in soundwavelength indicates a change in pitch. The high-er the pitch, the greater the frequency, and,hence, the shorter the wavelength. As with lightwaves—though, of course, to a much lesser


Diffraction


extent—short-wavelength sound waves are lesscapable of diffracting around large objects thanare long-wavelength sound waves. Chances are,then, that the most easily audible sounds frominside the concert hall are the bass and drums;higher-pitched notes from a guitar or otherinstruments, such as a Hammond organ, are notas likely to reach a listener outside.

Observing Diffraction in Light

Due to the much wider range of areas in whichlight diffraction has been applied by scientists,diffraction of light and not sound will be theprincipal topic for the remainder of this essay. We

have already seen that wavelength plays a role indiffraction; so, too, does the size of the aperturerelative to the wavelength. Hence, most studies ofdiffraction in light involve very small openings,as, for instance, in the diffraction grating dis-cussed below.

But light does not only diffract when passingthrough an aperture, such as the concert-halldoor in the earlier illustration; it also diffractsaround obstacles, as, for instance, the post or pil-lar mentioned earlier. This can be observed bylooking closely at the shadow of a flagpole on abright morning. At first, it appears that the shad-ow is “solid,” but if one looks closely enough, itbecomes clear that, at the edges, there is a blur-

HOLOGRAMS ARE MADE POSSIBLE THROUGH THE PRINCIPLE OF DIFFRACTION. SHOWN HERE IS A HOLOGRAM OF A

SPACE SHUTTLE ORBITING EARTH. (Photograph by Roger Ressmeyer/Corbis. Reproduced by permission.)


Diffraction


ring from darkness to light. This “gray area” is anexample of light diffraction.

Where the aperture or obstruction is largecompared to the wave passing through or aroundit, there is only a little “fuzziness” at the edge, asin the case of the flagpole. When light passesthrough an aperture, most of the beam goesstraight through without disturbance, with onlythe edges experiencing diffraction. If, however,the size of the aperture is close to that of thewavelength, the diffraction pattern will widen.Sound waves diffract at large angles through anopen door, which, as noted, is comparable in sizeto a sound wave; similarly, when light is passedthrough extremely narrow openings, its diffrac-tion is more noticeable.

Early Studies in Diffraction

Though his greatest contributions lay in hisepochal studies of gravitation and motion, SirIsaac Newton (1642-1727) also studied the pro-duction and propagation of light. Using a prism,he separated the colors of the visible light spec-trum—something that had already been done byother scientists—but it was Newton who dis-cerned that the colors of the spectrum could berecombined to form white light again.

Newton also became embroiled in a debateas the nature of light itself—a debate in whichdiffraction studies played an important role.Newton’s view, known at the time as the corpus-cular theory of light, was that light travels as astream of particles. Yet, his contemporary, Dutchphysicist and astronomer Christiaan Huygens(1629-1695), advanced the wave theory, or theidea that light travels by means of waves. Huy-gens maintained that a number of factors,including the phenomena of reflection andrefraction, indicate that light is a wave. Newton,on the other hand, challenged wave theorists bystating that if light were actually a wave, it shouldbe able to bend around corners—in other words,to diffract.

GRIMALDI IDENTIFIES DIF -

FRACTION. Though it did not becomewidely known until some time later, in 1648—more than a decade before the particle-wave con-troversy erupted—Johannes Marcus von Kron-land (1595-1667), a scientist in Bohemia (nowpart of the Czech Republic), discovered the dif-fraction of light waves. However, his findingswere not recognized until some time later; nordid he give a name to the phenomenon he hadobserved. Then, in 1660, Italian physicistFrancesco Grimaldi (1618-1663) conducted an

THE CHECKOUT SCANNERS IN GROCERY STORES USE HOLOGRAPHIC TECHNOLOGY THAT CAN READ A UNIVERSAL

PRODUCT CODE (UPC) FROM ANY ANGLE. (Photograph by Bob Rowan; Progressive Image/Corbis. Reproduced by permission.)


Diffractionexperiment with diffraction that gained wide-spread attention.

Grimaldi allowed a beam of light to passthrough two narrow apertures, one behind theother, and then onto a blank surface. When hedid so, he observed that the band of light hittingthe surface was slightly wider than it should be,based on the width of the ray that entered thefirst aperture. He concluded that the beam hadbeen bent slightly outward, and gave this phe-nomenon the name by which it is known today:diffraction.

FRESNEL AND FRAUNHOFER

DIFFRACTION. Particle theory continuedto have its adherents in England, Newton’shomeland, but by the time of French physicistAugustin Jean Fresnel (1788-1827), an increasingnumber of scientists on the European continenthad come to accept the wave theory. Fresnel’swork, which he published in 1818, served toadvance that theory, and, in particular, the idea oflight as a transverse wave.

In Memoire sur la diffraction de la lumiere,Fresnel showed that the transverse-wave modelaccounted for a number of phenomena, includ-ing diffraction, reflection, refraction, interfer-ence, and polarization, or a change in the oscilla-tion patterns of a light wave. Four years afterpublishing this important work, Fresnel put hisideas into action, using the transverse model tocreate a pencil-beam of light that was ideal forlighthouses. This prism system, whereby all thelight emitted from a source is refracted into ahorizontal beam, replaced the older method ofmirrors used since ancient times. Thus Fresnel’swork revolutionized the effectiveness of light-houses, and helped save lives of countless sailorsat sea.

The term “Fresnel diffraction” refers to a sit-uation in which the light source or the screen areclose to the aperture; but there are situations inwhich source, aperture, and screen (or at leasttwo of the three) are widely separated. This isknown as Fraunhofer diffraction, after Germanphysicist Joseph von Fraunhofer (1787-1826),who in 1814 discovered the lines of the solarspectrum (source) while using a prism (aper-ture). His work had an enormous impact in thearea of spectroscopy, or studies of the interactionbetween electromagnetic radiation and matter.


Diffraction Studies Come of Age

Eventually the work of Scottish physicist JamesClerk Maxwell (1831-1879), German physicistHeinrich Rudolf Hertz (1857-1894), and othersconfirmed that light did indeed travel in waves.Later, however, Albert Einstein (1879-1955)showed that light behaves both as a wave and, incertain circumstances, as a particle.

In 1912, a few years after Einstein publishedhis findings, German physicist Max TheodorFelix von Laue (1879-1960) created a diffractiongrating, discussed below. Using crystals in hisgrating, he proved that x rays are part of the elec-tromagnetic spectrum. Laue’s work, whichearned him the Nobel Prize in physics in 1914,also made it possible to measure the length ofx rays, and, ultimately, provided a means forstudying the atomic structure of crystals andpolymers.

SCIENTIFIC BREAKTHROUGHS

MADE POSSIBLE BY DIFFRAC-

TION STUDIES. Studies in diffractionadvanced during the early twentieth century. In1926, English physicist J. D. Bernal (1901-1971)developed the Bernal chart, enabling scientists todeduce the crystal structure of a solid by analyz-ing photographs of x-ray diffraction patterns. Adecade later, Dutch-American physical chemistPeter Joseph William Debye (1884-1966) won theNobel Prize in Chemistry for his studies in thediffraction of x rays and electrons in gases, whichadvanced understanding of molecular structure.In 1937, a year after Debye’s Nobel, two other sci-entists—American physicist Clinton JosephDavisson (1881-1958) and English physicistGeorge Paget Thomson (1892-1975)—won thePrize in Physics for their discovery that crystalscan bring about the diffraction of electrons.

Also, in 1937, English physicist WilliamThomas Astbury (1898-1961) used x-ray diffrac-tion to discover the first information concerningnucleic acid, which led to advances in the studyof DNA (deoxyribonucleic acid), the building-blocks of human genetics. In 1952, English bio-physicist Maurice Hugh Frederick Wilkins(1916-) and molecular biologist Rosalind ElsieFranklin (1920-1958) used x-ray diffraction tophotograph DNA. Their work directly influenced



Diffraction a breakthrough event that followed a year later:the discovery of the double-helix or double-spi-ral model of DNA by American molecular biolo-gists James D. Watson (1928-) and Francis Crick(1916-). Today, studies in DNA are at the fron-tiers of research in biology and related fields.

Diffraction Grating

Much of the work described in the precedingparagraphs made use of a diffraction grating,first developed in the 1870s by American physi-cist Henry Augustus Rowland (1848-1901). Adiffraction grating is an optical device that con-sists of not one but many thousands of apertures:Rowland’s machine used a fine diamond point torule glass gratings, with about 15,000 lines per in(2.2 cm). Diffraction gratings today can have asmany as 100,000 apertures per inch. The aper-tures in a diffraction grating are not mere holes,but extremely narrow parallel slits that transforma beam of light into a spectrum.

Each of these openings diffracts the lightbeam, but because they are evenly spaced and thesame in width, the diffracted waves experienceconstructive interference. (The latter phenome-non, which describes a situation in which two ormore waves combine to produce a wave ofgreater magnitude than either, is discussed in theessay on Interference.) This constructive interfer-ence pattern makes it possible to view compo-nents of the spectrum separately, thus enabling ascientist to observe characteristics ranging fromthe structure of atoms and molecules to thechemical composition of stars.

X-RAY DIFFRACTION. Becausethey are much higher in frequency and energylevels, x rays are even shorter in wavelength thanvisible light waves. Hence, for x-ray diffraction, itis necessary to have gratings in which lines areseparated by infinitesimal distances. These dis-tances are typically measured in units called anangstrom, of which there are 10 million to a mil-limeter. Angstroms are used in measuring atoms,and, indeed, the spaces between lines in an x-raydiffraction grating are comparable to the size ofatoms.

When x rays irradiate a crystal—in otherwords, when the crystal absorbs radiation in theform of x rays—atoms in the crystal diffract therays. One of the characteristics of a crystal is thatits atoms are equally spaced, and, because of this,it is possible to discover the location and distance

between atoms by studying x-ray diffraction pat-terns. Bragg’s law—named after the father-and-son team of English physicists William HenryBragg (1862-1942) and William Lawrence Bragg(1890-1971)—describes x-ray diffraction pat-terns in crystals.

Though much about x-ray diffraction andcrystallography seems rather abstract, its applica-tion in areas such as DNA research indicates thatit has numerous applications for improvinghuman life. The elder Bragg expressed this fact in1915, the year he and his son received the NobelPrize in physics, saying that “We are now able tolook ten thousand times deeper into the struc-ture of the matter that makes up our universethan when we had to depend on the microscopealone.” Today, physicists applying x-ray diffrac-tion use an instrument called a diffractometer,which helps them compare diffraction patternswith those of known crystals, as a means ofdetermining the structure of new materials.

Holograms

A hologram—a word derived from the Greekholos, “whole,” and gram, “message”—is a three-dimensional (3-D) impression of an object, andthe method of producing these images is knownas holography. Holograms make use of laserbeams that mix at an angle, producing an inter-ference pattern of alternating bright and darklines. The surface of the hologram itself is a sortof diffraction grating, with alternating strips ofclear and opaque material. By mixing a laserbeam and the unfocused diffraction pattern of anobject, an image can be recorded. An illuminat-ing laser beam is diffracted at specific angles, inaccordance with Bragg’s law, on the surfaces ofthe hologram, making it possible for an observerto see a three-dimensional image.

Holograms are not to be confused with ordi-nary three-dimensional images that use only vis-ible light. The latter are produced by a methodknown as stereoscopy, which creates a singleimage from two, superimposing the images tocreate the impression of a picture with depth.Though stereoscopic images make it seem asthough one can “step into” the picture, a holo-gram actually enables the viewer to glimpse theimage from any angle. Thus, stereoscopic imagescan be compared to looking through the plate-glass window of a store display, whereas holo-



Diffraction


grams convey the sensation that one has actuallystepped into the store window itself.

DEVELOPMENTS IN HOLOG-

RAPHY. While attempting to improve the res-olution of electron microscopes in 1947, Hun-garian-English physicist and engineer DennisGabor (1900-1979) developed the concept ofholography and coined the term “hologram.” Hiswork in this area could not progress by a greatmeasure, however, until the creation of the laserin 1960. By the early 1960s, scientists were using

lasers to create 3-D images, and in 1971, Gaborreceived the Nobel Prize in physics for the dis-covery he had made a generation before.

Today, holograms are used on credit cards orother identification cards as a security measure,providing an image that can be read by an opti-cal scanner. Supermarket checkout scanners useholographic optical elements (HOEs), which canread a universal product code (UPC) from anyangle. Use of holograms in daily life and scientif-ic research is likely to increase as scientists find

APERTURE: An opening.

DIFFRACTION: The bending of waves

around obstacles, or the spreading of waves

by passing them through an aperture.

ELECTROMAGNETIC SPECTRUM:

The complete range of electromagnetic

waves on a continuous distribution from a

very low range of frequencies and energy

levels, with a correspondingly long wave-

length, to a very high range of frequencies

and energy levels, with a correspondingly

short wavelength. Included on the electro-

magnetic spectrum are long-wave and

short-wave radio; microwaves; infrared,

visible, and ultraviolet light; x rays, and

gamma rays.




quency, the shorter the wavelength.



same direction as the wave itself. A sound

wave is an example of a longitudinal wave.

PRISM: A three-dimensional glass

shape used for the diffusion of light rays.

PROPAGATION: The act or state of

traveling from one place to another.

RADIATION: In a general sense, radia-

tion can refer to anything that travels in a

stream, whether that stream be composed

of subatomic particles or electromagnetic

waves.

REFLECTION: A phenomenon where-

by a light ray is returned toward its source

rather than being absorbed at the interface.

REFRACTION: The bending of a light

ray that occurs when it passes through a

dense medium, such as water or glass.

SPECTRUM: The continuous distribu-

tion of properties in an ordered arrange-

ment across an unbroken range. Examples

of spectra (the plural of “spectrum”)

include the colors of visible light, or the

electromagnetic spectrum of which visible

light is a part.




moving.



and an adjacent trough, of a wave. The

shorter the wavelength, the higher the

frequency.

KEY TERMS


Diffraction new applications: for instance, holographicimages will aid the design of everything frombridges to automobiles.

HOLOGRAPHIC MEMORY. One ofthe most fascinating areas of research in the fieldof holography is holographic memory. Comput-ers use a binary code, a pattern of ones andzeroes that is translated into an electronic pulse,but holographic memory would greatly extendthe capabilities of computer memory systems.Unlike most images, a hologram is not simply thesum of its constituent parts: the data in a holo-graphic image is contained in every part of theimage, meaning that part of the image can bedestroyed without a loss of data.

To bring the story full-circle, holographicmemory calls to mind an idea advanced by a sci-entist who, along with Huygens, was one of New-ton’s great professional rivals, German mathe-matician and philosopher Gottfried WilhelmLeibniz (1646-1716). Though Newton is usuallycredited as the father of calculus, Leibniz devel-oped his own version of calculus at around thesame time.

As a philosopher, Leibniz had apparentlyhad a number of strange ideas, which made himthe butt of jokes among some sectors of Euro-pean intellectual society: hence, the Frenchwriter and thinker Voltaire (François-MarieArouet; 1694-1778) satirized him with the char-acter Dr. Pangloss in Candide (1759). Few ofLeibniz’s ideas were more bizarre than that of themonad: an elementary particle of existence thatreflected the whole of the universe.

In advancing the concept of a monad, Leib-niz was not making a statement after the mannerof a scientist: there was no proof that monadsexisted, nor was it possible to prove this in any

scientific way. Yet, a hologram appears to be verymuch like a manifestation of Leibniz’s imaginedmonads, and both the hologram and the monadrelate to a more fundamental aspect of life:human memory. Neurological research in thelate twentieth century suggested that the struc-ture of memory in the human mind is holo-graphic. Thus, for instance, a patient suffering aninjury affecting 90% of the brain experiencesonly a 10% memory loss.

WHERE TO LEARN MORE

Barrett, Norman S. Lasers and Holograms. New York: F.Watts, 1985.

“Bragg’s Law and Diffraction: How Waves Reveal theAtomic Structure of Crystals” (Web site).<http://www.journey.sunysb.edu/ProjectJava/Bragg/home.html> (May 6, 2001).

Burkig, Valerie. Photonics: The New Science of Light. Hill-side, N.J.: Enslow Publishers, 1986.

“Diffraction of Sound” (Web site).<http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html> (May 6, 2001).

Gardner, Robert. Experimenting with Light. New York: F.Watts, 1991.

Graham, Ian. Lasers and Holograms. New York: ShootingStar Press, 1993.

Holoworld: Holography, Lasers, and Holograms (Website). <http://www.holoworld.com> (May 6, 2001).

Proffen, T. H. and R. B. Neder. Interactive Tutorial AboutDiffraction (Web site). <http://www.uniwuerzburg.de/mineralogie/crystal/teaching/teaching.html> (May6, 2001).

Snedden, Robert. Light and Sound. Des Plaines, IL:Heinemann Library, 1999.

“Wave-Like Behaviors of Light.” The Physics Classroom(Web site).<http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1a.html> (May 6, 2001).




DOPPLER EFFECTDoppler Effect

CONCEPTAlmost everyone has experienced the Dopplereffect, though perhaps without knowing whatcauses it. For example, if one is standing on astreet corner and an ambulance approaches withits siren blaring, the sound of the siren steadilygains in pitch as it comes closer. Then, as it pass-es, the pitch suddenly lowers perceptibly. This isan example of the Doppler effect: the change inthe observed frequency of a wave when thesource of the wave is moving with respect to theobserver. The Doppler effect, which occurs bothin sound and electromagnetic waves—includinglight waves—has a number of applications.Astronomers use it, for instance, to gauge themovement of stars relative to Earth. Closer tohome, principles relating to the Doppler effectfind application in radar technology. Dopplerradar provides information concerning weatherpatterns, but some people experience it in a less pleasant way: when a police officer uses it to measure their driving speed before writing aticket.

HOW IT WORKS

Wave Motion and Its Properties

Sound and light are both examples of energy, andboth are carried on waves. Wave motion is a typeof harmonic motion that carries energy from oneplace to another without actually moving anymatter. It is related to oscillation, a type of har-monic motion in one or more dimensions. Oscil-lation involves no net movement, only move-ment in place; yet individual points in the wave

medium are oscillating even as the overall wavepattern moves.

The term periodic motion, or movementrepeated at regular intervals called periods,describes the behavior of periodic waves—wavesin which a uniform series of crests and troughsfollow each other in regular succession. A period(represented by the symbol T) is the amount oftime required to complete one full cycle of thewave, from trough to crest and back to trough.

Period is mathematically related to severalother aspects of wave motion, including wavespeed, frequency, and wavelength. Frequency(abbreviated f) is the number of waves passingthrough a given point during the interval of onesecond. It is measured in Hertz (Hz), named afternineteenth-century German physicist HeinrichRudolf Hertz (1857-1894), and a Hertz is equalto one cycle of oscillation per second. Higher fre-quencies are expressed in terms of kilohertz(kHz; 103 or 1,000 cycles per second); megahertz(MHz; 106 or 1 million cycles per second); andgigahertz (GHz; 109 or 1 billion cycles per sec-ond.) Wavelength (represented by the symbol λ,the Greek letter lambda) is the distance betweena crest and the adjacent crest, or a trough and anadjacent trough, of a wave. The higher the fre-quency, the shorter the wavelength.

Amplitude, though mathematically inde-pendent from the parameters discussed, is criti-cal to the understanding of sound. Defined as themaximum displacement of a vibrating material,amplitude is the “size” of a wave. The greater theamplitude, the greater the energy the wave con-tains: amplitude indicates intensity, which, in thecase of sound waves, is manifested as what peo-ple commonly call “volume.” Similarly, the


DopplerEffect


amplitude of a light wave determines the intensi-ty of the light.

Frame of Reference

A knowledge of the fundamentals involved inwave motion is critical to understanding theDoppler effect; so, too, is an appreciation ofanother phenomenon, which is as much relatedto human psychology and perception as it is tophysics. Frame of reference is the perspective ofan observer with regard to an object or event.Things may look different for one person in oneframe of reference than they do to someone inanother.

For example, if you are sitting across thetable from a friend at lunch, and you see that hehas a spot of ketchup to the right of his mouth,the tendency is to say, “You have some ketchupright here”—and then point to the left of yourown mouth, since you are directly across thetable from his right. Then he will rub the left sideof his face with his napkin, missing the spotentirely, unless you say something like, “No—mirror image.” The problem is that each of youhas a different frame of reference, yet only yourfriend took this into account.

RELATIVE MOTION. Physicists oftenspeak of relative motion, or the motion of one

object in relation to another. For instance, themolecules in the human body are in a constantstate of motion, but they are not moving relativeto the body itself: they are moving relative to oneanother.

On a larger scale, Earth is rotating at a rate ofabout 1,000 MPH (1,600 km/h), and orbiting theSun at 67,000 MPH (107,826 km/h)—almostthree times as fast as humans have ever traveledin a powered vehicle. Yet no one senses the speedof Earth’s movement in the way that one sensesthe movement of a car—or, indeed, the way theastronauts aboard Apollo 11 in 1969 perceivedthat their spacecraft was moving at about 25,000MPH (40,000 km/h). In the case of the car or thespacecraft, movement can be perceived in rela-tion to other objects: road signs and buildings onthe one hand, Earth and the Moon on the other.But humans have no frame of reference fromwhich to perceive the movement of Earth itself.

If one were traveling in a train alongsideanother train at constant velocity, it would beimpossible to perceive that either train was actu-ally moving, unless one looked at a referencepoint, such as the trees or mountains in the back-ground. Likewise, if two trains were sitting sideby side, and one train started to move, the rela-tive motion might cause a passenger in theunmoving train to believe that his or her train

THE DOPPLER EFFECT.


DopplerEffect


was the one moving. In fact, as Albert Einstein

(1879-1955) demonstrated with his Theory of

Relativity, all motion is relative: when we say that

something is moving, we mean that it is moving

in relation to something else.

Doppler’s Discovery

Long before Einstein was born, Austrian physicist

Christian Johann Doppler (1803-1853) made an

important discovery regarding the relative

motion of sound waves or light waves. While

teaching in Prague, now the capital of the Czech

Republic, but then a part of the Austro-Hungari-

an Empire, Doppler became fascinated with a

common, but previously unexplained, phenome-non. When an observer is standing beside a rail-road track and a train approaches, Dopplernoticed, the train’s whistle has a high pitch. As itpasses by, however, the sound of the train whistlesuddenly becomes much lower.

By Doppler’s time, physicists had recognizedthe existence of sound waves, as well as the fact asound’s pitch is a function of frequency—inother words, the closer the waves are to oneanother, the higher the pitch. Taking this knowl-edge, he reasoned that if a source of sound ismoving toward a listener, the waves in front ofthe source are compressed, thus creating a higherfrequency. On the other hand, the waves behind

DOPPLER RADAR, LIKE THE WIND SPEED RADAR SHOWN HERE, HAVE BECOME A FUNDAMENTAL TOOL FOR METE-OROLOGISTS. (Photograph by Roger Ressmeyer/Corbis. Reproduced by permission.)


DopplerEffect

the moving source are stretched out, resulting ina lower frequency.

After developing a mathematical formula todescribe this effect, Doppler presented his find-ings in 1842. Three years later, he and Dutchmeteorologist Christopher Heinrich Buys-Ballot(1817-1890) conducted a highly unusual experi-ment to demonstrate the theory. Buys-Ballotarranged for a band of trumpet players to per-form on an open railroad flatcar, while ridingpast a platform on which a group of musicianswith perfect pitch (that is, a finely tuned sense ofhearing) sat listening.

The experiment went on for two days, theflatcar passing by again and again, while thehorns blasted and the musicians on the platformrecorded their observations. Though Dopplerand Buys-Ballot must have seemed like crazymen to those who were not involved in the exper-iment, the result—as interpreted from the musi-cians’ written impressions of the pitches theyheard—confirmed Doppler’s theory.


Sound Compression and theDoppler Effect

As stated in the introduction, one can observethe Doppler effect in a number of settings. If aperson is standing by the side of a road and a carapproaches at a significant rate of speed, the fre-quency of the sound waves grows until the carpasses the observer, then the frequency suddenlydrops. But Doppler, of course, never heard thesound of an automobile, or the siren of a motor-ized ambulance or fire truck.

In his day, the horse-drawn carriage stillconstituted the principal means of transporta-tion for short distances, and such vehicles did notattain the speeds necessary for the Doppler effectto become noticeable. Only one mode of trans-portation in the mid-nineteenth century made itpossible to observe and record the effect: asteam-powered locomotive. Therefore, let usconsider the Doppler effect as Doppler himselfdid—in terms of a train passing through a station.

THE SOUND OF A TRAIN WHIS-

TLE. When a train is sitting in a station prior toleaving, it blows its whistle, but listeners standing

nearby notice nothing unusual. There is no dif-ference—except perhaps in degree of intensity—between the sound heard by someone on theplatform, and the sound of the train as heard bysomeone standing behind the caboose. This isbecause a stationary train is at the center of thesound waves it produces, which radiate in con-centric circles (like a bulls-eye) around it.

As the train begins to move, however, it is nolonger at the center of the sound waves emanat-ing from it. Instead, the circle of waves is movingforward, along with the train itself, and, thus, thelocomotive compresses waves toward the front. Ifsomeone is standing further ahead along thetrack, that person hears the compressed soundwaves. Due to their compression, these have amuch higher frequency than the waves producedby a stationary train.

At the same time, someone standing behindthe train—a listener on the platform at the sta-tion, watching the train recede into the dis-tance—hears the sound waves that emanate frombehind the train. It is the same train making thesame sound, but because the train has com-pressed the sound waves in front of it, the wavesbehind it are spread out, producing a sound ofmuch lower frequency. Thus, the sound of thetrain, as perceived by two different listeners,varies with frame of reference.

THE SONIC BOOM: A RELAT-

ED EFFECT. Some people today have hadthe experience of hearing a jet fly high overhead,producing a shock wave known as a sonic boom.A sonic boom, needless to say, is certainly notsomething of which Doppler would have had anyknowledge, nor is it an illustration of theDoppler effect, per se. But it is an example ofsound compression, and, therefore, it deservesattention here.

The speed of sound, unlike the speed oflight, is dependant on the medium throughwhich it travels. Hence, there is no such thing asa fixed “speed of sound”; rather, there is only aspeed at which sound waves are transmittedthrough a given type of material. Its speedthrough a gas, such as air, is proportional to thesquare root of the pressure divided by the density. This, in turn, means that the higher thealtitude, the slower the speed of sound: for thealtitudes at which jets fly, it is about 660 MPH(1,622 km/h).



DopplerEffect

As a jet moves through the air, it too pro-duces sound waves which compress toward thefront, and widen toward the rear. Since soundwaves themselves are really just fluctuations inpressure, this means that the faster a jet goes, thegreater the pressure of the sound waves bunchedup in front of it. Jet pilots speak of “breaking thesound barrier,” which is more than just a figure ofspeech. As the craft approaches the speed ofsound, the pilot becomes aware of a wall of highpressure to the front of the plane, and as a resultof this high-pressure wall, the jet experiencesenormous turbulence.

The speed of sound is referred to as Mach 1,and at a speed of between Mach 1.2 and Mach1.4, even stranger things begin to happen. Nowthe jet is moving faster than the sound wavesemanating from it, and, therefore, an observer onthe ground sees the jet move by well before hear-ing the sound. Of course, this would happen tosome extent anyway, since light travels so muchfaster than sound; but the difference between thearrival time of the light waves and the soundwaves is even more noticeable in this situation.

Meanwhile, up in the air, every protrudingsurface of the aircraft experiences intense pres-sure: in particular, sound waves tend to becomehighly compressed along the aircraft’s nose andtail. Eventually these compressed sound wavesbuild up, resulting in a shock wave. Down on theground, the shock wave manifests as a “sonicboom”—or rather, two sonic booms—one fromthe nose of the craft, and one from the tail. Peo-ple in the aircraft do not hear the boom, but theshock waves produced by the compressed soundcan cause sudden changes in pressure, density,and temperature that can pose dangers to theoperation of the airplane. To overcome this prob-lem, designers of supersonic aircraft have devel-oped planes with wings that are swept back, sothey fit within the cone of pressure.

Doppler Radar and OtherSensing Technology

The Doppler effect has a number of applicationsrelating to the sensing of movement. Forinstance, physicians and medical techniciansapply it to measure the rate and direction ofblood flow in a patient’s body, along with ultra-sound. As blood moves through an artery, its topspeed is 0.89 MPH (0.4 m/s)—not very fast, yetfast enough, given the small area in which move-

ment is taking place, for the Doppler effect to beobserved. A beam of ultrasound is pointedtoward an artery, and the reflected waves exhibita shift in frequency, because the blood cells areacting as moving sources of sound waves—justlike the trains Doppler observed.

Not all applications of the Doppler effect fallunder the heading of “technology”: some can befound in nature. Bats use the Doppler effect tohunt for prey. As a bat flies, it navigates by emit-ting whistles and listening for the echoes. Whenit is chasing down food, its brain detects a changein pitch between the emitted whistle, and theecho it receives. This tells the bat the speed ofits quarry, and the bat adjusts its own speedaccordingly.

DOPPLER RADAR. Police officersmay not enjoy the comparison—given the pub-lic’s general impression of bats as evil, blood-thirsty creatures—but in using radar as a basis tocheck for speeding violations, the police areapplying a principle similar to that used by bats.Doppler radar, which uses the Doppler effect tocalculate the speed of moving objects, is a formof technology used not only by law-enforcementofficers, but also by meteorologists.

The change in frequency experienced as aresult of the Doppler effect is exactly twice theratio between the velocity of the target (forinstance, a speeding car) and the speed withwhich the radar pulse is directed toward the tar-get. From this formula, it is possible to determinethe velocity of the target when the frequencychange and speed of radar propagation areknown. The police officer’s Doppler radar per-forms these calculations; then all the officer hasto do is pull over the speeder and write a ticket.

Meteorologists use Doppler radar to trackthe movement of storm systems. By detecting thedirection and velocity of raindrops or hail, forinstance, Doppler radar can be used to determinethe motion of winds and, thus, to predict weath-er patterns that will follow in the next minutes orhours. But Doppler radar can do more than sim-ply detect a storm in progress: Doppler technol-ogy also aids meteorologists by interpreting winddirection, as an indicator of coming storms.

The Doppler Effect in LightWaves

So far the Doppler effect has been discussedpurely in terms of sound waves; but Doppler



DopplerEffect



ment of a vibrating material. In wave

motion, amplitude is the “size” of a wave,

an indicator of the energy and intensity of

the wave.

CYCLE: One complete oscillation. In

wave motion, this is equivalent to the

movement of a wave from trough to crest

and back to trough. For a sound wave,

in particular, a cycle is one complete

vibration.

DOPPLER EFFECT: The change in

the observed frequency of a wave when the

source of the wave is moving with respect

to the observer. It is named after Austrian

physicist Johann Christian Doppler (1803-

1853), who discovered it.

FRAME OF REFERENCE: The per-

spective an observer has with regard to an

object or action. Frame of reference affects

perception of various physical properties,

and plays a significant role in the Doppler

effect.





the shorter the wavelength. Measured in

Hertz, frequency is mathematically related

to wave speed, wavelength, and period.




HERTZ: A unit for measuring fre-

quency, named after nineteenth-century

German physicist Heinrich Rudolf Hertz



or 1,000 cycles per second); megahertz

(MHz; 106 or 1 million cycles per second);

and gigahertz (GHz; 109 or 1 billion cycles

per second.)

INTENSITY: Intensity is the rate at

which a wave moves energy per unit of

cross-sectional area. Where sound waves

are concerned, intensity is commonly

known as “volume.”



dimensions.





speed.







RELATIVE MOTION: The motion of

one object in relation to another.




length, symbolized λ (the Greek letter






matter.

KEY TERMS


DopplerEffect

himself maintained that it could be applied tolight waves as well, and experimentation con-ducted in 1901 proved him correct. This was farfrom an obvious point, since light is quite differ-ent from sound.

Not only does light travel much, muchfaster—186,000 mi (299,339 km) a second—butunlike sound, light does not need to travelthrough a medium. Whereas sound cannot betransmitted in outer space, light is transmitted byradiation, a form of energy transfer that can bedirected as easily through a vacuum as throughmatter.

The Doppler effect in light can be demon-strated by using a device called a spectroscope,which measures the spectral lines from an objectof known chemical composition. These spectrallines are produced either by the absorption oremission of specific frequencies of light by elec-trons in the source material. If the light wavesappear at the blue, or high-frequency end of thevisible light spectrum, this means that the objectis moving toward the observer. If, on the otherhand, the light waves appear at the red, or low-frequency end of the spectrum, the object ismoving away.

HUBBLE AND THE RED SHIFT.

In 1923, American astronomer Edwin Hubble(1889-1953) observed that the light waves fromdistant galaxies were shifted so much to the redend of the light spectrum that they must be mov-ing away from the Milky Way, the galaxy in whichEarth is located, at a high rate. At the same time,nearer galaxies experienced much less of a redshift, as this phenomenon came to be known,meaning that they were moving away at relative-ly slower speeds.

Six years later, Hubble and another astron-omer, Milton Humason, developed a mathemat-

ical formula whereby astronomers could deter-mine the distance to another galaxy by measur-ing that galaxy’s red shifts. The formula came tobe known as Hubble’s constant, and it establishedthe relationship between red shift and the veloc-ity at which a galaxy or object was receding fromEarth. From Hubble’s work, it became clear thatthe universe was expanding, and research by anumber of physicists and astronomers led to thedevelopment of the “big bang” theory—the ideathat the universe emerged almost instantaneous-ly, in some sort of explosion, from a compressedstate of matter.

WHERE TO LEARN MORE


Bryant-Mole, Karen. Sound and Light. Crystal Lake, IL:Rigby Interactive Library, 1997.

Challoner, Jack. Sound and Light. New York: Kingfisher,2001.

Dispenzio, Michael A. Awesome Experiments in Light andSound. Illustrated by Catherine Leary. New York:Sterling Publishing Company, 1999.

“The Doppler Effect.” The Physics Classroom (Web site).<http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l3d.html> (April 29, 2001).

Maton, Anthea. Exploring Physical Science. Upper SaddleRiver, N.J.: Prentice Hall, 1997.

Russell, David A. “The Doppler Effect and Sonic Booms”Kettering University (Web site). <http://www.kettering.edu/~drussell/Demos/doppler/doppler.html> (April 29, 2001).

Snedden, Robert. Light and Sound. Des Plaines, IL:Heinemann Library, 1999.

“Sound Wave—Doppler Effect” (Web site).<http://csgrad.cs.vt.edu/~chin/doppler.html> (April29, 2001).

“Wave Motion—Doppler Effect” (Web site).<http://members.aol.com/cepeirce/b21.html> (April29, 2001).



309


SOUNDSOUND

ACOUST ICS

ULTRASON ICS



A COUST ICSAcoustics

CONCEPTThe area of physics known as acoustics is devot-ed to the study of the production, transmission,and reception of sound. Thus, wherever sound isproduced and transmitted, it will have an effectsomewhere, even if there is no one present tohear it. The medium of sound transmission is anall-important, key factor. Among the areasaddressed within the realm of acoustics are theproduction of sounds by the human voice andvarious instruments, as well as the reception ofsound waves by the human ear.

HOW IT WORKS

Wave Motion and Soundwaves

Sound waves are an example of a larger phenom-enon known as wave motion, and wave motionis, in turn, a subset of harmonic motion—that is,repeated movement of a particle about a positionof equilibrium, or balance. In the case of sound,the “particle” is not an item of matter, but ofenergy, and wave motion is a type of harmonicmovement that carries energy from one place toanother without actually moving any matter.

Particles in waves experience oscillation,harmonic motion in one or more dimensions.Oscillation itself involves little movement,though some particles do move short distances asthey interact with other particles. Primarily, how-ever, it involves only movement in place. Thewaves themselves, on the other hand, moveacross space, ending up in a position differentfrom the one in which they started.

A transverse wave forms a regular up-and-down pattern in which the oscillation is perpen-

dicular to the direction the wave is moving. Thisis a fairly easy type of wave to visualize: imaginea curve moving up and down along a straightline. Sound waves, on the other hand, are longi-tudinal waves, in which oscillation occurs in thesame direction as the wave itself.

These oscillations are really just fluctuationsin pressure. As a sound wave moves through amedium such as air, these changes in pressurecause the medium to experience alternations ofdensity and rarefaction (a decrease in density).This, in turn, produces vibrations in the humanear or in any other object that receives the soundwaves.

Properties of Sound Waves

CYCLE AND PERIOD. The termcycle has a definition that varies slightly, depend-ing on whether the type of motion being dis-cussed is oscillation, the movement of transversewaves, or the motion of a longitudinal soundwave. In the latter case, a cycle is defined as a sin-gle complete vibration.

A period (represented by the symbol T) isthe amount of time required to complete one fullcycle. The period of a sound wave can be mathe-matically related to several other aspects of wavemotion, including wave speed, frequency, andwavelength.

THE SPEED OF SOUND IN

VARIOUS MEDIA. People often refer tothe “speed of sound” as though this were a fixedvalue like the speed of light, but, in fact, the speedof sound is a function of the medium throughwhich it travels. What people ordinarily mean bythe “speed of sound” is the speed of soundthrough air at a specific temperature. For sound


Acoustics


traveling at sea level, the speed at 32°F (0°C) is740 MPH (331 m/s), and at 68°F (20°C), it is 767MPH (343 m/s).

In the essay on aerodynamics, the speed ofsound for aircraft was given at 660 MPH (451m/s). This is much less than the figures givenabove for the speed of sound through air at sealevel, because obviously, aircraft are not flying atsea level, but well above it, and the air throughwhich they pass is well below freezing tem-perature.

The speed of sound through a gas is propor-tional to the square root of the pressure dividedby the density. According to Gay-Lussac’s law,pressure is directly related to temperature, mean-ing that the lower the pressure, the lower thetemperature—and vice versa. At high altitudes,the temperature is low, and, therefore, so is thepressure; and, due to the relatively small gravita-tional pull that Earth exerts on the air at thatheight, the density is also low. Hence, the speed ofsound is also low.

It follows that the higher the pressure of thematerial, and the greater the density, the fastersound travels through it: thus sound travels fasterthrough a liquid than through a gas. This mightseem a bit surprising: at first glance, it wouldseem that sound travels fastest through air, but

only because we are just more accustomed tohearing sounds that travel through that medium.The speed of sound in water varies from about3,244 MPH (1,450 m/s) to about 3,355 MPH(1500 m/s). Sound travels even faster through asolid—typically about 11,185 MPH (5,000m/s)—than it does through a liquid.

FREQUENCY. Frequency (abbreviatedf) is the number of waves passing through a givenpoint during the interval of one second. It ismeasured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz(1857-1894) and a Hertz is equal to one cycle ofoscillation per second. Higher frequencies areexpressed in terms of kilohertz (kHz; 103 or 1,000cycles per second) or megahertz (MHz; 106 or 1million cycles per second.)

The human ear is capable of hearing soundsfrom 20 to approximately 20,000 Hz—a relative-ly small range for a mammal, considering thatbats, whales, and dolphins can hear sounds at afrequency up to 150 kHz. Human speech is in therange of about 1 kHz, and the 88 keys on a pianovary in frequency from 27 Hz to 4,186 Hz. Eachnote has its own frequency, with middle C (the“white key” in the very middle of a piano key-board) at 264 Hz. The quality of harmony or dis-sonance when two notes are played together is a

BECAUSE THE SOUND GENERATED BY A JET ENGINE CAN DAMAGE A PERSON’S HEARING, AIRPORT GROUND CREWS

ALWAYS WEAR PROTECTIVE HEADGEAR. (Photograph by Patrick Bennett/Corbis. Reproduced by permission.)


Acoustics


function of the relationship between the fre-quencies of the two.

Frequencies below the range of human audi-bility are called infrasound, and those above itare referred to as ultrasound. There are a numberof practical applications for ultrasonic technolo-gy in medicine, navigation, and other fields.

WAVELENGTH. Wavelength (repre-sented by the symbol λ, the Greek letter lambda)is the distance between a crest and the adjacentcrest, or a trough and an adjacent trough, of awave. The higher the frequency, the shorter thewavelength, and vice versa. Thus, a frequency of20 Hz, at the bottom end of human audibility,has a very large wavelength: 56 ft (17 m). The topend frequency of 20,000 Hz is only 0.67 inches (17 mm).

There is a special type of high-frequencysound wave beyond ultrasound: hypersound,which has frequencies above 107 MHz, or 10 tril-lion Hz. It is almost impossible for hypersoundwaves to travel through all but the densest media,because their wavelengths are so short. In orderto be transmitted properly, hypersound requiresan extremely tight molecular structure; other-wise, the wave would get lost between molecules.

Wavelengths of visible light, part of the elec-tromagnetic spectrum, have a frequency muchhigher even than hypersound waves: about 109

MHz, 100 times greater than for hypersound.This, in turn, means that these wavelengths areincredibly small, and this is why light waves caneasily be blocked out by using one’s hand or acurtain.

The same does not hold for sound waves,because the wavelengths of sounds in the rangeof human audibility are comparable to the size ofordinary objects. To block out a sound wave, oneneeds something of much greater dimensions—width, height, and depth—than a mere cloth cur-tain. A thick concrete wall, for instance, may beenough to block out the waves. Better still wouldbe the use of materials that absorb sound, such ascork, or even the use of machines that producesound waves which destructively interfere withthe offending sound.

AMPLITUDE AND INTENSITY.

Amplitude is critical to the understanding ofsound, though it is mathematically independentfrom the parameters so far discussed. Defined asthe maximum displacement of a vibrating mate-rial, amplitude is the “size” of a wave. The greaterthe amplitude, the greater the energy the wave

PIANO STRINGS GENERATE SOUND AS THEY ARE SET INTO VIBRATION BY THE HAMMERS. THE HAMMERS, IN TURN,ARE ATTACHED TO THE BLACK-AND-WHITE KEYS ON THE OUTSIDE OF THE PIANO. (Photograph by Bob Krist/Corbis. Reproduced

by permission.)


Acoustics respond to sounds in a linear, or straight-line,progression. If the intensity of a sound is dou-bled, a person perceives a greater intensity, butnothing approaching twice that of the originalsound. Instead, a different system—known inmathematics as a logarithmic scale—is applied.

In measuring the effect of sound intensityon the human ear, a unit called the decibel(abbreviated dB) is used. A sound of minimalaudibility (10-12 W/m2) is assigned the value of 0dB, and 10 dB is 10 times as great—10-11 W/m2.But 20 dB is not 20 times as intense as 0 dB; it is100 times as intense, or 10-10 W/m2. Everyincrease of 10 dB thus indicates a tenfold increasein intensity. Therefore, 120 dB, the maximumdecibel level that a human ear can endure with-out experiencing damage, is not 120 times asgreat as the minimal level for audibility, but 1012

(1 trillion) times as great—equal to 1 W/m2,referred to above as the highest safe intensitylevel.

Of course, sounds can be much louder than120 dB: a rock band, for instance, can generatesounds of 125 dB, which is 5 times the maximumsafe decibel level. A gunshot, firecracker, or ajet—if one is exposed to these sounds at a suffi-ciently close proximity—can be as high as 140dB, or 20 times the maximum safe level. Nor is120 dB safe for prolonged periods: hearingexperts indicate that regular and repeated expo-sure to even 85 dB (5 less than a lawn mower) cancause permanent damage to one’s hearing.

Production of Sound Waves

MUSICAL INSTRUMENTS. Soundwaves are vibrations; thus, in order to producesound, vibrations must be produced. For astringed instrument, such as a guitar, harp, orpiano, the strings must be set into vibration,either by the musician’s fingers or the mechanismthat connects piano keys to the strings inside thecase of the piano.

In other woodwind instruments and horns,the musician causes vibrations by blowing intothe mouthpiece. The exact process by which thevibrations emerge as sound differs betweenwoodwind instruments, such as a clarinet or sax-ophone on the one hand, and brass instruments,such as a trumpet or trombone on the other.Then there is a drum or other percussion instru-ment, which produces vibrations, if not musicalnotes.


contains: amplitude indicates intensity, com-monly known as “volume,” which is the rate atwhich a wave moves energy per unit of a cross-sectional area.

Intensity can be measured in watts persquare meter, or W/m2. A sound wave of mini-mum intensity for human audibility would havea value of 10-12, or 0.000000000001, W/m2. As abasis of comparison, a person speaking in anordinary tone of voice generates about 10-4, or0.0001, watts. On the other hand, a sound withan intensity of 1 W/m2 would be powerfulenough to damage a person’s ears.


Decibel Levels

For measuring the intensity of a sound as experi-enced by the human ear, we use a unit other thanthe watt per square meter, because ears do not

THE HUMAN VOICE, WHETHER IN SPEECH OR IN SONG,IS A REMARKABLE SOUND-PRODUCING INSTRUMENT: AT

ANY GIVEN MOMENT AS A PERSON IS TALKING OR

SINGING, PARTS OF THE VOCAL CORDS ARE OPENED,AND PARTS ARE CLOSED. SHOWN HERE IS OPERA

SUPERSTAR JOAN SUTHERLAND. (Hulton-Deutsch Collec-

tion/Corbis. Reproduced by permission.)


AcousticsELECTRONIC AMPLIFICATION.

Sound is a form of energy: thus, when an auto-mobile or other machine produces sound inci-dental to its operation, this actually representsenergy that is lost. Energy itself is conserved, butnot all of the energy put into the machine canever be realized as useful energy; thus, the auto-mobile loses some energy in the form of soundand heat.

The fact that sound is energy, however, alsomeans that it can be converted to other forms ofenergy, and this is precisely what a microphonedoes: it receives sound waves and converts themto electrical energy. These electrical signals aretransmitted to an amplifier, and next to a loud-speaker, which turns electrical energy back intosound energy—only now, the intensity of thesound is much greater.

Inside a loudspeaker is a diaphragm, a thin,flexible disk that vibrates with the intensity of thesound it produces. When it pushes outward, thediaphragm forces nearby air molecules closertogether, creating a high-pressure region aroundthe loudspeaker. (Remember, as stated earlier,that sound is a matter of fluctuations in pres-sure.) The diaphragm is then pushed backwardin response, freeing up an area of space for the airmolecules. These, then, rush toward thediaphragm, creating a low-pressure regionbehind the high-pressure one. The loudspeakerthus sends out alternating waves of high and lowpressure, vibrations on the same frequency of theoriginal sound.

THE HUMAN VOICE. As impressiveas the electronic means of sound production are (and of course the description just given ishighly simplified), this technology pales in com-parison to the greatest of all sound-producingmechanisms: the human voice. Speech itself is ahighly complex physical process, much tooinvolved to be discussed in any depth here. Forour present purpose, it is important only to rec-ognize that speech is essentially a matter of pro-ducing vibrations on the vocal cords, and thentransmitting those vibrations.

Before a person speaks, the brain sends sig-nals to the vocal cords, causing them to tighten.As speech begins, air is forced across the vocalcords, and this produces vibrations. The action ofthe vocal cords in producing these vibrations is,like everything about the miracle of speech,exceedingly involved: at any given moment as a

person is talking, parts of the vocal cords areopened, and parts are closed.

The sound of a person’s voice is affected by anumber of factors: the size and shape of thesinuses and other cavities in the head, the shapeof the mouth, and the placement of the teeth andtongue. These factors influence the production ofspecific frequencies of sound, and result in dif-fering vocal qualities. Again, the mechanisms ofspeech are highly complicated, involving actionof the diaphragm (a partition of muscle and tis-sue between the chest and abdominal cavities),larynx, pharynx, glottis, hard and soft palates,and so on. But, it all begins with the productionof vibrations.

Propagation: Does It Make a Sound?

As stated in the introduction, acoustics is con-cerned with the production, transmission (some-times called propagation), and reception ofsound. Transmission has already been examinedin terms of the speed at which sound travelsthrough various media. One aspect of soundtransmission needs to be reiterated, however:for sound to be propagated, there must be amedium.

There is an age-old “philosophical” questionthat goes something like this: If a tree falls in thewoods and there is no one to hear it, does it makea sound? In fact, the question is not a matter ofphilosophy at all, but of physics, and the answeris, of course, “yes.” As the tree falls, it releasesenergy in a number of forms, and part of thisenergy is manifested as sound waves.

Consider, on the other hand, this rephrasedversion of the question: “If a tree falls in a vacu-um—an area completely devoid of matter,including air—does it make a sound?” Theanswer is now a qualified “no”: certainly, there isa release of energy, as before, but the sound wavescannot be transmitted. Without air or any othermatter to carry the waves, there is literally nosound.

Hence, there is a great deal of truth to thetagline associated with the 1979 science-fictionfilm Alien: “In space, no one can hear youscream.” Inside an astronaut’s suit, there is pres-sure and an oxygen supply; without either, theastronaut would perish quickly. The pressure andair inside the suit also allow the astronaut to hearsounds within the suit, including communica-



Acoustics


tions via microphone from other astronauts. But,if there were an explosion in the vacuum of deepspace outside the spacecraft, no one inside wouldbe able to hear it.

Reception of Sound

RECORDING. Earlier the structure ofelectronic amplification was described in verysimple terms. Some of the same processes—specifically, the conversion of sound to electricalenergy—are used in the recording of sound. Insound recording, when a sound wave is emitted,it causes vibrations in a diaphragm attached toan electrical condenser. This causes variations inthe electrical current passed on by the condenser.

These electrical pulses are processed and

ultimately passed on to an electromagnetic

“recording head.” The magnetic field of the

recording head extends over the section of tape

being recorded: what began as loud sounds now

produce strong magnetic fields, and soft sounds

produce weak fields. Yet, just as electronic means

of sound production and transmission are still

not as impressive as the mechanisms of the

human voice, so electronic sound reception and

recording technology is a less magnificent device

than the human ear.

HOW THE EAR HEARS. As almost

everyone has noticed, a change in altitude (and,

hence, of atmospheric pressure) leads to a

ACOUSTICS: An area of physics

devoted to the study of the production,

transmission, and reception of sound.




and for sound waves, amplitude indicates

the intensity or volume of sound.

CYCLE: For a sound wave, a cycle is a

single complete vibration.

DECIBEL: A unit for measuring inten-

sity of sound. Decibels, abbreviated dB, are

calibrated along a logarithmic scale where-

by every increase of 10 dB indicates an

increase in intensity by a factor of 10. Thus

if the level of intensity is increased from 30

to 60 dB, the resulting intensity is not twice

as great as that of the earlier sound—it is

1,000 times as great.

ENERGY: The ability to perform work,

which is the exertion of force over a given

distance. Work is the product of force and

distance, where force and distance are

exerted in the same direction.




















cross-sectional area. Where sound waves

are concerned, intensity is commonly

known as “volume.”

KEY TERMS


Acoustics


strange “popping” sensation in the ears. Usually,

this condition can be overcome by swallowing, or

even better, by yawning. This opens the Eustachi-

an tube, a passageway that maintains atmospher-

ic pressure in the ear. Useful as it is, the Eustachi-

an tube is just one of the human ear’s many parts.

The “funny” shape of the ear helps it to cap-

ture and amplify sound waves, which pass

through the ear canal and cause the eardrum to

vibrate. Though humans can hear sounds over a

much wider range, the optimal range of audibil-

ity is from 3,000 to 4,000 Hz. This is because the

structure of the ear canal is such that sounds in

this frequency produce magnified pressure fluc-

tuations. Thanks to this, as well as other specificproperties, the ear acts as an amplifier of sounds.

Beyond the eardrum is the middle ear, anintricate sound-reception device containingsome of the smallest bones in the human body—bones commonly known, because of theirshapes, as the hammer, anvil, and stirrup. Vibra-tions pass from the hammer to the anvil to thestirrup, through the membrane that covers theoval window, and into the inner ear.

Filled with liquid, the inner ear contains thesemicircular canals responsible for providing asense of balance or orientation: without these, aperson literally “would not know which way isup.” Also, in the inner ear is the cochlea, an organ



same direction as the wave itself. A sound

wave is an example of a longitudinal wave.




energy.

MEDIUM: Material through which

sound travels. (It cannot travel through a

vacuum.) The most common medium

(plural, media) of sound transmission

experienced in daily life is air, but in fact

sound can travel through any type of

matter.

OSCILLATION: The vibration experi-

enced by individual waves even as the wave

itself is moving through space. Oscillation

is a type of harmonic motion, typically

periodic, in one or more dimensions.





speed.




RAREFACTION: A decrease in density.

ULTRASOUND : Sound waves with a

frequency above 20,000 Hertz, which

makes them inaudible to the human ear.

VACUUM: An area entirely devoid of





length, symbolized by λ (the Greek letter






matter.



Acoustics shaped like a snail. Waves of pressure from thefluids of the inner ear are passed through thecochlea to the auditory nerve, which then trans-mits these signals to the brain.

The basilar membrane of the cochlea is aparticularly wondrous instrument, responsible inlarge part for the ability to discriminate betweensounds of different frequencies and intensities.The surface of the membrane is covered withthousands of fibers, which are highly sensitive todisturbances, and it transmits information con-cerning these disturbances to the auditory nerve.The brain, in turn, forms a relation between theposition of the nerve ending and the frequency ofthe sound. It also equates the degree of distur-bance in the basilar membrane with the intensityof the sound: the greater the disturbance, thelouder the sound.

WHERE TO LEARN MORE

Adams, Richard C. and Peter H. Goodwin. EngineeringProjects for Young Scientists. New York: FranklinWatts, 2000.


Friedhoffer, Robert. Sound. Illustrated by Richard Kauf-man and Linda Eisenberg; photographs by TimothyWhite. New York: F. Watts, 1992.

Gardner, Robert. Science Projects About Sound. BerkeleyHeights, NJ: Enslow Publishers, 2000.


“Music and Sound Waves” (Web site). <http://www.silcom.com/~aludwig/musicand.htm> (April 28,2001).

Oxlade, Chris. Light and Sound. Des Plaines, IL: Heine-mann Library, 2000.

Physics Tutorial System: Sound Waves Modules (Web site).<http://csgrad.cs.vt.edu/~chin/chin_sound.html>(April 25, 2001).

“Sound Waves and Music.” The Physics Classroom (Website). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/soundtoc.h tml> (April 28, 2001).

“What Are Sound Waves?” (Web site).<http://rustam.uwp.edu/GWWM/sound_waves.html> (April 28, 2001).




U LTR ASON ICSUltrasonics

CONCEPTThe word ultrasonic combines the Latin rootsultra, meaning “beyond,” and sonic, or sound.The field of ultrasonics thus involves the use ofsound waves outside the audible range forhumans. These sounds have applications forimaging, detection, and navigation—from help-ing prospective parents get a glimpse of theirunborn child to guiding submarines through theoceans. Ultrasonics can be used to join materials,as for instance in welding or the homogenizationof milk, or to separate them, as for example inextremely delicate cleaning operations. Amongthe broad sectors of society that regularly applyultrasonic technology are the medical communi-ty, industry, the military, and private citizens.

HOW IT WORKSIn the realm of physics, ultrasonics falls underthe category of studies in sound. Sound itself fitswithin the larger heading of wave motion, whichis in turn closely related to vibration, or harmon-ic (back-and-forth) motion. Both wave motionand vibration involve the regular repetition of acertain form of movement; and in both, potentialenergy (think of the energy in a sled at the top ofa hill) is continually converted to kinetic energy(like the energy of a sled as it is sliding down thehill) and back again.

Wave motion carries energy from one placeto another without actually moving any matter.Waves themselves may consist of matter, as forinstance in the case of a wave on a plucked stringor the waves on the ocean. This type of wave iscalled a mechanical wave, but again, the matteritself does not undergo any net displacementover horizontal space: contrary to what our eyes

tell us, molecules of water in an ocean wave moveup and down, but they do not actually travel withthe wave itself. Only the energy is moved.

Sound Waves

Then there are waves of pulses, such as light,sound, radio, or electromagnetic waves. Soundtravels by means of periodic waves, a periodbeing the amount of time it takes a completewave, from trough to crest and back again, topass through a given point. These periodic wavesare typified by a sinusoidal pattern. To picture asinusoidal wave, one need only imagine an x-axiscrossed at regular intervals by a curve that risesabove the line to point y before moving down-ward, below the axis, to point y. This may beexpressed also as a graph of sin x versus x. In anycase, the wave varies by equal distances upwardand downward as it moves along the x-axis in aregular, unvarying pattern.

Periodic waves have three notable interrelat-ed characteristics. One of these is speed, typical-ly calculated in seconds. Another is wavelength,or the distance between a crest and the adjacentcrest, or a trough and the adjacent trough, alonga plane parallel to that of the wave itself. Finally,there is frequency, the number of waves passingthrough a given point during the interval of onesecond.

Frequency is measured in terms of cycles persecond, or Hertz (Hz), named in honor of thenineteenth-century German physicist HeinrichHertz. If a wave has a frequency of 100 Hz, thismeans that 100 waves are passing through a givenpoint during the interval of one second. Higherfrequencies are expressed in terms of kilohertz


Ultrasonics


(kHz; 103 or 1,000 cycles per second) or mega-hertz (MHz; 106 or 1 million cycles per second.)

Clearly, frequency is a function of the wave’sspeed or velocity, and the same relationship—though it is not so obvious intuitively—existsbetween wavelength and speed. Over the intervalof one second, a given number of waves pass acertain point (frequency), and each wave occu-pies a certain distance (wavelength). Multipliedby one another, these two properties equal thevelocity of the wave.

An additional characteristic of waves(though one that is not related mathematically tothe three named above) is amplitude, or maxi-mum displacement, which can be described asthe distance from the x-axis to either the crest orthe trough. Amplitude is related to the intensityor the amount of energy in the wave.

These four qualities are easiest to imagine ona transverse wave, described earlier with refer-ence to the x-axis—a wave, in other words, inwhich vibration or harmonic motion occurs per-pendicular to the direction in which the wave ismoving.

Such a wave is much easier to picture, for thepurposes of illustrating concepts such as fre-quency, than a longitudinal wave; but in fact,

sound waves are longitudinal. A longitudinalwave is one in which the individual segmentsvibrate in the same direction as the wave itself.The shock waves of an explosion, or the concen-tric waves of a radio transmission as it goes outfrom the station to all points within receivingdistance, are examples of longitudinal waves. Inthis type of wave pattern, the crests and troughsare not side by side in a line; they radiate out-ward. Wavelength is the distance between eachconcentric circle or semicircle (that is, wave), andamplitude the “width” of each wave, which onemay imagine by likening it to the relative widthof colors on a rainbow.

Having identified its shape, it is reasonableto ask what, exactly, a sound wave is. Simply put,sound waves are changes in pressure, or an alter-nation between condensation and rarefaction.Imagine a set of longitudinal waves—representedas concentric circles—radiating from a soundsource. The waves themselves are relatively high-er in pressure, or denser, than the “spaces”between them, though this is just an illustrationfor the purposes of clarity: in fact the “spaces” arewaves of lower pressure that alternate with high-er-pressure waves.

Vibration is integral to the generation ofsound. When the diaphragm of a loudspeaker

SUBMARINES, SUCH AS THE U.S. NAVY SUBMARINE PICTURED HERE, RELY HEAVILY ON SONAR. (Corbis. Reproduced by

permission.)


Ultrasonics


pushes outward, it forces nearby air moleculescloser together, creating a high-pressure regionall around the loudspeaker. The diaphragm ispushed backward in response, thus freeing up avolume of space for the air molecules. These thenrush toward the diaphragm, creating a low-pres-sure region behind the high-pressure one. As aresult, the loudspeaker sends out alternatingwaves of high pressure (condensation) and lowpressure (rarefaction). Furthermore, as soundwaves pass through a medium—air, for the pur-poses of this discussion—they create fluctuationsbetween density and rarefaction. These result inpressure changes that cause the listener’seardrum to vibrate with the same frequency asthe sound wave, a vibration that the ear’s innermechanisms translate and pass on to the brain.

The Speed of Sound: Consider the Medium

The speed of sound varies with the hardness ofthe medium through which it passes: contrary towhat you might imagine, it travels faster throughliquids than through gasses such as air, and fasterthrough solids than through liquids. By defini-tion, molecules are closer together in hardermaterial, and thus more quickly responsive tosignals from neighboring particles. In granite, for

instance, sound travels at 19,680 ft per second(6,000 mps), whereas in air, the speed of sound isonly 1,086 ft per second (331 mps). It followsthat sound travels faster in water—5,023 ft persecond (1,531 mps), to be exact—than in air. Itshould be clear, then, that there is a correlationbetween density and the ease with which a soundtravels. Thus, sound cannot travel in a vacuum,giving credence to the famous tagline from the1979 science fiction thriller Alien: “In space, noone can hear you scream.”

When sound travels through a medium suchas air, however, two factors govern its audibility:intensity or volume (related to amplitude andmeasured in decibels, or dB) and frequency.There is no direct correlation between intensityand frequency, though for a person to hear a verylow-frequency sound, it must be above a certaindecibel level. (At all frequencies, however, thethreshold of discomfort is around 120 decibels.)

In any case, when discussing ultrasonics, fre-quency and not intensity is of principal concern.The range of audibility for the human ear is from20 Hz to 20,000 Hz, with frequencies below thatrange dubbed infrasound and those above itreferred to as ultrasound. (There is a third cate-gory, hypersound, which refers to frequenciesabove 1013, or 10 trillion Hz. It is almost impos-

A FISHING REVOLUTION? IT’S POSSIBLE, THANKS TO THIS ELECTRONIC FISH-FINDER DEVELOPED BY MATSUSHITA.THE DEVICE INCLUDES A DETACHABLE SONAR SENSOR. (AFP/Corbis. Reproduced by permission.)


Ultrasonics


sible for hypersound waves to travel throughmost media, because its wavelengths are soshort.)

What Makes the Glass Shatter

The lowest note of the eighty-eight keys on apiano is 27 Hz and the highest 4,186 Hz. Thisplaces the middle and upper register of the pianowell within the optimal range for audibility,which is between 3,000 and 4,000 Hz. Clearly, thehigher the note, the higher the frequency—but itis not high frequency, per se, that causes a glass toshatter when a singer or a violinist hits a certainnote. All objects, or at least all rigid ones, possesstheir own natural frequency of vibration or oscil-lation. This frequency depends on a number offactors, including material composition andshape, and its characteristics are much morecomplex than those of sound frequencydescribed above. In any case, a musician cannotcause a glass to shatter simply by hitting a veryhigh note; rather, the note must be on the exactfrequency at which the glass itself oscillates.Under such conditions, all the energy from thevoice or musical instrument is transferred to theglass, a sudden burst that overloads the objectand causes it to shatter.

To create ultrasonic waves, technicians use atransducer, a device that converts energy intoultrasonic sound waves. The most basic type oftransducer is mechanical, involving oscillators orvibrating blades powered either by gas or thepressure of gas or liquids—that is, pneumatic orhydrodynamic pressure, respectively. The vibra-tions from these mechanical devices are on a rel-atively low ultrasonic frequency, and most com-monly they are applied in industry for purposessuch as drying or cleaning.

An electromechanical transducer, which hasa much wider range of applications, convertselectrical energy, in the form of current, tomechanical energy—that is, sound waves. This itdoes either by a magnetostrictive or a piezoelec-tric device. The term “magnetostrictive” comesfrom magneto, or magnetic, and strictio, or“drawing together.” This type of transducerinvolves the magnetization of iron or nickel,which causes a change in dimension by forcingthe atoms together. This change in dimension inturn produces a high-frequency vibration. Again,the frequency is relatively low in ultrasonicterms, and likewise the application is primarilyindustrial, for purposes such as cleaning andmachining.

TINY LISTENING DEVICES, LIKE THE ONE SHOWN HERE, HAVE A HOST OF MODERN APPLICATIONS, FROM ELECTRON-IC EAVESDROPPING TO ULTRASONIC STEREO SYSTEMS. (Photograph by Jeffrey L. Rotman/Corbis. Reproduced by permission.)


UltrasonicsMost widely used is a transducer equippedwith a specially cut piezoelectric quartz crystal.Piezoelectricity involves the application ofmechanical pressure to a nonconducting crystal,which results in polarization of electrical charges,with all positive charges at one end of the crystaland all negative charges at the other end. By suc-cessively compressing and stretching the crystalat an appropriate frequency, an alternating elec-trical current is generated that can be convertedinto mechanical energy—specifically, ultrasonicwaves.

Scientists use different shapes and materials(including quartz and varieties of ceramic) infashioning piezoelectric crystals: for instance, aconcave shape is best for an ultrasonic wave thatwill be focused on a very tight point. Piezoelec-tric transducers have a variety of applications inultrasonic technology, and are capable of actingas receivers for ultrasonic vibrations.


Pets and Pests: UltrasonicBehavior Modification

Some of the simplest ultrasonic applicationsbuild on the fact that the upper range of audibil-ity for human beings is relatively low among ani-mals. Cats, by comparison, have an infrasoundthreshold only slightly higher than that ofhumans (100 Hz), but their ultrasound range of audibility is much greater—32,000 Hz in-stead of a mere 20,000. This explains why a catsometimes seems to respond mysteriously tonoises its owner is incapable of hearing.

For dogs, the difference is even moreremarkable: their lower threshold is 40 Hz, andtheir high end 46,000 Hz, giving them a rangemore than twice that of humans. It has been saidPaul McCartney, who was fond of his sheepdogMartha, arranged for the Beatles’ sound engineerat Abbey Road Studios to add a short 20,000-Hztone at the very end of Sgt. Peppers’ Lonely HeartsClub Band in 1967. Thus—if the story is true—the Beatles’ human fans would never hear thenote, but it would be a special signal to Marthaand all the dogs of England.

On a more practical level, a dog whistle is anextremely simple ultrasonic or near-ultrasonicdevice, one that obviously involves no transduc-

ers. The owner blows the whistle, which utters atone nearly inaudible to humans but—likeMcCartney’s 20,000-Hz tone—well within adog’s range. In fact, the Acme Silent Dog Whistle,which the company has produced since 1935,emits a tone that humans can hear (the listedrange is 5,800 to 12,400 Hz), but which dogs canhear much better.

There are numerous products on the marketthat use ultrasonic waves for animal behaviormodification of one kind or another; however,most such items are intended to repel rather thanattract the animal. Hence, there are ultrasonicdevices to discourage animals from relievingthemselves in the wrong places, as well as somewhich keep unwanted dogs and cats away.

Then there is one of the most well-knownuses of ultrasound for pets, which, rather thankeeping other animals out, is designed to keepone’s own animals in the yard. Many peopleknow this item as an “Invisible Fence,” though infact that term is a registered trademark of theInvisible Fence Company. The “Invisible Fence”and similar products literally create a barrier ofsound, using both radio signals and ultrasonics.The pet is outfitted with a collar that contains aradio receiver, and a radio transmitter is placedin some centrally located place on the owner’sproperty—a basement, perhaps, or a garage. The“fence” itself is “visible,” though usually buried,and consists of an antenna wire at the perimeterof the property. The transmitter sends a signal tothe wire, which in turn signals the pet’s collar. Atiny computer in the collar emits an ultrasonicsound if the animal tries to stray beyond theboundaries.

Not all animals have a higher range of hear-ing than humans: elephants, for instance, cannothear tones above 12,000 Hz. On the other hand,some are drastically more sensitive acousticallythan dogs: bats, whales, and dolphins all have anupper range of 150,000 Hz, though both have alow-end threshold of 1,000. Mice, at 100,000 Hz,are also at the high end, while a number of otherpests—rodents and insects—fall into the regionbetween 40,000 and 100,000 Hz. This fact hasgiven rise to another type of ultrasonic device,for repelling all kinds of unwanted householdcreatures by bombarding them with ear-splittingtones.

An example of this device is the Transonic1X-L, which offers three frequency ranges: “loud



Ultrasonics mode” (1,000-50,000 Hz); “medium mode”(10,000-50,000 Hz); and “quiet mode” (20,000-50,000 Hz). The lowest of these can be used forrepelling pest birds and small animals, the medi-um range for insects, and the “quiet mode” forrodents.

Ultrasonic Detection in Medicine

Medicine represents one of the widest areas ofapplication for ultrasound. Though the machin-ery used to provide parents-to-be with an imageof their unborn child is the most well-knownform of medical ultrasound, it is far from theonly one. Developed in 1957 by British physicianIan Donald (1910-1987), also a pioneer in the useof ultrasonics to detect flaws in machinery, ultra-sound was first used to diagnosis a patient’s heartcondition. Within a year, British hospitals beganusing it with pregnant women.

High-frequency waves penetrate soft tissuewith ease, but they bounce off of harder tissuesuch as organs and bones, and thus send back amessage to the transducer. Because each type oftissue absorbs or deflects sound differently,according to its density, the ultrasound machinecan interpret these signals, creating an image ofwhat it “sees” inside the patient’s body. The tech-nician scans the area to be studied with a series ofultrasonic waves in succession, and this results inthe creation of a moving picture. It is this thatcreates the sight so memorable in the lives ofmany a modern parent: their first glimpse oftheir child in its mother’s womb.

Though ultrasound enables physicians andnurses to determine the child’s sex, this is farfrom being the only reason it is used. It also givesthem data concerning the fetus’s size; position(for instance, if the head is in a place that sug-gests the baby will have to be delivered by meansof cesarean section); and other abnormalities.

The beauty of ultrasound is that it can pro-vide this information without the danger posedby x rays or incisions. Doctors and ultrasoundtechnicians use ultrasonic technology to detectbody parts as small as 0.004 in (0.1 mm), makingit possible to conduct procedures safely, such aslocating foreign objects in the eye or measuringthe depth of a severe burn. Furthermore, ultra-sonic microscopes can image cellular structuresto within 0.2 microns (0.002 mm).

Ultrasonic heart examination can locatetumors, valve diseases, and accumulations offluid. Using the Doppler effect—the fact that asound’s perceived frequency changes as its sourcemoves past the observer—physicians observeshifts in the frequency of ultrasonic measure-ments to determine the direction of blood flowin the body. Not only can ultrasound be used todifferentiate tumors from healthy tissue, it cansometimes be used to destroy those tumors. Insome cases, ultrasound actually destroys cancercells, making use of a principle called cavita-tion— a promising area of ultrasound research.

Perhaps the best example of cavitationoccurs when you are boiling a pot of water: bub-bles—temporary cavities in the water itself—riseup from the bottom to the surface, then collapse,making a popping sound as they do. Among theresearch areas combining cavitation and ultra-sonics are studies of light emissions produced inthe collapse of a cavity created by an ultrasonicwave. These emissions are so intense that for aninfinitesimal moment, they produce heat of stag-gering proportions—hotter than the surface ofthe Sun, some scientists maintain. (Again, itshould be stressed that this occurs during a peri-od too small to measure with any but the mostsophisticated instruments.)

As for the use of cavitation in attacking can-cer cells, ultrasonic waves can be used to createmicroscopic bubbles which, when they collapse,produce intense shock waves that destroy thecells. Doctors are now using a similar techniqueagainst gallstones and kidney stones. Other med-ical uses of ultrasound technology include ultra-sonic heat for treating muscle strain, or—in aprocess similar to some industrial applications—the use of 25,000-Hz signals to clean teeth.

Sonar and Other DetectionDevices

Airplane pilots typically use radar, but the crewof a ocean-going vessel relies on sonar (SOundNavigation and Ranging) to guide their vesselthrough the ocean depths. This technology takesadvantage of the fact that sound waves travel wellunder water—much better, in fact, than lightwaves. Whereas a high-powered light would be oflimited value underwater, particularly in themurky realms of the deep sea, sonar providesexcellent data on the water’s depth, as well as thelocation of shipwrecks, large obstacles—and, for



Ultrasonicscommercial or even recreational fishermen—thepresence of fish.

At the bottom of the craft’s hull is a trans-ducer, which emits an ultrasonic pulse. Thesesound waves travel through the water to the bot-tom, where they bounce back. Upon receivingthe echo, the transducer sends this informationto an onboard computer, which converts data onthe amount of time the signal took, providing areading of distance that gives an accurate meas-urement of the vessel’s clearance. For instance, ittakes one second for sound waves from a depthof 2,500 ft (750 m) to return to the ship. Theonboard computer converts this data into arough picture of what lies below: the ocean floor,and schools of fish or other significant objectsbetween it and the ship.

Even more useful is a scanning sonar, whichadds dimension to the scope of the ship’s ultra-sonic detection: not only does the sonar beammove forward along with the vessel, but it movesfrom side-to-side, providing a picture of a widerarea along the ship’s path. Sonar in general, andparticularly scanning sonar, is of particularimportance to a submarine’s crew. Despite thefact that the periscope is perhaps the mostnotable feature of these underwater craft, fromthe viewpoint of a casual observer, in fact, thepurely visual data provided by the periscope is oflimited value—and that value decreases as thesub descends. It is thanks to sonar (which pro-duces the pinging sound one so often hears inmovie scenes depicting the submarine controlroom), combined with nuclear technology, thatmakes it possible for today’s U.S. Navy sub-marines to stay submerged for months.

Sonar is perhaps the most dramatic use ofultrasonic technology for detection; less well-known—but equally intriguing, especially for itsconnection with clandestine activity—is the useof ultrasonics for electronic eavesdropping. Pri-vate detectives, suspicious spouses, and no doubtinternational spies from the CIA or Britain’s MI5,use ultrasonic waves to listen to conversations inplaces where they cannot insert a microphone.For example, an operative might want to listen inon an encounter taking place on the seventhfloor of a building with heavy security, meaningit would be impossible to plant a microphoneeither inside the room or on the window ledge.

Instead, the operative uses ultrasonic waves,which a transducer beams toward the window of

the room being monitored. If people are speak-ing inside the room, this will produce vibrationson the window the transducer can detect,although the sounds would not be decipherableas conversation by a person with unaided percep-tion. Speech vibrations from inside producecharacteristic effects on the ultrasonic wavesbeamed back to the transducer and the opera-tive’s monitoring technology. The transducerthen converts these reflected vibrations into elec-trical signals, which analysts can then reconstructas intelligible sounds.

Much less dramatic, but highly significant, isthe use of ultrasonic technology for detection inindustry. Here the purpose is to test materials forfaults, holes, cracks, or signs of corrosion. Again,the transducer beams an ultrasonic signal, andthe way in which the material reflects this signalcan alert the operator to issues such as metalfatigue or a faulty weld. Another method is tosubject the material or materials to stress, thenlook for characteristic acoustic emissions fromthe stressed materials. (The latter is a developingfield of acoustics known as acoustic emission.)

Though industrial detection applicationscan be used on materials such as porcelain (totest for microscopic cracks) or concrete (to eval-uate how well it was poured), ultrasonics is par-ticularly effective on metal, in which soundmoves more quickly and freely than any othertype of wave. Not only does ultrasonics providean opportunity for thorough, informative, butnondestructive testing, it also allows techniciansto penetrate areas where they otherwise couldnot go—or, in the case of ultrasonic inspection ofthe interior of a nuclear reactor while in opera-tion—would not and should not go.

Binding and Loosening: A Host of Industrial Applications

Materials testing is but one among myriad usesfor ultrasonics in industry, applications that canbe described broadly as “binding and loosen-ing”—either bringing materials together, orpulling them apart.

For instance, ultrasound is often used tobind, or coagulate, loose particles of dust, mist,or smoke. This makes it possible to clean a facto-ry smokestack before it exhales pollutants intothe atmosphere, or to clear clumps of fog and



Ultrasonics mist off a runway. Another form of “binding” isthe use of ultrasonic vibrations to heat and weldtogether materials. Ultrasonics provides an even,localized flow of molten material, and is effectiveboth on plastics and metals.

Ultrasonic soldering implements the princi-ple of cavitation, producing microscopic bubblesin molten solder, a process that removes metaloxides. Hence, this is a case of both “binding”(soldering) and “loosening”—removing impuri-ties from the area to be soldered. The dairyindustry, too, uses ultrasonics for both purposes:ultrasonic waves break up fat globules in milk, sothat the fat can be mixed together with the milkin the well-known process of homogenization.Similarly, ultrasonic pasteurization facilitates theseparation of the milk from harmful bacteria andother microorganisms.

The uses of ultrasonics to “loosen” includeultrasonic humidification, wherein ultrasonicvibrations reduce water to a fine spray. Similarly,ultrasonic cleaning uses ultrasound to breakdown the attraction between two different typesof materials. Though it is not yet practical forhome use, the technology exists today to useultrasonics for laundering clothes without usingwater: the ultrasonic vibrations break the bondbetween dirt particles and the fibers of a gar-ment, shaking loose the dirt and subjecting thefabric to far less trauma than the agitation of awashing machine does.

As noted earlier, dentists use ultrasound forcleaning teeth, another example of loosening thebond between materials. In most of these formsof ultrasonic cleaning, a critical part of theprocess is the production of microscopic shockwaves in the process of cavitation. The frequencyof sound waves in these operations ranges from15,000 Hz (15 kHz) to 2 million Hz (2 MHz).Ultrasonic cleaning has been used on metals,plastics, and ceramics, as well as for cleaning pre-cision instruments used in the optical, surgical,and dental fields. Nor is it just for small objects:the electronics, automotive, and aircraft indus-tries make heavy use of ultrasonic cleaning for avariety of machines.

Ultrasonic “loosening” makes it possible todrill though extremely hard or brittle materials,including tungsten carbide or precious stones.Just as a dental hygienist cleaning a person’s teethbombards the enamel with gentle abrasives, thisform of high-intensity drilling works hand-in-

hand with the use of abrasive materials such assilicon carbide or aluminum oxide.

A World of Applications

Scientists often use ultrasound in research, forinstance to break up high molecular weight poly-mers, thus creating new plastic materials. Indeed,ultrasound also makes it possible to determinethe molecular weight of liquid polymers, and toconduct other forms of investigation on thephysical properties of materials.

Ultrasonics can also speed up certain chem-ical reactions. Hence, it has gained application inagriculture, thanks to research which revealedthat seeds subjected to ultrasound may germi-nate more rapidly and produce higher yields. Inaddition to its uses in the dairy industry, notedabove, ultrasonics is of value to farmers in therelated beef industry, who use it to measure cows’fat layers before taking them to market.

In contrast to the use of ultrasonics for elec-tronic eavesdropping, as noted earlier, todayultrasonic technology is available to persons whothink someone might be spying on them: nowthey can use ultrasonics to detect the presence ofelectronic eavesdropping, and thus circumvent it.Closer to home is another promising applicationof ultrasonics for remote sensing of sounds:ultrasonic stereo speakers.

These make use of research dating back tothe 1960s, which showed that ultrasound wavesof relatively low frequency can carry audiblesound to pinpointed locations. In 1996, WoodyNorris had perfected the technology necessary toreduce distortion, and soon he and his son Joebegan selling the ultrasonic speakers through theelder Norris’s company, American TechnologyCorporation of San Diego, California.

Eric Niiler in Business Week described ademonstration: “Joe Norris twists a few knobs ona receiver, takes aim with a 10-inch-square gold-covered flat speaker, and blasts an invisiblebeam.... Thirty feet away, the tinny but easily rec-ognizable sound of Vivaldi’s Four Seasons rushesover you. Step to the right or left, however, and itfades away. The exotic-looking speaker emits`sound beams’ that envelop the listener but aresilent to those nearby. `We use the air as our vir-tual speakers,’ says Norris....” Niiler went to noteseveral other applications suggested by Norris:“Airline passengers could listen to their own



Ultrasonics


music channelsans headphones without disturb-ing neighbors. Troops could confuse the enemywith `virtual’ artillery fire, or talk to each otherwithout having their radio communicationspicked up by eavesdroppers.”

WHERE TO LEARN MORE


Crocker, Malcolm J. Encyclopedia of Acoustics. New York:John Wiley & Sons, 1997.

Knight, David C. Silent Sound: The World of Ultrasonics.New York: Morrow, 1980.

Langone, John. National Geographic’s How Things Work.

Washington, D.C.: National Geographic Society,

1999.

Medical Ultrasound WWW Directory (Web site).

<http://www.ultrasoundinsider.com> (February 16,

2001).

Niiler, Eric; edited by Alex Salkever. “Now Here This—If

You’re in the Sweet Spot.” Business Week, October 16,

2000.

Meire, Hylton B. and Pat Farrant. Basic Ultrasound.

Chichester, N.Y.: John Wiley & Sons, 1995.








cy, equal to one cycle per second. If a sound

wave has a frequency of 20,000 Hz, this

means that 20,000 waves are passing


of one second. Higher frequencies are




Hence 20,000 Hz—the threshold of ultra-

sonic sound—would be rendered as 20

kHz.

INFRASOUND: Sound of a frequency

between 20 Hz, which places it outside the

range of audibility for human beings. Its

opposite is ultrasound.


which the individual segments vibrate in

the same direction as the wave itself. This is

in contrast to a transverse wave, or one in

which the vibration or harmonic motion

occurs perpendicular to the direction in

which the wave is moving. Waves on the

ocean are an example of transverse waves;

by contrast, the shock waves of an explo-

sion, the concentric waves of a radio trans-

mission, and sound waves are all examples

of longitudinal waves.

TRANSDUCER: A device that con-

verts energy into ultrasonic sound waves.

ULTRASOUND: Sound waves with a

frequency above 20,000 Hz, which makes

them inaudible to the human ear. Its oppo-

site is infrasound.

WAVELENGTH: The distance, meas-

ured on a plane parallel to that of the wave

itself, between a crest and the adjacent

crest, or the trough and an adjacent trough.

On a longitudinal wave, this is simply the

distance between waves, which constitute a

series of concentric circles radiating from

the source.

WAVE MOTION: Activity that carries

energy from one place to another without

actually moving any matter.

KEY TERMS


329


L I GHT AND ELECTROMAGNET ISM

L IGHT AND ELECTROMAGNET ISM

MAGNET ISM

ELECTROMAGNET IC SPECTRUM

L IGHT

LUM INESCENCE



MAGNET ISMMagnetism

CONCEPTMost people are familiar with magnets primarilyas toys, or as simple objects for keeping papersattached to a metal surface such as a refrigeratordoor. In fact the areas of application for magnet-ism are much broader, and range from security tohealth care to communication, transportation,and numerous other aspects of daily life. Closelyrelated to electricity, magnetism results from spe-cific forms of alignment on the part of electroncharges in certain varieties of metal and alloy.

HOW IT WORKSMagnetism, along with electricity, belongs to alarger phenomenon, electromagnetism, or theforce generated by the passage of an electric cur-rent through matter. When two electric chargesare at rest, it appears to the observer that theforce between them is merely electric. If thecharges are in motion, however—and in thisinstance motion or rest is understood in relationto the observer—then it appears as though a dif-ferent sort of force, known as magnetism, existsbetween them.

In fact, the difference between magnetismand electricity is purely artificial. Both are mani-festations of a single fundamental force, with“magnetism” simply being an abstraction thatpeople use for the changes in electromagneticforce created by the motion of electric charges. Itis a distinction on the order of that betweenwater and wetness; nonetheless, it is often usefuland convenient to discuss the two phenomena asthough they were separate.

At the atomic level, magnetism is the resultof motion by electrons, negatively charged sub-

atomic particles, relative to one another. Ratherlike planets in a solar system, electrons bothrevolve around the atom’s nucleus and rotate ontheir own axes. (In fact the exact nature of theirmovement is much more complex, but this anal-ogy is accurate enough for the present purposes.)Both types of movement create a magnetic forcefield between electrons, and as a result the elec-tron takes on the properties of a tiny bar magnetwith a north pole and south pole. Surroundingthis infinitesimal magnet are lines of magneticforce, which begin at the north pole and curveoutward, describing an ellipse as they return tothe south pole.

In most atomic elements, the structure ofthe atom is such that the electrons align in a ran-dom manner, rather like a bunch of basketballsbumping into one another as they float in aswimming pool. Because of this random align-ment, the small magnetic fields cancel out oneanother. Two such self-canceling particles arereferred to as paired electrons, and again, theanalogy to bar magnets is an appropriate one: ifone were to shake a bag containing an even num-ber of bar magnets, they would all wind up inpairs, joined at opposing (north-south) poles.

There are, however, a very few elements inwhich the fields line up to create what is knownas a net magnetic dipole, or a unity of direc-tion—rather like a bunch of basketballs simulta-neously thrown from in the same direction at thesame time. These elements, among them iron,cobalt, and nickel, as well as various alloys ormixtures, are commonly known as magneticmetals or natural magnets.

It should be noted that in magnetic metals,magnetism comes purely from the alignment of


Magnetism


forces exerted by electrons as they spin on theiraxes, whereas the forces created by their orbitalmotion around the nucleus tend to cancel oneanother out. But in magnetic rare earth elementssuch as cerium, magnetism comes both fromrotational and orbital forms of motion. Of prin-cipal concern in this discussion, however, is thebehavior of natural magnets on the one hand,and of nonmagnetic materials on the other.

There are five different types of magnet-ism—diamagnetism, paramagnetism, ferromag-netism, ferrimagnetism, and antiferromagnet-ism. Actually, these terms describe five differenttypes of response to the process of magnetiza-tion, which occurs when an object is placed in amagnetic field.

A magnetic field is an area in which a mag-netic force acts on a moving charged particlesuch that the particle would experience no forceif it moved in the direction of the magneticfield—in other words, it would be “drawn,” as aten-penny nail is drawn to a common bar orhorseshoe (U-shaped) magnet. An electric cur-rent is an example of a moving charge, andindeed one of the best ways to create a magneticfield is with a current. Often this is done bymeans of a solenoid, a current-carrying wire coil

through which the material to be magnetized ispassed, much as one would pass an objectthrough the interior of a spring.

All materials respond to a magnetic field;they just respond in different ways. Some non-magnetic substances, when placed within a mag-netic field, slightly reduce the strength of thatfield, a phenomenon known as diamagnetism.On the other hand, there are nonmagnetic sub-stances possessing an uneven number of elec-trons per atom, and in these instances a slightincrease in magnetism, known as paramagnet-ism, occurs. Paramagnetism always has to over-come diamagnetism, however, and hence thegain in magnetic force is very small. In addition,the thermal motion of atoms and molecules pre-vents the objects’ magnetic fields from cominginto alignment with the external field. Lowertemperatures, on the other hand, enhance theprocess of paramagnetism.

In contrast to diamagnetism and paramag-netism, ferro-, ferri-, and antiferromagnetism alldescribe the behavior of natural magnets whenexposed to a magnetic field. The name ferromag-netism suggests a connection with iron, but infact the term can apply to any of those materialsin which the magnitude of the object’s magnetic

THE RECORDING HEAD IS A SMALL ELECTROMAGNET WHOSE MAGNETIC FIELD EXTENDS OVER THE SECTION OF TAPE

BEING RECORDED. LOUD SOUNDS PRODUCE STRONG MAGNETIC FIELDS, AND SOFT ONES WEAK FIELDS. (Illustration by

Hans & Cassidy. The Gale Group.)


Magnetism


field increases greatly when it is placed within an

external field. When a natural magnet becomes

magnetized (that is, when a metal or alloy comes

into contact with an external magnetic field), a

change occurs at the level of the domain, a group

of atoms equal in size to about 5 � 10-5 meters

across—just large enough to be visible under a

microscope.

In an unmagnetized sample, there may be an

alignment of unpaired electron spins within a

domain, but the direction of the various

domains’ magnetic forces in relation to one

another is random. Once a natural magnet is

placed within an external magnetic force field,

however, one of two things happens to the

domains. Either they all come into alignment

with the field or, in certain types of material,

those domains in alignment with the field grow

while the others shrink to nonexistence.

The first of these processes is called domain

alignment or ferromagnetism, the second

domain growth or ferrimagnetism. Both process-

es turn a natural magnet into what is known as a

permanent magnet—or, in common parlance,

simply a “magnet.” The latter is then capable of

temporarily magnetizing a ferromagnetic item,

as for instance when one rubs a paper clip against

a permanent magnet and then uses the magnet-

THE PERMANENT MAGNETIZATION OF A NATURAL MAGNET IS DIFFICULT TO REVERSE, BUT REVERSAL OF A TAPE’S MAG-NETIZATION—IN OTHER WORDS, ERASING THE TAPE—IS EASY. AN ERASE HEAD, AN ELECTROMAGNET OPERATING AT

A FREQUENCY TOO HIGH FOR THE HUMAN EAR TO HEAR, SIMPLY SCRAMBLES THE MAGNETIC PARTICLES ON A PIECE

OF TAPE. (Illustration by Hans & Cassidy. The Gale Group.)


Magnetism er, and a pair of like poles—for whom the lines offorce are moving away from each other—repels.This is a fact particularly applicable to the opera-tion of MAGLEV trains, as discussed later.

A magnetic compass works because Earthitself is like a giant bar magnet, complete withvast arcs of magnetic force, called the geomag-netic field, surrounding the planet. The first sci-entist to recognize the magnetic properties ofEarth was the English physicist William Gilbert(1544-1603). Scientists today believe that thesource of Earth’s magnetism lies in a core ofmolten iron some 4,320 mi (6,940 km) across,constituting half the planet’s diameter. Withinthis core run powerful electric currents that ulti-mately create the geomagnetic field.

Just as a powerful magnet causes all thedomains in a magnetic metal to align with it, abar magnet placed in a magnetic field will rotateuntil it lines up with the field’s direction. Thesame thing happens when one suspends a mag-net from a string: it lines up with Earth’s mag-netic field, and points in a north-south direction.The Chinese of the first century B.C., thoughunaware of the electromagnetic forces thatcaused this to happen, discovered that a strip ofmagnetic metal always tended to point towardgeographic north.

This led ultimately to the development ofthe magnetic compass, which typically consists ofa magnetized iron needle suspended over a cardmarked with the four cardinal directions. Theneedle is attached to a pivoting mechanism at its center, which allows it to move freely so that the “north” end will always point the usernorthward.

The magnetic compass proved so importantthat it is typically ranked alongside paper, print-ing, and gunpowder as one of premodern China’sfour great gifts to the West. Prior to the compass,mariners had to depend purely on the position ofthe Sun and other, less reliable, means of deter-mining direction; hence the invention quite liter-ally helped open up the world. But there is asomewhat irksome anomaly lurking in the seem-ing simplicity of the magnetic compass.

In fact magnetic north is not the same thingas true north; or, to put it another way, if onecontinued to follow a compass northward, itwould lead not to the Earth’s North Pole, but to apoint identified in 1984 as 77°N, 102°18’ W—that is, in the Queen Elizabeth Islands of far


ized clip to lift other paper clips. Of the two vari-eties, however, a ferromagnetic metal is strongerbecause it requires a more powerful magneticforce field in order to become magnetized. Mostpowerful of all is a saturated ferromagneticmetal, one in which all the unpaired electronspins are aligned.

Once magnetized, it is very hard for a ferro-magnetic metal to experience demagnetization,or antiferromagnetism. Again, there is a connec-tion between temperature and magnetism, withheat acting as a force to reduce the strength of amagnetic field. Thus at temperatures above1,418°F (770°C), the atoms within a domain takeon enough kinetic energy to overpower the forcesholding the electron spins in alignment. In addi-tion, mechanical disturbances—for instance,battering a permanent magnet with a hammer—can result in some reduction of magnetic force.

Many of the best permanent magnets aremade of steel, which, because it is an alloy of ironwith carbon and other elements, has an irregularstructure that lends itself well to the ferromag-netic process of domain alignment. Iron, by con-trast, will typically lose its magnetization whenan external magnetic force field is removed; butthis actually makes it a better material for somevarieties of electromagnet.

The latter, in its simplest form, consists of aniron rod inside a solenoid. When a current ispassing through the solenoid, it creates a mag-netic force field, activating the iron rod and turn-ing it into an electromagnet. But as soon as thecurrent is turned off, the rod loses its magneticforce. Not only can an electromagnet thus becontrolled, but it is often stronger than a perma-nent magnet: hence, for instance, giant electro-magnets are used for lifting cars in junkyards.


Finding the Way: Magnets inCompasses

A north-south bar magnet exerts exactly thesame sort of magnetic field as a solenoid. Lines ofmagnetic run through it in one direction, from“south” to “north,” and upon leaving the northpole of the magnet, these lines describe an ellipseas they curve back around to the south pole. Inview of this model, it is also easy to comprehendwhy a pair of opposing poles attracts one anoth-


Magnetismnorthern Canada. The reason for this is thatEarth’s magnetic field describes a current loopwhose center is 11° off the planet’s equator, andthus the north and south magnetic poles—whichare on a plane perpendicular to that of theEarth’s magnetic field—are 11° off of the planet’saxis.

The magnetic field of Earth is changingposition slowly, and every few years the UnitedStates Geological Survey updates magnetic decli-nation, or the shift in the magnetic field. In addi-tion, Earth’s magnetic field is slowly weakeningas well. The behavior, both in terms of weakeningand movement, appears to be similar to changestaking place in the magnetic field of the Sun.

Magnets for Detection: Burglar Alarms, Magnetometers, and MRI

A compass is a simple magnetic instrument, anda burglar alarm is not much more complex. Amagnetometer, on the other hand, is a muchmore sophisticated piece of machinery fordetecting the strength of magnetic fields.Nonetheless, the magnetometer bears a relationto its simpler cousins: like a compass, certainkinds of magnetometers respond to a planet’smagnetic field; and like a burglar alarm, othervarieties of magnetometer are employed forsecurity.

At heart, a burglar alarm consists of a con-tact switch, which responds to changes in theenvironment and sends a signal to a noisemakingdevice. The contact switch may be mechanical—a simple fastener, for instance—or magnetic. Inthe latter case, a permanent magnet may beinstalled in the frame of a window or door, and apiece of magnetized material in the window ordoor itself. Once the alarm is activated, it willrespond to any change in the magnetic field—i.e., when someone slides open the door or win-dow, thus breaking the connection between mag-net and metal.

Though burglar alarms may vary in com-plexity, and indeed there may be much moreadvanced systems using microwaves or infraredrays, the application of magnetism in home secu-rity is a simple matter of responding to changesin a magnetic field. In this regard, the principlegoverning magnetometers used at securitycheckpoints is even simpler. Whether at an air-port or at the entrance to some other high-secu-

rity venue, whether handheld or stationary, amagnetometer merely detects the presence ofmagnetic metals. Since the vast majority offirearms, knife-blades, and other weapons aremade of iron or steel, this provides a fairly effi-cient means of detection.

At a much larger scale, magnetometers usedby astronomers detect the strength and some-times the direction of magnetic fields surround-ing Earth and other bodies in space. This varietyof magnetometer dates back to 1832, whenmathematician and scientist Carl FriedrichGauss (1777-1855) developed a simple instru-ment consisting of a permanent bar magnet sus-pended horizontally by means of a gold wire. Bymeasuring the period of the magnet’s oscillationin Earth’s magnetic field (or magnetosphere),Gauss was able to measure the strength of thatfield. Gauss’s name, incidentally, would later beapplied to the term for a unit of magnetic force.The gauss, however, has in recent years beenlargely replaced by the tesla, named after NikolaTesla (1856-1943), which is equal to one new-ton/ampere meter (1 N/A•m) or 104 (10,000)gauss.

As for magnetometers used in astronomicalresearch, perhaps the most prominent—and cer-tainly one of the most distant—ones is onGalileo, a craft launched by the U.S. NationalAeronautics and Space Administration (NASA)toward Jupiter on October 15, 1989. Amongother instruments on board Galileo, which hasbeen in orbit around the solar system’s largestplanet since 1995, is a magnetometer for measur-ing Jupiter’s magnetosphere and that of its sur-rounding asteroids and moons.

Closer to home, but no less impressive, isanother application of magnetism for the pur-poses of detection: magnetic resonance imagin-ing, or MRI. First developed in the early 1970s,MRI permits doctors to make intensive diag-noses without invading the patient’s body eitherwith a surgical knife or x rays.

The heart of the MRI machine is a large tubeinto which the patient is placed in a supine posi-tion. A technician then activates a powerful mag-netic field, which causes atoms within thepatient’s body to spin at precise frequencies. Themachine then beams radio signals at a frequencymatching that of the atoms in the cells (e.g., can-cer cells) being sought. Upon shutting off theradio signals and magnetic field, those atoms



Magnetism emit bursts of energy that they have absorbedfrom the radio waves. At that point a computerscans the body for frequencies matching specifictypes of atoms, and translates these into three-dimensional images for diagnosis.

Magnets for ProjectingSound: Microphones, Loud-speakers, Car Horns, andElectric Bells

The magnets used in Galileo or an MRI machineare, needless to say, very powerful ones, and asnoted earlier, the best way to create a super-strong, controllable magnet is with an electricalcurrent. When that current is properly coiledaround a magnetic metal, this creates an electro-magnet, which can be used in a variety of appli-cations.

As discussed above, the most powerful elec-tromagnets typically use nonpermanent magnetsso as to facilitate an easy transition from anextremely strong magnetic field to a weak ornonexistent one. On the other hand, permanentmagnets are also used in loudspeakers and simi-lar electromagnetic devices, which seldomrequire enormous levels of power.

In discussing the operation of a loudspeaker,it is first necessary to gain a basic understandingof how a microphone works. The latter containsa capacitor, a system for storing charges in theform of an electrical field. The capacitor’s nega-tively charged plate constitutes the microphone’sdiaphragm, which, when it is hit by sound waves,vibrates at the same frequency as those waves.Current flows back and forth between thediaphragm and the positive plate of the capaci-tor, depending on whether the electrostatic orelectrical pull is increasing or decreasing. This inturn produces an alternating current, at the samefrequency as the sound waves, which travelsthrough a mixer and then an amplifier to thespeaker.

A loudspeaker typically contains a circularpermanent magnet, which surrounds an electri-cal coil and is in turn attached to a cone-shapeddiaphragm. Current enters the speaker ultimate-ly from the microphone, alternating at the samefrequency as the source of the sound (a singer’svoice, for instance). As it enters the coil, this cur-rent induces an alternating magnetic field, whichcauses the coil to vibrate. This in turn vibrates

the cone-shaped diaphragm, and the latter repro-duces sounds generated at the source.

A car horn also uses magnetism to createsound by means of vibration. When a personpresses down on the horn embedded in his or hersteering wheel, this in turn depresses an iron barthat passes through an electromagnet surround-ed by wires from the car’s battery. The bar movesup and down within the electromagnetic field,causing the diaphragm to vibrate and producinga sound that is magnified greatly when releasedthrough a bell-shaped horn.

Electromagnetically induced vibration isalso the secret behind another noise-makingdevice, a vibrating electric doorbell used in manyapartments. The button that a visitor presses isconnected directly to a power source, whichsends current flowing through a spring sur-rounding an electromagnet. The latter generatesa magnetic field, drawing toward it an iron arma-ture attached to a hammer. The hammer thenstrikes the bell. The result is a mechanical reac-tion that pushes the armature away from theelectromagnet, but the spring forces the arma-ture back against the electromagnet again. Thiscycle of contact and release continues for as longas the button is depressed, causing a continualringing of the bell.

Recording and Reading Data Using Magnets: From Records and Tapes to Disk Drives

Just as magnetism plays a critical role in project-ing the volume of sound, it is also crucial to therecording and retrieval of sound and other data.Of course terms such as “retrieval” and “data”have an information-age sound to them, but theidea of using magnetism to record sound is anold one—much older than computers or com-pact discs (CDs). The latter, of course, replacedcassettes in the late 1980s as the preferred modefor listening to recorded music, just as cassetteshad recently made powerful gains against phono-graph records.

Despite the fact that cassettes entered themarket much later than records, however,recording engineers from the mid-twentieth cen-tury onward typically used magnetic tape formaster recordings of songs. This master wouldthen be used to create a metal master record disk



Magnetismby means of a cutting head that responded tovibrations from the master tape; then, the recordcompany could produce endless plastic copies ofthe metal record.

In recording a tape—whether a stereo mas-ter or a mere home recording of a conversation—the principles at work are more or less the same.As noted in the earlier illustration involving amicrophone and loudspeaker, sound comesthrough a microphone in the form of alternatingcurrent. The strength of this current in turnaffects the “recording head,” a small electromag-net whose magnetic field extends over the sectionof tape being recorded. Loud sounds producestrong magnetic fields, and soft ones weak fields.

All of this information becomes embeddedon the cassette tape through a process of mag-netic alignment not so different from the processdescribed earlier for creating a permanent mag-net. But whereas the permanent magnetizationof a natural magnet is difficult to reverse, reversalof a tape’s magnetization—in other words, eras-ing the tape—is easy. An erase head, an electro-magnet operating at a frequency too high for thehuman ear to hear, simply scrambles the magnet-ic particles on a piece of tape.

A CD, as one might expect, is much moreclosely related to a computer disk-drive than it isto earlier forms of recording technology. Thedisk drive receives electronic on-off signals fromthe computer, and translates these into magneticcodes that it records on the surface of a floppydisk. The disk drive itself includes two electricmotors: a disk motor, which rotates the disk at ahigh speed, and a head motor, which moves thecomputer’s read-write head across the disk. (Itshould be noted that most electric motors,including the universal motors used in a varietyof household appliances, also use electro-magnets.)

A third motor, called a stepper motor,ensures that the drive turns at a precise rate ofspeed. The stepper motor contains its own mag-net, in this case a permanent one of cylindricalshape that sends signals to rows of metal teethsurrounding it, and these teeth act as gears toregulate the drive’s speed. Likewise a CD player,which actually uses laser beams rather than mag-netic fields to retrieve data from a disc, also has adrive system that regulates the speed at which thedisk spins.

MAGLEV Trains: The Futureof Transport?

One promising application of electromagnetictechnology relates to a form of transportationthat might, at first glance, appear to be old news:trains. But MAGLEV, or magnetic levitation,trains are as far removed from the old steamengines of the Union Pacific as the space shuttleis from the Wright brothers’ experimental air-plane.

As discussed earlier, magnetic poles of likedirection (i.e., north-north or south-south) repelone another such that, theoretically at least, it ispossible to keep one magnet suspended in the airover another magnet. Actually it is impossible toproduce these results with simple bar magnets,because their magnetic force is too small; but anelectromagnet can create a magnetic field power-ful enough that, if used properly, it exerts enoughrepulsive force to lift extremely heavy objects.Specifically, if one could activate train tracks witha strong electromagnetic field, it might be possi-ble to “levitate” an entire train. This in turn


MAGLEV TRAINS, LIKE THIS EXPERIMENTAL ONE IN

MIYAZAKI, JAPAN, MAY REPRESENT THE FUTURE OF

MASS TRANSIT. (Photograph by Michael S. Yamashita/Corbis.



Magnetism


would make possible a form of transport thatcould move large numbers of people in relativecomfort, thus decreasing the environmentalimpact of automobiles, and do so at much high-er speeds than a car could safely attain.

Actually the idea of MAGLEV trains goesback to a time when trains held completesupremacy over automobiles as a mode of trans-portation: specifically, 1907, when rocket pioneerRobert Goddard (1882-1945) wrote a storydescribing a vehicle that traveled by means ofmagnetic levitation. Just five years later, Frenchengineer Emile Bachelet produced a workingmodel for a MAGLEV train. But the amount ofmagnetic force required to lift such a vehiclemade it impractical, and the idea fell to the wayside.

Then, in the 1960s, the advent of supercon-ductivity—the use of extremely low tempera-tures, which facilitate the transfer of electricalcurrent through a conducting material with vir-tually no resistance—made possible electromag-nets of staggering force. Researchers began build-ing MAGLEV prototypes using superconductingcoils with strong currents to create a powerfulmagnetic field. The field in turn created a repul-sive force capable of lifting a train several inchesabove a railroad track. Electrical current sentthrough guideway coils on the track allowed forenormous propulsive force, pushing trains forward at speeds up to and beyond 250 MPH (402 km/h).

Initially, researchers in the United Stateswere optimistic about MAGLEV trains, but safe-ty concerns led to the shelving of the idea for sev-eral decades. Meanwhile, other industrializednations moved forward with MAGLEVs: inJapan, engineers built a 27-mi (43.5-km) experi-mental MAGLEV line, while German designersexperimented with attractive (as opposed torepulsive) force in their Transrapid 07. MAGLEVtrains gained a new defender in the United Stateswith now-retired Senator Daniel Patrick Moyni-han (D-NY), who as chairman of a Senate sub-committee overseeing the interstate highway sys-tem introduced legislation to fund MAGLEVresearch. The 1998 transportation bill allocated$950 million toward the Magnetic LevitationPrototype Development Program. As part of thisprogram, in January 2001 the U.S. Department ofTransportation selected projects in Marylandand Pennsylvania as the two finalists in the com-

ELECTROMAGNET: A type of magnet

in which an object is charged by an electri-

cal current. Typically the object used is

made of iron, which quickly loses magnet-

ic force when current is reduced. Thus an

electromagnet can be turned on or off, and

its magnetic force altered, making it poten-

tially much more powerful than a natural

magnet.

ELECTROMAGNETISM: The unified

electrical and magnetic force field generat-

ed by the passage of an electric current

through matter.

ELECTRONS: Negatively charged sub-

atomic particles whose motion relative to

one another creates magnetic force.

MAGNETIC FIELD: Wherever a mag-

netic force acts on a moving charged parti-

cle, a magnetic field is said to exist. Mag-

netic fields are typically measured by a unit

called a tesla.

NATURAL MAGNET: A chemical ele-

ment in which the magnetic fields created

by electrons’ relative motion align uni-

formly to create a net magnetic dipole, or

unity of direction. Such elements, among

them iron, cobalt, and nickel, are also

known as magnetic metals.

PERMANENT MAGNET: A magnetic

material in which groups of atoms, known

as domains, are brought into alignment,

and in which magnetization cannot be

changed merely by attempting to realign

the domains. Permanent magnetization is

reversible only at very high temperatures—

for example, 1,418°F (770°C) in the case

of iron.

KEY TERMS


Magnetismpetition to build the first MAGLEV train service

in the United States. The goal is to have the serv-

ice in place by approximately 2010.

WHERE TO LEARN MORE

Barr, George. Science Projects for Young People. New York:Dover, 1964.


Hann, Judith. How Science Works. Pleasantville, NY:Reader’s Digest, 1991.


Molecular Expressions: Electricity and Magnetism: Interac-tive Java Tutorials (Web site). <http://micro.magnet.fsu.edu/electromag/java/> (January 26, 2001).

Topical Group on Magnetism (Web site).<http://www.aps.org/units/gmag/> (January 26,2001).

VanCleave, Janice. Magnets. New York: John Wiley &Sons, 1993.

Wood, Robert W. Physics for Kids: 49 Easy Experimentswith Electricity and Magnetism. New York: Tab, 1990.




E LECTROMAGNET ICSPECTRUMElectromagnetic Spectrum

CONCEPTOne of the most amazing aspects of physics is theelectromagnetic spectrum—radio waves,microwaves, infrared light, visible light, ultravio-let light, x rays, and gamma rays—as well as therelationship between the spectrum and electro-magnetic force. The applications of the electro-magnetic spectrum in daily life begin themoment a person wakes up in the morning and“sees the light.” Yet visible light, the only familiarpart of the spectrum prior to the eighteenth andnineteenth centuries, is also its narrowest region.Since the beginning of the twentieth century,uses for other bands in the electromagnetic spec-trum have proliferated. At the low-frequency endare radio, short-wave radio, and television sig-nals, as well as the microwaves used in cooking.Higher-frequency waves, all of which can be gen-erally described as light, provide the means forlooking deep into the universe—and deep intothe human body.

HOW IT WORKS

Electromagnetism

The ancient Romans observed that a brushedcomb would attract particles, a phenomenonnow known as static electricity and studied with-in the realm of electrostatics in physics. Yet, theRoman understanding of electricity did notextend any further, and as progress was made inthe science of physics—after a period of morethan a thousand years, during which scientificlearning in Europe progressed very slowly—itdeveloped in areas that had nothing to do withthe strange force observed by the Romans.

The fathers of physics as a serious science,Galileo Galilei (1564-1642) and Sir Isaac Newton(1642-1727), were concerned with gravitation,which Newton identified as a fundamental forcein the universe. For nearly two centuries, physi-cists continued to believe that there was only onetype of force. Yet, as scientists became increasing-ly aware of molecules and atoms, anomaliesbegan to arise—in particular, the fact that gravi-tation alone could not account for the strongforces holding atoms and molecules together toform matter.

FOUNDATIONS OF ELECTRO-

MAGNETIC THEORY. At the same time,a number of thinkers conducted experimentsconcerning the nature of electricity and magnet-ism, and the relationship between them. Amongthese were several giants in physics and other dis-ciplines—including one of America’s greatestfounding fathers. In addition to his famous (andhighly dangerous) experiment with lightning,Benjamin Franklin (1706-1790) also contributedthe names “positive” and “negative” to the differ-ing electrical charges discovered earlier by Frenchphysicist Charles Du Fay (1698-1739).

In 1785, French physicist and inventorCharles Coulomb (1736-1806) established thebasic laws of electrostatics and magnetism. Hemaintained that there is an attractive force that,like gravitation, can be explained in terms of theinverse of the square of the distance betweenobjects. That attraction itself, however, resultednot from gravity, but from electrical charge,according to Coulomb.

A few years later, German mathematicianJohann Karl Friedrich Gauss (1777-1855) devel-oped a mathematical theory for finding the mag-netic potential of any point on Earth, and his


Electro-magnetic

Spectrum

contemporary, Danish physicist Hans ChristianOersted (1777-1851), became the first scientist toestablish the existence of a clear relationshipbetween electricity and magnetism. This led tothe foundation of electromagnetism, the branchof physics devoted to the study of electrical andmagnetic phenomena.

French mathematician and physicist AndréMarie Ampère (1775-1836) concluded that mag-netism is the result of electricity in motion, and,in 1831, British physicist and chemist MichaelFaraday (1791-1867) published his theory ofelectromagnetic induction. This theory showshow an electrical current in one coil can set up acurrent in another through the development of amagnetic field. This enabled Faraday to developthe first generator, and for the first time in histo-ry, humans were able to convert mechanicalenergy systematically into electrical energy.

MAXWELL AND ELECTROMAG-

NETIC FORCE. A number of other figurescontributed along the way; but, as yet, no onehad developed a “unified theory” explaining therelationship between electricity and magnetism.Then, in 1865, Scottish physicist James ClerkMaxwell (1831-1879) published a groundbreak-ing paper,“On Faraday’s Lines of Force,” in whichhe outlined a theory of electromagnetic force—the total force on an electrically charged particle,which is a combination of forces due to electricaland/or magnetic fields around the particle.

Maxwell had thus discovered a type of forcein addition to gravity, and this reflected a “new”type of fundamental interaction, or a basic modeby which particles interact in nature. Newton hadidentified the first, gravitational interaction, andin the twentieth century, two other forms of fun-damental interaction—strong nuclear and weaknuclear—were identified as well.

In his work, Maxwell drew on the studiesconducted by his predecessors, but added a newstatement: that electrical charge is conserved.This statement, which did not contradict any ofthe experimental work done by the other physi-cists, was based on Maxwell’s predictions regard-ing what should happen in situations of electro-magnetism; subsequent studies have supportedhis predictions.

Electromagnetic Radiation

So far, what we have seen is the foundation formodern understanding of electricity and mag-


netism. This understanding grew enormously inthe late nineteenth and early twentieth centuries,thanks both to the theoretical work of physicists,and the practical labors of inventors such asThomas Alva Edison (1847-1931) and Serbian-American electrical engineer Nikola Tesla (1856-1943). But our concern in the present context iswith electromagnetic radiation, of which thewaves on the electromagnetic spectrum are aparticularly significant example.

Energy can travel by conduction or convec-tion, two principal means of heat transfer. Butthe energy Earth receives from the Sun—theenergy conveyed through the electromagneticspectrum—is transferred by another method,radiation. Whereas conduction of convection canonly take place where there is matter, which pro-vides a medium for the energy transfer, radiationrequires no medium. Thus, electromagneticenergy passes from the Sun to Earth through thevacuum of empty space.

ELECTROMAGNETIC WAVES.

The connection between electromagnetic radia-tion and electromagnetic force is far from obvi-ous. Even today, few people not scientificallytrained understand that there is a clear relation-ship between electricity and magnetism—letalone a connection between these and visiblelight. The breakthrough in establishing that con-nection can be attributed both to Maxwell and toGerman physicist Heinrich Rudolf Hertz (1857-1894).

Maxwell had suggested that electromagneticforce carried with it a certain wave phenomenon,and predicted that these waves traveled at a cer-tain speed. In his Treatise on Electricity and Mag-netism (1873), he predicted that the speed ofthese waves was the same as that of light—186,000 mi (299,339 km) per second—and theo-rized that the electromagnetic interactionincluded not only electricity and magnetism, butlight as well. A few years later, while studying thebehavior of electrical currents, Hertz confirmedMaxwell’s proposition regarding the wave phenomenon by showing that an electrical cur-rent generated some sort of electromagneticradiation.

In addition, Hertz found that the flow ofelectrical charges could be affected by light undercertain conditions. Ultraviolet light had alreadybeen identified, and Hertz shone an ultravioletbeam on the negatively charged side of a gap in a


Electro-magneticSpectrum


THE HUBBLE SPACE TELESCOPE INCLUDES AN ULTRAVIOLET LIGHT INSTRUMENT CALLED THE GODDARD HIGH RES-OLUTION SPECTROGRAPH THAT IT IS CAPABLE OF OBSERVING EXTREMELY DISTANT OBJECTS. (Photograph by Roger Ress-

meyer/Corbis. Reproduced by permission.)

current loop. This made it easier for an electricalspark to jump the gap. Hertz could not explainthis phenomenon, which came to be known asthe photoelectric effect. Indeed, no one elsecould explain it until quantum theory was devel-oped in the early twentieth century. In the mean-time, however, Hertz’s discovery of electromag-netic waves radiating from a current loop led tothe invention of radio by Italian physicist and engineer Guglielmo Marconi (1874-1937) andothers.

Light: Waves or Particles?

At this point, it is necessary to jump backward inhistory, to explain the progression of scientists’

understanding of light. Advancement in this area

took place over a long period of time: at the end

of the first millennium A.D., the Arab physicist

Alhasen (Ibn al-Haytham; c. 965-1039) showed

that light comes from the Sun and other self-illu-

minated bodies—not, as had been believed up to

that time—from the eye itself. Thus, studies in

optics, or the study of light and vision, were—

compared to understanding of electromagnetism

itself—relatively advanced by 1666, when New-

ton discovered the spectrum of colors in light. As

Newton showed, colors are arranged in a

sequence, and white light is a combination of all

colors.


Electro-magnetic

Spectrum

Newton put forth the corpuscular theory oflight—that is, the idea that light is made up ofparticles—but his contemporary ChristiaanHuygens (1629-1695), a Dutch physicist andastronomer, maintained that light appears in theform of a wave. For the next century, adherents ofNewton’s corpuscular theory and of Huygens’swave theory continued to disagree. Physicists onthe European continent began increasingly toaccept wave theory, but corpuscular theoryremained strong in Newton’s homeland.

Thus, it was ironic that the physicist whosework struck the most forceful blow against cor-puscular theory was himself an Englishman:Thomas Young (1773-1829), who in 1801demonstrated interference in light. Young direct-ed a beam of light through two closely spacedpinholes onto a screen, reasoning that if lighttruly were made of particles, the beams wouldproject two distinct points onto the screen.Instead, what he saw was a pattern of interfer-ence—a wave phenomenon.

By the time of Hertz, wave theory hadbecome dominant; but the photoelectric effectalso exhibited aspects of particle behavior. Thus,for the first time in more than a century, particletheory gained support again. Yet, it was clear thatlight had certain wave characteristics, and thisraised the question—which is it, a wave or a setof particles streaming through space?

The work of German physicist Max Planck(1858-1947), father of quantum theory, and ofAlbert Einstein (1879-1955), helped resolve thisapparent contradiction. Using Planck’s quantumprinciples, Einstein, in 1905, showed that lightappears in “bundles” of energy, which travel aswaves but behave as particles in certain situa-tions. Eighteen years later, American physicistArthur Holly Compton (1892-1962) showedthat, depending on the way it is tested, lightappears as either a particle or a wave. These par-ticles he called photons.

Wave Motion and Electro-magnetic Waves

The particle behavior of electromagnetic energyis beyond the scope of the present discussion,though aspects of it are discussed elsewhere. Forthe present purposes, it is necessary only to viewthe electromagnetic spectrum as a series ofwaves, and in the paragraphs that follow, the

rudiments of wave motion will be presented inshort form.

A type of harmonic motion that carriesenergy from one place to another without actual-ly moving any matter, wave motion is related tooscillation, harmonic—and typically periodic—motion in one or more dimensions. Oscillationinvolves no net movement, but only movementin place; yet individual waves themselves areoscillating, even as the overall wave patternmoves.

The term periodic motion, or movementrepeated at regular intervals called periods,describes the behavior of periodic waves: wavesin which a uniform series of crests and troughsfollow each other in regular succession. Periodicwaves are divided into longitudinal and trans-verse waves, the latter (of which light waves arean example) being waves in which the vibrationor motion is perpendicular to the direction inwhich the wave is moving. Unlike longitudinalwaves, such as those that carry sound energy,transverse waves are fairly easy to visualize, andassume the shape that most people imagine whenthey think of waves: a regular up-and-down pat-tern, called “sinusoidal” in mathematical terms.

PARAMETERS OF WAVE MO-

TION. A period (represented by the symbol T)is the amount of time required to complete onefull cycle of the wave, from trough to crest andback to trough. Period is mathematically relatedto several other aspects of wave motion, includ-ing wave speed, frequency, and wavelength.

Frequency (abbreviated f) is the number ofwaves passing through a given point during theinterval of one second. It is measured in Hertz(Hz), named after Hertz himself: a single Hertz(the term is both singular and plural) is equal toone cycle of oscillation per second. Higher fre-quencies are expressed in terms of kilohertz(kHz; 103 or 1,000 cycles per second); megahertz(MHz; 106 or 1 million cycles per second);and gigahertz (GHz; 109 or 1 billion cycles persecond.)

Wavelength (represented by the symbol λ,the Greek letter lambda) is the distance betweena crest and the adjacent crest, or a trough and anadjacent trough, of a wave. The higher the fre-quency, the shorter the wavelength; and, thus, itis possible to describe waves in terms of either.According to quantum theory, however, electro-magnetic waves can also be described in terms of




photon energy level, or the amount of energy ineach photon. Thus, the electromagnetic spec-trum, as we shall see, varies from relatively long-wavelength, low-frequency, low-energy radiowaves on the one end to extremely short-wave-length, high-frequency, high-energy gamma rayson the other.

The other significant parameter for describ-ing a wave—one mathematically independentfrom those so far discussed—is amplitude.Defined as the maximum displacement of avibrating material, amplitude is the “size” of awave. The greater the amplitude, the greater theenergy the wave contains: amplitude indicatesintensity. The amplitude of a light wave, forinstance, determines the intensity of the light.

A RIGHT-HAND RULE. Physicstextbooks use a number of “right-hand rules”:devices for remembering certain complex physi-cal interactions by comparing the lines of move-ment or force to parts of the right hand. In thepresent context, a right-hand rule makes it easierto visualize the mutually perpendicular direc-tions of electromagnetic waves, electric field, andmagnetic field.

A field is a region of space in which it is pos-sible to define the physical properties of eachpoint in the region at any given moment in time.Thus, an electrical field and magnetic field aresimply regions in which electrical and magneticcomponents, respectively, of electromagneticforce are exerted.

Hold out your right hand, palm perpendicu-lar to the floor and thumb upright. Your fingersindicate the direction that an electromagneticwave is moving. Your thumb points in the direc-tion of the electrical field, as does the heel of yourhand: the electrical field forms a plane perpendi-cular to the direction of wave propagation. Simi-larly, both your palm and the back of your handindicate the direction of the magnetic field,which is perpendicular both to the electrical fieldand the direction of wave propagation.


As stated earlier, an electromagnetic wave istransverse, meaning that even as it moves for-ward, it oscillates in a direction perpendicular tothe line of propagation. An electromagnetic wavecan thus be defined as a transverse wave with

mutually perpendicular electrical and magneticfields that emanate from it.

The electromagnetic spectrum is the com-plete range of electromagnetic waves on a con-tinuous distribution from a very low range offrequencies and energy levels, with a correspond-ingly long wavelength, to a very high range offrequencies and energy levels, with a corre-spondingly short wavelength. Included on theelectromagnetic spectrum are radio waves andmicrowaves; infrared, visible, and ultravioletlight; x rays, and gamma rays. Though each occu-pies a definite place on the spectrum, the divi-sions between them are not firm: as befits thenature of a spectrum, one simply “blurs” intoanother.

FREQUENCY RANGE OF THE

ELECTROMAGNETIC SPECTRUM.

The range of frequencies for waves in the electro-magnetic spectrum is from approximately 102 Hzto more than 1025 Hz. These numbers are anexample of scientific notation, which makes itpossible to write large numbers without havingto include a string of zeroes. Without scientificnotation, the large numbers used for discussingproperties of the electromagnetic spectrum canbecome bewildering.

The first number given, for extremely low-frequency radio waves, is simple enough—100—but the second would be written as 1 followed by 25 zeroes. (A good rule of thumb for scien-tific notation is this: for any power n of 10,simply attach that number of zeroes to 1. Thus106 is 1 followed by 6 zeroes, and so on.) In any case, 1025 is a much simpler figure than10,000,000,000,000,000,000,000,000—or 10 tril-lion trillion. As noted earlier, gigahertz, or unitsof 1 billion Hertz, are often used in describingextremely high frequencies, in which case thenumber is written as 1016 GHz. For simplicity’ssake, however, in the present context, the simpleunit of Hertz (rather than kilo-, mega-, or giga-hertz) is used wherever it is convenient to do so.

WAVELENGTHS ON THE ELEC-

TROMAGNETIC SPECTRUM. Therange of wavelengths found in the electromag-netic spectrum is from about 108 centimeters toless than 10-15 centimeters. The first number,equal to 1 million meters (about 621 mi), obvi-ously expresses a great length. This figure is forradio waves of extremely low frequency; ordinaryradio waves of the kind used for actual radio



Electro-magnetic

Spectrum

broadcasts are closer to 105 centimeters (about328 ft).

For such large wavelengths, the use of cen-timeters might seem a bit cumbersome; but, aswith the use of Hertz for frequencies, centimetersprovide a simple unit that can be used to meas-ure all wavelengths. Some charts of the electro-magnetic spectrum nonetheless give figures inmeters, but for parts of the spectrum beyondmicrowaves, this, too, can become challenging.The ultra-short wavelengths of gamma rays, afterall, are equal to one-trillionth of a centimeter. Bycomparison, the angstrom—a unit so small it isused to measure the diameter of an atom—is 10million times as large.

ENERGY LEVELS ON THE ELEC-

TROMAGNETIC SPECTRUM. Finally, interms of photon energy, the unit of measurementis the electron volt (eV), which is used for quan-tifying the energy in atomic particles. The rangeof photon energy in the electromagnetic spec-trum is from about 10-13 to more than 1010 elec-tron volts. Expressed in terms of joules, an elec-tron volt is equal to 1.6 • 10-19 J.

To equate these figures to ordinary languagewould require a lengthy digression; suffice it tosay that even the highest ranges of the electro-magnetic spectrum possess a small amount ofenergy in terms of joules. Remember, however,that the energy level identified is for a photon—a light particle. Again, without going into a greatdeal of detail, one can just imagine how many ofthese particles, which are much smaller thanatoms, would fit into even the smallest of spaces.Given the fact that electromagnetic waves aretraveling at a speed equal to that of light, theamount of photon energy transmitted in a singlesecond is impressive, even for the lower ranges ofthe spectrum. Where gamma rays are concerned,the energy levels are positively staggering.


The Radio Sub-Spectrum

Among the most familiar parts of the electro-magnetic spectrum, in modern life at least, isradio. In most schematic representations of thespectrum, radio waves are shown either at the leftend or the bottom, as an indication of the factthat these are the electromagnetic waves with the

lowest frequencies, the longest wavelengths, andthe smallest levels of photon energy. Included inthis broad sub-spectrum, with frequencies up toabout 107 Hertz, are long-wave radio, short-waveradio, and microwaves. The areas of commu-nication affected are many: broadcast radio,television, mobile phones, radar—and evenhighly specific forms of technology such as babymonitors.

Though the work of Maxwell and Hertz wasfoundational to the harnessing of radio waves forhuman use, the practical use of radio had itsbeginnings with Marconi. During the 1890s, hemade the first radio transmissions, and, by theend of the century, he had succeeded in trans-mitting telegraph messages across the AtlanticOcean—a feat which earned him the Nobel Prizefor physics in 1909.

Marconi’s spark transmitters could sendonly coded messages, and due to the broad, long-wavelength signals used, only a few stations couldbroadcast at the same time. The development ofthe electron tube in the early years of the twenti-eth century, however, made it possible to trans-mit narrower signals on stable frequencies. This,in turn, enabled the development of technologyfor sending speech and music over the airwaves.

Broadcast Radio

THE DEVELOPMENT OF AM AND

FM. A radio signal is simply a carrier: theprocess of adding information—that is, complexsounds such as those of speech or music—iscalled modulation. The first type of modulationdeveloped was AM, or amplitude modulation,which Canadian-American physicist ReginaldAubrey Fessenden (1866-1932) demonstratedwith the first United States radio broadcast in1906. Amplitude modulation varies the instanta-neous amplitude of the radio wave, a function ofthe radio station’s power, as a means of transmit-ting information.

By the end of World War I, radio hademerged as a popular mode of communication:for the first time in history, entire nations couldhear the same sounds at the same time. Duringthe 1930s, radio became increasingly important,both for entertainment and information. Fami-lies in the era of the Great Depression wouldgather around large “cathedral radios”—sonamed for their size and shape—to hear comedyprograms, soap operas, news programs, and




speeches by important public figures such asPresident Franklin D. Roosevelt.

Throughout this era—indeed, for more thana half-century from the end of the first WorldWar to the height of the Vietnam Conflict in themid-1960s—AM held a dominant position inradio. This remained the case despite a numberof limitations inherent in amplitude modulation:AM broadcasts flickered with popping noisesfrom lightning, for instance, and cars with AMradios tended to lose their signal when goingunder a bridge. Yet, another mode of radio trans-mission was developed in the 1930s, thanks toAmerican inventor and electrical engineer EdwinH. Armstrong (1890-1954). This was FM, or fre-quency modulation, which varied the radio sig-nal’s frequency rather than its amplitude.

Not only did FM offer a different type ofmodulation; it was on an entirely different fre-quency range. Whereas AM is an example of along-wave radio transmission, FM is on themicrowave sector of the electromagnetic spec-trum, along with television and radar. Due to itshigh frequency and form of modulation, FMoffered a “clean” sound as compared with AM.The addition of FM stereo broadcasts in the1950s offered still further improvements; yetdespite the advantages of FM, audiences wereslow to change, and FM did not become popularuntil the mid- to late 1960s.

SIGNAL PROPAGATION. AM sig-nals have much longer wavelengths, and smallerfrequencies, than do FM signals, and this, in turn,affects the means by which AM signals are prop-agated. There are, of course, much longer radiowavelengths; hence, AM signals are described asintermediate in wavelength. These intermediate-wavelength signals reflect off highly charged lay-ers in the ionosphere between 25 and 200 mi (40-332 km) above Earth’s surface. Short-wave-length signals, such as those of FM, on the otherhand, follow a straight-line path. As a result, AMbroadcasts extend much farther than FM, partic-ularly at night.

At a low level in the ionosphere is the Dlayer, created by the Sun when it is high in thesky. The D layer absorbs medium-wavelengthsignals during the day, and for this reason, AMsignals do not travel far during daytime hours.After the Sun goes down, however, the D layersoon fades, and this makes it possible for AM sig-nals to reflect off a much higher layer of the ion-

osphere known as the F layer. (This is also some-times known as the Heaviside layer, or the Ken-nelly-Heaviside layer, after English physicistOliver Heaviside and British-American electricalengineer Arthur Edwin Kennelly, who independ-ently discovered the ionosphere in 1902.) AMsignals “bounce” off the F layer as though it werea mirror, making it possible for a listener at night to pick up a signal from halfway across thecountry.

The Sun has other effects on long-wave and intermediate-wave radio transmissions.Sunspots, or dark areas that appear on the Sun incycles of about 11 years, can result in a heavierbuildup of the ionosphere than normal, thusimpeding radio-signal propagation. In addition,occasional bombardment of Earth by chargedparticles from the Sun can also disrupt trans-missions.

Due to the high frequencies of FM signals,these do not reflect off the ionosphere; instead,they are received as direct waves. For this reason,an FM station has a fairly short broadcast range,and this varies little with regard to day or night.The limited range of FM stations as compared toAM means that there is much less interference onthe FM dial than for AM.

Distribution of Radio Frequencies

In the United States and most other countries,one cannot simply broadcast at will; the airwavesare regulated, and, in America, the governingauthority is the Federal Communications Com-mission (FCC). The FCC, established in 1934,was an outgrowth of the Federal Radio Commis-sion, founded by Congress seven years earlier.The FCC actually “sells air,” charging companiesa fee to gain rights to a certain frequency. Thosecompanies may in turn sell that air to others fora profit.

At the time of the FCC’s establishment, AMwas widely used, and the federal governmentassigned AM stations the frequency range of 535kHz to 1.7 MHz. Thus, if an AM station today iscalled, for instance, “AM 640,” this means that itoperates at 640 kHz on the dial. The FCCassigned the range of 5.9 to 26.1 MHz to short-wave radio, and later the area of 26.96 to 27.41MHz to citizens’ band (CB) radio. Above theseare microwave regions assigned to television sta-



Electro-magnetic

Spectrum

tions, as well as FM, which occupies the rangefrom 88 to 108 MHz.

The organization of the electromagneticspectrum’s radio frequencies—which, of course,is an entirely arbitrary, humanmade process—isfascinating. It includes assigned frequencies foreverything from garage-door openers to deep-space radio communications. The FCC recog-nizes seven divisions of radio carriers, using asystem that is not so much based on rationalrules as it is on the way that the communicationsindustries happened to develop over time.

THE SEVEN FCC DIVISIONS.

Most of what has so far been described fallsunder the heading of “Public Fixed Radio Ser-vices”: AM and FM radio, other types of radiosuch as shortwave, television, various otherforms of microwave broadcasting, satellite sys-tems, and communication systems for federaldepartments and agencies. “Public Mobile Ser-vices” include pagers, air-to-ground service (forexample, aircraft-to-tower communications),offshore service for sailing vessels, and ruralradio-telephone service. “Commercial MobileRadio Services” is the realm of cellular phones,and “Personal Communications Service” that ofthe newer wireless technology that began to chal-lenge cellular for market dominance in the late1990s.

“Private Land Mobile Radio Service” (PMR)and “Private Operational-Fixed Microwave Ser-vices” (OFS) are rather difficult to distinguish,the principal difference being that the former isused exclusively by profit-making businesses, andthe latter mostly by nonprofit institutions. Anexample of PMR technology is the dispatchingradios used by taxis, but this is only one of themore well-known forms of internal electroniccommunications for industry. For instance, whena film production company is shooting a pictureand the director needs to speak to someone at theproducer’s trailer a mile away, she may use PMRradio technology. OFS was initially designatedpurely for nonprofit use, and is used often byschools; but banks and other profit-making insti-tutions often use OFS because of its low cost.

Finally, there is the realm of “Personal RadioServices,” created by the FCC in 1992. Thisbranch, still in its infancy, will probably one dayinclude video-on-demand, interactive polling,online shopping and banking, and other activi-ties classified under the heading of Interactive

Video and Data Services, or IVDS. Unlike othertypes of video technology, these will all be wire-less, and, therefore, represent a telecommunica-tions revolution all their own.

Microwaves

MICROWAVE COMMUNICATION.

Though microwaves are treated separately fromradio waves, in fact, they are just radio signals ofa very short wavelength. As noted earlier, FM sig-nals are actually carried on microwaves, and, aswith FM in particular, microwave signals in gen-eral are very clear and very strong, but do notextend over a great geographical area. Nor doesmicrowave include only high-frequency radioand television; in fact, any type of informationthat can be transmitted via telephone wires orcoaxial cables can also be sent via a microwavecircuit.

Microwaves have a very narrow, focusedbeam: thus, the signal is amplified considerablywhen an antenna receives it. This phenomenon,known as “high antenna gain,” means thatmicrowave transmitters need not be highly pow-erful to produce a strong signal. To further thereach of microwave broadcasts, transmitters areoften placed atop mountain peaks, hilltops, ortall buildings. In the past, a microwave-transmit-ting network such as NBC (National Broadcast-ing Company) or CBS (Columbia BroadcastingSystem) required a network of ground-basedrelay stations to move its signal across the conti-nent. The advent of satellite broadcasting in the1960s, however, changed much about the waysignals are beamed: today, networks typicallyreplace, or at least augment, ground-based relayswith satellite relays.

The first worldwide satellite TV broadcast,in the summer of 1967, featured the Beatlessinging their latest song “All You Need Is Love.”Due to the international character of the broad-cast, with an estimated 200 million viewers, JohnLennon and Paul McCartney wrote a song withsimple, universal lyrics, and the result was justanother example of electronic communicationuniting large populations. Indeed, the phenome-non of rock music, and of superstardom as peo-ple know it today, would be impossible withoutmany of the forms of technology discussed here.Long before the TV broadcast, the Beatles hadcome to fame through the playing of their music




on the radio waves—and, thus, they owed muchto Maxwell, Hertz, and Marconi.

MICROWAVE OVENS. The samemicrowaves that transmit FM and television sig-nals—to name only the most obviously applica-tions of microwave for communication—canalso be harnessed to cook food. The microwaveoven, introduced commercially in 1955, was anoutgrowth of military technology developed adecade before.

During World War II, the Raytheon Manu-facturing Company had experimented with amagnetron, a device for generating extremelyshort-wavelength radio signals as a means ofimproving the efficiency of military radar. Whileworking with a magnetron, a technician namedPercy Spencer was surprised to discover that acandy bar in his pocket had melted, even thoughhe had not felt any heat. This led him to consid-ering the possibilities of applying the magnetronto peacetime uses, and a decade later, Raytheon’s“radar range” hit the market.

Those early microwave ovens had none ofvaried power settings to which modern users ofthe microwave—found today in two-thirds of allAmerican homes—are accustomed. In the firstmicrowaves, the only settings were “on” and “off,”because there were only two possible adjust-ments: either the magnetron would produce, ornot produce, microwaves. Today, it is possible to use a microwave for almost anything that involves the heating of food that containswater—from defrosting a steak to popping popcorn.

As noted much earlier, in the general discus-sion of electromagnetic radiation, there are threebasic types of heat transfer: conduction, convec-tion, and radiation. Without going into too muchdetail here, conduction generally involves heattransfer between molecules in a solid; convectiontakes place in a fluid (a gas such as air or a liquidsuch as water); and radiation, of course, requiresno medium.

A conventional oven cooks through convec-tion, though conduction also carries heat fromthe outer layers of a solid (for example, a turkey)to the interior. A microwave, on the other hand,uses radiation to heat the outer layers of the food;then conduction, as with a conventional oven,does the rest. The difference is that themicrowave heats only the food—or, more specif-ically, the water, which then transfers heat

throughout the item being heated—and not thedish or plate. Thus, many materials, as long asthey do not contain water, can be placed in amicrowave oven without being melted orburned. Metal, though it contains no water, isunsafe because the microwaves bounce off themetal surfaces, creating a microwave buildupthat can produce sparks and damage the oven.

In a microwave oven, microwaves emitted bya small antenna are directed into the cookingcompartment, and as they enter, they pass a set ofturning metal fan blades. This is the stirrer,which disperses the microwaves uniformly overthe surface of the food to be heated. As amicrowave strikes a water molecule, resonancecauses the molecule to align with the direction ofthe wave. An oscillating magnetron causes themicrowaves to oscillate as well, and this, in turn,compels the water molecules to do the same.Thus, the water molecules are shifting in positionseveral million times a second, and this vibrationgenerates energy that heats the water.

Radio Waves for Measure-ment and Ranging

RADAR. Radio waves can be used to sendcommunication signals, or even to cook food;they can also be used to find and measure things.One of the most obvious applications in thisregard is radar, an acronym for RAdio DetectionAnd Ranging.

Radio makes it possible for pilots to “see”through clouds, rain, fog, and all manner of nat-ural phenomena—not least of which is darkness.It can also identify objects, both natural andmanmade, thus enabling a peacetime pilot toavoid hitting another craft or the side of a moun-tain. On the other hand, radar may help a pilot inwartime to detect the presence of an enemy. Noris radar used only in the skies, or for militarypurposes, such as guiding missiles: on theground, it is used to detect the speeds of objectssuch as automobiles on an interstate highway, aswell as to track storms.

In the simplest model of radar operation,the unit sends out microwaves toward the target,and the waves bounce back off the target to theunit. Though the speed of light is reduced some-what, due to the fact that waves are travelingthrough air rather than through a vacuum, it is,nonetheless, possible to account for this differ-ence. Hence, the distance to the target can be cal-



Electro-magnetic

Spectrum

culated using the simple formula d = vt, where dis distance, v is velocity, and t is time.

Typically, a radar system includes the follow-ing: a frequency generator and a unit for control-ling the timing of signals; a transmitter and, aswith broadcast radio, a modulator; a duplexer,which switches back and forth between transmis-sion and reception mode; an antenna; a receiver,which detects and amplifies the signals bouncedback to the antenna; signal and data processingunits; and data display units. In a monostaticunit—one in which the transmitter and receiverare in the same location—the unit has to be con-tinually switched between sending and receivingmodes. Clearly, a bistatic unit—one in which thetransmitter and receiver antennas are at differentlocations—is generally preferable; but on an air-plane, for instance, there is no choice but to use amonostatic unit.

In order to determine the range to a target—whether that target be a mountain, an enemy air-craft, or a storm—the target itself must first bedetected. This can be challenging, because only asmall portion of the transmitted pulse comesback to the receiving antenna. At the same time,the antenna receives reflections from a numberof other objects, and it can be difficult to deter-mine which signal comes from the target. For anaircraft in a wartime situation, these problemsare compounded by the use of enemy counter-measures such as radar “jamming.” Still anotherdifficulty facing a military flyer is the fact that theuse of radar itself—that is, the transmission ofmicrowaves—makes the aircraft detectable toopposing forces.

TELEMETRY. Telemetry is the processof making measurements from a remote locationand transmitting those measurements to receiv-ing equipment. The earliest telemetry systems,developed in the United States during the 1880s,monitored the distribution and use of electricityin a given region, and relayed this informationback to power companies using telephone lines.By the end of World War I, electric companiesused the power lines themselves as informationrelays, and though such electrical telemetry sys-tems remain in use in some sectors, most mod-ern telemetry systems apply radio signals.

An example of a modern telemetry applica-tion is the use of an input device called a trans-ducer to measure information concerning anastronaut’s vital signs (heartbeat, blood pressure,

body temperature, and so on) during a mannedspace flight. The transducer takes this informa-tion and converts it into an electrical impulse,which is then beamed to the space monitoringstation on Earth. Because this signal carriesinformation, it must be modulated, but there islittle danger of interference with broadcast trans-missions on Earth. Typically, signals from space-craft are sent in a range above 1010 Hz, far abovethe frequencies of most microwave transmissionsfor commercial purposes.

Light: Invisible, Visible, andInvisible Again

Between about 1013 and 1017 Hz on the electro-magnetic spectrum is the range of light: infrared,visible, and ultraviolet. Light actually constitutesa small portion of the spectrum, and the area ofvisible light is very small indeed, extending fromabout 4.3 • 1014 to 7.5 • 1014 Hz. The latter, inci-dentally, is another example of scientific nota-tion: not only is it easier not to use a string ofzeroes, but where a coefficient or factor (forexample, 4.3 or 7.5) is other than a multiple of10, it is preferable to use what are called signifi-cant figures—usually a single digit followed by adecimal point and up to 3 decimal places.

Infrared light lies just below visible light infrequency, and this is easy to remember becauseof the name: red is the lowest in frequency of allthe colors. Similarly, ultraviolet lies beyond thehighest-frequency color, violet. Visible light itself,by far the most familiar part of the spectrum—especially prior to the age of radio communica-tions—is discussed in detail elsewhere.

INFRARED LIGHT. Though we can-not see infrared light, we feel it as heat. German-English astronomer William Herschel (1738-1822), first scientist to detect infrared radiationfrom the Sun, demonstrated its existence in 1800by using a thermometer. Holding a prism, athree-dimensional glass shape used for diffusingbeams of light, he directed a beam of sunlighttoward the thermometer, which registered theheat of the infrared rays.

Eighty years later, English scientist SirWilliam Abney (1843-1920) developed infraredphotography, a method of capturing infraredradiation, rather than visible light, on film. By themid-twentieth century, infrared photographyhad come into use for a variety of purposes. Mil-itary forces, for instance, may use infrared to




detect the presence of enemy troops. Medicinemakes use of infrared photography for detectingtumors, and astronomers use infrared to detectstars too dim to be seen using ordinary visiblelight.

The uses of infrared imaging in astronomy,as a matter of fact, are many. The development inthe 1980s of infrared arrays, two-dimensionalgrids which produce reliable images of infraredphenomena, revolutionized infrared astronomy.Because infrared penetrates dust much more eas-ily than does visible light, infrared astronomymakes it easier to see regions of the universewhere stars—formed from collapsing clouds ofgas and dust—are in the process of developing.Because hydrogen molecules emit infrared radia-tion, infrared astronomy helps provide cluesregarding the distribution of this highly signifi-cant chemical element throughout the universe.

ULTRAVIOLET LIGHT. Very little ofthe Sun’s ultraviolet light penetrates Earth’satmosphere—a fortunate thing, since ultraviolet(UV) radiation can be very harmful to human

skin. A suntan, as a matter of fact, is actually theskin’s defense against these harmful UV rays. Dueto the fact that Earth is largely opaque, or resist-ant, to ultraviolet light, the most significant tech-nological applications of UV radiation are foundin outer space.

In 1978 the United States, in cooperationwith several European space agencies, launchedthe International Ultraviolet Explorer (IUE),which measured the UV radiation from tens ofthousands of stars, nebulae, and galaxies. Despitethe progress made with IUE, awareness of its lim-itations—including a mirror of only 17 in (45cm) on the telescope itself—led to the develop-ment of a replacement in 1992.

This was the Extreme Ultraviolet Explorer(EUVE), which could observe UV phenomenaover a much higher range of wavelengths thanthose observed by IUE. In addition, the HubbleSpace Telescope, launched by the United States in1990, includes a UV instrument called the God-dard High Resolution Spectrograph. With a mir-ror measuring 8.5 ft (2.6 m), it is capable ofobserving objects much more faint than thosedetected earlier by IUE.

Ultraviolet astronomy is used to study thewinds created by hot stars, as well as stars still inthe process of forming, and even stars that aredying. It is also useful for analyzing the denselypacked, highly active sectors near the centers ofgalaxies, where both energy and temperatures areextremely high.

X Rays

Though they are much higher in frequency thanvisible light—with wavelengths about 1,000times shorter than for ordinary light rays—x raysare a familiar part of modern life due to theiruses in medicine. German scientist WilhelmRöntgen (1845-1923) developed the first x-raydevice in 1895, and, thus, the science of using x-ray machines is called roentgenology.

The new invention became a curiosity, withcarnivals offering patrons an opportunity to lookat the insides of their hands. And just as manypeople today fear the opportunities for invasionof privacy offered by computer technology, manyat the time worried that x rays would allow robbers and peeping toms to look into people’shouses. Soon, however, it became clear that the most important application of x rays lay in medicine.


“SOFT” X-RAY MACHINES, SUCH AS THIS ONE BEING

USED BY A DENTIST TO PHOTOGRAPH THE PATIENT’STEETH, OPERATE AT RELATIVELY LOW FREQUENCIES AND

THUS DON’T HARM THE PATIENT. (Photograph by Richard T.

Nowitz/Corbis. Reproduced by permission.)


Electro-magnetic

Spectrum





an indicator of the energy and intensity of

the wave.

CYCLE: One complete oscillation. In

wave motion, this is equivalent to the

movement of a wave from trough to crest

and back to trough.

ELECTROMAGNETIC FORCE: The

total force on an electrically charged parti-

cle, which is a combination of forces due to

electrical and/or magnetic fields around

the particle. Electromagnetic force reflects

electromagnetic interaction, one of the

four fundamental interactions in nature.












gamma rays.

ELECTROMAGNETIC WAVE: A

transverse wave with electrical and mag-

netic fields that emanate from it. The direc-

tions of these fields are perpendicular to

one another, and both are perpendicular to

the line of propagation for the wave itself.

ELECTROMAGNETISM: The branch

of physics devoted to the study of electrical

and magnetic phenomena.

FIELD: A region of space in which it is

possible to define the physical properties of

each point in the region at any given

moment in time.








FUNDAMENTAL INTERACTION: The

basic mode by which particles interact.

There are four known fundamental inter-

actions in nature: gravitational, electro-

magnetic, strong nuclear, and weak

nuclear.







(1857-1894). High frequencies are ex-

pressed in terms of kilohertz (kHz; 103 or

1,000 cycles per second); megahertz (MHz;

106 or 1 million cycles per second); and

gigahertz (GHz; 109 or 1 billion cycles per

second.)



cross-sectional area.



dimensions.





speed.

KEY TERMS










PHOTON: A particle of electromagnet-

ic radiation carrying a specific amount of

energy, measured in electron volts (eV).

For parts of the electromagnetic spectrum

with a low frequency and long wavelength,

photon energy is relatively low; but for

parts with a high frequency and short

wavelength, the value of photon energy is

very high.



RADIATION: The transfer of energy by




the Sun’s energy, via the electromagnetic

spectrum, by means of radiation.

SCIENTIFIC NOTATION: A method

used by scientists for writing extremely

large numbers. This usually involves a coef-

ficient, or factor, of a single digit followed

by a decimal point and up to three decimal

places, multiplied by 10 to a given expo-

nent. Thus, instead of writing 75,120,000,

the preferred scientific notation is 7.512 •

107. To visualize the value of very large

multiples of 10, it is helpful to remember

that the value of 10 raised to any power n is

the same as 1 followed by that number of

zeroes. Hence 1025, for instance, is simply 1

followed by 25 zeroes.




moving.




length, symbolized λ (the Greek letter






matter.


HOW A MEDICAL X-RAY MA-

CHINE WORKS. Due to their very short

wavelengths, x rays can pass through substances

of low density—for example, fat and other forms

of soft tissue—without their movement being

interrupted. But in materials of higher density,

such as bone, atoms are packed closely together,

and this provides x rays with less space through

which to travel. As a result, x-ray images show

dark areas where the rays traveled completely

through the target, and light images of dense

materials that blocked the movement of the rays.

Medical x-ray machines are typicallyreferred to either as “hard” or “soft.” Soft x raysare the ones with which most people are morefamiliar. Operating at a relatively low frequency,these are used to photograph bones and internalorgans, and provided the patient does not receiveprolonged exposure to the rays, they cause littledamage. Hard x rays, on the other hand, aredesigned precisely to cause damage—not to thepatient, but to cancer cells. Because they use highvoltage and high-frequency rays, hard x rays canbe quite dangerous to the patient as well.


Electro-magnetic

Spectrum

OTHER APPLICATIONS. X-raycrystallography, developed in the early twentiethcentury, is devoted to the study of the interfer-ence patterns produced by x rays passing throughmaterials that are crystalline in Structure. Each ofthese discoveries, in turn, transformed daily life:insulin, by offering hope to diabetics, penicillin,by providing a treatment for a number of previ-ously fatal illnesses, and DNA, by enabling scien-tists to make complex assessments of geneticinformation.

In addition to the medical applications, thescanning capabilities of x-ray machines makethem useful for security. A healthy personreceives an x ray at a doctor’s office only once ina while; but everyone who carries items past acertain point in a major airport must submit tox-ray security scanning. If one is carrying a purseor briefcase, for instance, this is placed on a mov-ing belt and subjected to scanning by a low-power device that can reveal the contents.

Gamma Rays

At the furthest known reaches of the electromag-netic spectrum are gamma rays, ultra high-fre-quency, high-energy, and short- wavelengthforms of radiation. Human understanding ofgamma rays, including the awesome powers theycontain, is still in its infancy.

In 1979, a wave of enormous energy passedover the Solar System. Though its effects onEarth were negligible, instruments aboard sever-al satellites provided data concerning an enor-mous quantity of radiation caused by gammarays. As to the source of the rays themselves,believed to be a product of nuclear fusion onsome other body in the universe, scientists knewnothing.

The Compton Gamma Ray ObservatorySatellite, launched by NASA (National Aeronau-tics and Space Administration) in 1991, detecteda number of gamma-ray bursts over the next twoyears. The energy in these bursts was staggering:

just one of these, scientists calculated, containedmore than a thousand times as much energy asthe Sun will generate in its entire lifetime of 10billion years.

Some astronomers speculate that the sourceof these gamma-ray bursts may ultimately be adistant supernova, or exploding star. If this is thecase, scientists may have found the supernova;but do not expect to see it in the night sky. It isnot known just how long ago it exploded, but itslight appeared on Earth some 340,000 years ago,and during that time it was visible in daylight formore than two years. So great was its power thatthe effects of this stellar phenomenon are stillbeing experienced.

WHERE TO LEARN MORE

Branley, Franklyn Mansfield. The Electromagnetic Spec-trum: Key to the Universe. Illustrated by Leonard D.Dank. New York: Crowell, 1979.

Electromagnetic Spectrum (Web site). <http://www.jsc.mil/images/speccht.jpg> (April 25, 2001).

The Electromagnetic Spectrum (Web site).<http://library.thinkquest.org/11119/index.htm>(April 30, 2001).

The Electromagnetic Spectrum (Web site). <http://www.ospi.wednet.edu:8001/curric/space/lfs/emspectr.html> (April 30, 2001).

Electromagnetic Spectrum/NASA: National Aeronauticsand Space Administration (Web site). <http://imagine.gsfc.nasa.gov/docs/science/know_11/emspectrum.html> (April 30, 2001).

“How the Radio Spectrum Works.” How Stuff Works (Website). <http://www.howstuffworks.com/radio~spectrum.htm> (April 25, 2001).


Nassau, Kurt. Experimenting with Color. New York: F.Watts, 1997.

“Radio Electronics Pages” ePanorama.net (Web site).<http://www.epanorama.net/radio.html> (April 25,2001).

Skurzynski, Gloria. Waves: The Electromagnetic Universe.Washington, D.C.: National Geographic Society,1996.




L I GHTLight

CONCEPTLight exists along a relatively narrow bandwidth

of the electromagnetic spectrum, and the region

of visible light is more narrow still. Yet, within

that realm are an almost infinite array of hues

that quite literally give color to the entire world

of human experience. Light, of course, is more

than color: it is energy, which travels at incredible

speeds throughout the universe. From prehis-

toric times, humans harnessed light’s power

through fire, and later, through the invention of

illumination devices such as candles and gas

lamps. In the late nineteenth century, the first

electric-powered forms of light were invented,

which created a revolution in human existence.

Today, the power of lasers, highly focused beams

of high-intensity light, make possible a number

of technologies used in everything from surgery

to entertainment.

HOW IT WORKS

Early Progress in Under-standing of Light

The first useful observations concerning light

came from ancient Greece. The Greeks recog-

nized that light travels through air in rays, a term

from geometry describing that part of a straight

line that extends in one direction only. Upon

entering some denser medium, such as glass or

water, as Greek scientists noticed, the ray experi-

ences refraction, or bending. Another type of

incidence, or contact, between a light ray and any

surface, is reflection, whereby a light ray returns,

rather than being absorbed at the interface.

The Greeks worked out the basic laws gov-erning reflection and refraction, observing, forinstance, that in reflection, the angle of incidenceis approximately equal to the angle of reflection.Unfortunately, they also subscribed to the erro-neous concept of intromission—the belief thatlight rays originate in the eye and travel towardobjects, making them visible. Some 1,500 yearsafter the high point of Greek civilization, Arabphysicist Alhasen (Ibn al-Haytham; c. 965-1039),sometimes called the greatest scientist of theMiddle Ages, showed that light comes from asource such as the Sun, and reflects from anobject to the eyes.

The next great era of progress in studies oflight began with the Renaissance (c. 1300-c.1600.) However, the most profound scientificachievements in this area belonged not to scien-tists, but to painters, who were fascinated bycolor, shading, shadows, and other properties oflight. During the early seventeenth century,Galileo Galilei (1564-1642) and Germanastronomer Johannes Kepler (1571-1630) builtthe first refracting telescopes, while Dutch physi-cist and mathematician Willebrord Snell (1580-1626) further refined the laws of refraction.

The Spectrum

Sir Isaac Newton (1642-1727) was as intriguedwith light as he was with gravity and the otherconcepts associated with his work. Though it wasnot as epochal as his contributions to mechanics,Newton’s work in optics, an area of physics thatstudies the production and propagation of light,was certainly significant.

In Newton’s time, physicists understood thata prism could be used for the diffusion of light


Lightrays—in particular, to produce an array of colorsfrom a beam of white light. The prevailing beliefwas that white was a single color like the others,but Newton maintained that it was a combina-tion of all other colors. To prove this, he directeda beam of white light through a prism, thenallowed the diffused colors to enter anotherprism, at which point they recombined as whitelight.

Newton gave to the array of colors in visiblelight the term spectrum, (plural, “spectra”)meaning the continuous distribution of proper-ties in an ordered arrangement across an unbro-ken range. The term can be used for any set ofcharacteristics for which there is a gradation, asopposed to an excluded middle. An ordinarylight switch provides an example of a situation inwhich there is an excluded middle: there is noth-ing between “on” and “off.” A dimmer switch, onthe other hand, is a spectrum, because a verylarge number of gradations exist between the twoextremes represented by a light switch.

SEVEN COLORS...OR SIX? Thedistribution of colors across the spectrum is asfollows: red-orange-yellow-green-blue-violet.The reasons for this arrangement, explainedbelow in the context of the electromagnetic spec-trum, were unknown to Newton. Not only did helive in an age that had almost no understandingof electromagnetism, but he was also a productof the era called the Enlightenment, when intel-lectuals (scientists included) viewed the world asa highly rational, ordered mechanism. HisEnlightenment viewpoint undoubtedly influ-enced his interpretation of the spectrum as a setof seven colors, just as there are seven notes onthe musical scale.

In addition to the six basic colors listedabove, Newton identified a seventh, indigo,between blue and violet. In fact, there is a notice-able band of color between blue and violet, butthis is because one color fades into another. Witha spectrum, there is a blurring of lines betweenone color and the next: for instance, orange existsat a certain point along the spectrum, as does yel-low, but between them is a nearly unlimitednumber of orange-yellow and yellow-orange gradations.

Indigo itself is not really a distinct color—just a deep, purplish blue. But its inclusion in thelisting of colors on the spectrum has given gener-ations of students a handy mnemonic (memo-


rization) device: the name “ROY G. BIV.” Theseletters form an acrostic (a word constructed fromthe first letters of other words) for the colors ofthe spectrum. Incidentally, there is somethingarbitrary even in the idea of six colors, or for thatmatter seven musical notes: in both cases, thereexists a very large gradation of shades, yet also inboth cases, the divisions used were chosen forpractical purposes.

Waves, Particles, and OtherQuestions Concerning Light

THE WAVE-PARTICLE CONTRO-

VERSY BEGINS. Newton subscribed tothe corpuscular theory of light: the idea that lighttravels as a stream of particles. On the otherhand, Dutch physicist and astronomer Christi-aan Huygens (1629-1695) maintained that lighttravels in waves. During the century that fol-lowed, adherents of particle theory did intellec-tual battle with proponents of wave theory. “Bat-tle” is not too strong a word, because the conflictwas heated, and had a nationalistic element.Reflecting both the burgeoning awareness of thenation-state among Europeans, as well asBritons’ sense of their own island as an entityseparate from the European continent, particletheory had its strongest defenders in Newton’s

ISAAC NEWTON. (The Bettmann Archive. Reproduced by

permission.)


Light


homeland, while continental scientists generallyaccepted wave theory.

According to Huygens, the appearance of thespectrum, as well as the phenomena of reflectionand refraction, indicated that light was a wave.Newton responded by furnishing complex math-ematical calculations which showed that particlescould exhibit the behaviors of reflection andrefraction as well. Furthermore, Newton chal-lenged, if light were really a wave, it should beable to bend around corners. Yet, in 1660, anexperiment by Italian physicist FrancescoGrimaldi (1618-1663) proved that light could dojust that. Passing a beam of light through a nar-row aperture, or opening, Grimaldi observed aphenomenon called diffraction, or the bendingof light.

In view of the nationalistic character that thewave-particle debate assumed, it was ironic thatthe physicist whose work struck a particularlyforceful blow against corpuscular theory washimself an Englishman: Thomas Young (1773-1829), who in 1801 demonstrated interference inlight. Directing a light beam through two closelyspaced pinholes onto a screen, Young reasonedthat if light truly were made of particles, thebeams would project two distinct points onto thescreen. Instead, what he saw was a pattern ofinterference—a wave phenomenon.

THE QUESTION OF A MEDIUM.

As the nineteenth century progressed, evidencein favor of wave theory grew. Experiments in1850 by Jean Bernard Leon Foucault (1819-1868)—famous for his pendulum —showed thatlight traveled faster in air than through water.Based on studies of wave motion up to that time,Foucault’s work added substance to the view oflight as a wave.

Foucault also measured the speed of light ina vacuum, a speed which he calculated to within1% of its value as it is known today: 186,000 mi(299,339 km) per second. An understanding ofjust how fast light traveled, however, caused anagging question dating back to the days ofNewton and Huygens to resurface: how did lighttravel?

All types of waves known to that time trav-eled through some sort of medium: for instance,sound waves were propagated through air, water,or some other type of matter. If light was a wave,as Huygens said, then it, too, must have somemedium. Huygens and his followers proposed a

weak theory by suggesting the existence of aninvisible substance called ether, which existedthroughout the universe and which carried light.

Ether, of course, was really no answer at all.There was no evidence that it existed, and tomany scientists, it was merely a concept inventedto shore up an otherwise convincing argument.Then, in 1872, Scottish physicist James ClerkMaxwell (1831-1879) proposed a solution thatmust have surprised many scientists. The “medi-um” through which light travels, Maxwell pro-posed, was no medium at all; rather, the energyin light is transferred by means of radiation,which requires no medium.

Electromagnetism

Maxwell brought together a number of conceptsdeveloped by his predecessors, sorting these outand adding to them. His work led to the identifi-cation of a “new” fundamental interaction, inaddition to that associated with gravity. This wasthe mode of particle interaction associated withelectromagnetic force.

The particulars of electromagnetic force,waves, and radiation are a subject unto them-selves—really, many subjects. As for the electro-magnetic spectrum, it is treated at some length inan essay elsewhere in this volume, and the readeris encouraged to review that essay to gain agreater understanding of light and its place in thespectrum.

In addition, some awareness of wave motionand related phenomena would also be of greatvalue, and, for this purpose, other essays are rec-ommended. In the present context, a number oftopics relating to these larger subjects will behandled in short order, with a minimum ofexplanation, to enable a more speedy transitionto the subject of principal importance here: light.

ELECTROMAGNETIC WAVES.

There is, of course, no obvious connectionbetween light and the electromagnetic forceobserved in electrical and magnetic interactions.Yet, light is an example of an electromagneticwave, and is part of the electromagnetic spec-trum. The breakthrough in establishing the elec-tromagnetic quality of light can be attributedboth to Maxwell and German physicist HeinrichRudolf Hertz (1857-1894).

In his Electricity and Magnetism (1873),Maxwell suggested that electromagnetic force


Lightmight have aspects of a wave phenomenon, andhis experiments indicated that electromagneticwaves should travel at exactly the same speed aslight. This appeared to be more than just a coin-cidence, and his findings led him to theorize thatthe electromagnetic interaction included notonly electricity and magnetism, but light as well.Some time later, Hertz proved Maxwell’s hypoth-esis by showing that electromagnetic wavesobeyed the same laws of reflection, refraction,and diffraction as light.

Hertz also discovered the photoelectriceffect, the process by which certain metalsacquire an electrical potential when exposed tolight. He could not explain this behavior, and,indeed, there was nothing in wave theory thatcould account for it. Strangely, after more than acentury in which acceptance of wave theory hadgrown, he had encountered something thatapparently supported what Newton had saidlong before: that light traveled in particles ratherthan waves.

The Wave-Particle DebateRevisited

One of the modern physicists whose name ismost closely associated with the subject of light isAlbert Einstein (1879-1955). In the course ofproving that matter is convertible to energy, as hedid with the theory of relativity, Einstein predict-ed that this could be illustrated by accelerating tospeeds close to that of light. (Conversely, he alsoshowed that it is impossible for matter to reachthe speed of light, because to do so would—as heproved mathematically—result in the matteracquiring an infinite amount of mass, which, ofcourse, is impossible.)

Much of Einstein’s work was influenced bythat of German physicist Max Planck (1858-1947), father of quantum theory. Quantum the-ory and quantum mechanics are, of course, fartoo complicated to explain in any depth here. It isenough to say that they called into questioneverything physicists thought they knew, basedon Newton’s theories of classical mechanics. Inparticular, quantum mechanics showed that, atthe subatomic level, particles behave in ways notjust different from, but opposite to, the behaviorof larger physical objects in the observable world.When a quantity is “quantized,” its values orproperties at the atomic or subatomic level areseparate from one another—meaning that some-

thing can both be one thing and its opposite,depending on how it is viewed.

Interpreting Planck’s observations, Einsteinin a 1905 paper on the photoelectric effect main-tained that light is quantized—that it appears in“bundles” of energy that have characteristicsboth of waves and of particles. Though light trav-els in waves, as Einstein showed, these wavessometimes behave as particles, which is the casewith the photoelectric effect. Nearly two decadeslater, American physicist Arthur Holly Compton(1892-1962) confirmed Einstein’s findings andgave a name to the “particles” of light: photons.

Light’s Place in the Electro-magnetic Spectrum

The electromagnetic spectrum is the completerange of electromagnetic waves on a continuousdistribution from a very low range of frequenciesand energy levels, with a correspondingly longwavelength, to a very high range of frequenciesand energy levels, with a correspondingly shortwavelength. Included on the electromagneticspectrum are radio waves and microwaves;infrared, visible, and ultraviolet light; x rays, andgamma rays. As discussed earlier, concerning thevisible color spectrum, each of these occupies adefinite place on the spectrum, but the divisionsbetween them are not firm: in keeping with thenature of a spectrum, one band simply “blurs”into another.

Of principal concern here is an area near themiddle of the electromagnetic spectrum. Actual-ly, the very middle of the spectrum lies within thebroad area of infrared light, which has frequen-cies ranging from 1012 to just over 1014 Hz, withwavelengths of approximately 10-1 to 10-3 cen-timeters. Even at this point, the light waves areoscillating at a rate between 1 and 100 trilliontimes a second, and the wavelengths are from 1millimeter to 0.01 millimeters. Yet, over thebreadth of the electromagnetic spectrum, wave-lengths get much shorter, and frequencies muchgreater.

Infrared lies just below visible light in fre-quency, which is easy to remember because of thename: red is the lowest in frequency of all the col-ors, as discussed below. Similarly, ultraviolet liesbeyond the highest-frequency color, violet. Nei-ther infrared nor ultraviolet can be seen, yet weexperience them as heat. In the case of ultraviolet(UV) light, the rays are so powerful that exposure



Light to even the minuscule levels of UV radiation thatenter Earth’s atmosphere can cause skin cancer.

Ultraviolet light occupies a much narrowerband than infrared, in the area of about 1015 to1016 Hz—in other words, oscillations between 1and 10 quadrillion times a second. Wavelengthsin this region are from just above 10-6 to about10-7 centimeters. These are often measured interms of a nanometer (nm)—equal to one-mil-lionth of a millimeter—meaning that the wavelength range is from above 100 down toabout 10 nm.

Between infrared and ultraviolet light is theregion of visible light: the six colors that make upmuch of the world we know. Each has a specificrange and frequency, and together they occupyan extremely narrow band of the electromagnet-ic spectrum: from 4.3 • 1014 to 7.5 • 1014 Hz in fre-quency, and from 700 down to 400 nm in wave-length. To compare its frequency range to that ofthe entire spectrum, for instance, is the same ascomparing 3.2 to 100 billion.


Colors

Unlike many of the topics addressed by physics,color is far from abstract. Numerous expressionsin daily life describe the relationship betweenenergy and color: “red hot,” for instance, or “bluewith cold.” In fact, however, red—with a smallerfrequency and a longer wavelength than blue—actually has less energy; therefore, blue objectsshould be hotter.

The phenomenon of the red shift, discov-ered in 1923 by American astronomer EdwinHubble (1889-1953), provides a clue to thisapparent contradiction. As Hubble observed, thelight waves from distant galaxies are shifted tothe red end, and he reasoned that this must meanthose galaxies are moving away from the MilkyWay, the galaxy in which Earth is located.

To generalize from what Hubble observed,when something shows red, it is moving awayfrom the observer. The laws of thermodynamicsstate that where heat is involved, the movement isalways away from an area of high temperatureand toward an area of low temperature. Heatedmolecules that reflect red light are, thus, to use acolloquialism, “showing their tail end” as they

move toward an area of low temperature. By con-trast, molecules of low temperature reflect bluishor purple light because the tendency of heat is tomove toward them.

There are other reasons, aside from heat,that some objects tend to be red and othersblue—or another color. Chemical factors may beinvolved: atoms of neon, for example, can bemade to vibrate at a particular wavelength, pro-ducing a specific color. In any case, the color thatan object reflects is precisely the color that it doesnot absorb: thus, if something is red, that meansit has absorbed every color of the spectrum but red.

WHY IS THE SKY BLUE? Theplacement of colors on the electromagnetic spec-trum provides an answer to that age-old questionposed by generations of children to their parents:“Why is the sky blue?” Electromagnetic radiationis scattered as it enters the atmosphere, but allforms of radiation are not scattered equally.Those having shorter wavelengths—that is,toward the blue end of the spectrum—tend toscatter more than those with longer wavelengths,on the red and orange end.

Yet the longer-wavelength light becomes vis-ible at sunset, when the Sun’s light enters theatmosphere at an angle. In addition, the dimquality of evening light means that it is easiest tosee light of longer wavelengths. This effect isknown as Rayleigh scattering, after Englishphysicist John William Strutt, Lord Rayleigh(1842-1919), who discovered it in 1871. Thanksto Rayleigh’s discovery, there is an explanationnot only for the question of why the sky is blue,but why sunsets are red, orange, and gold.

RAINBOWS. On the subject of color aschildren perceive it, many a child has been fasci-nated by a rainbow, seeing in them somethingmagical. It is easy to understand why childrenperceive these beautiful phenomena this way, andwhy people have invented stories such as that ofthe pot of gold at the end of a rainbow. In fact, arainbow, like many other “magical” aspects ofdaily life, can be explained in terms of physics.

A rainbow, in fact, is simply an illustration ofthe visible light spectrum. Rain drops performthe role of tiny prisms, dispersing white sunlight,much as scientists before Newton had learned todo. But if there is a pot of gold at the end of therainbow, it would be impossible to find. In orderfor a rainbow to be seen, it must be viewed from



Lighta specific perspective: the observer must be in aposition between the sunlight and the raindrops.

Sunlight strikes raindrops in such a way thatthey are refracted, then reflected back at an angleso that they represent the entire visible light spec-trum. Though they are beautiful to see, rainbowsare neither magical nor impossible to reproduceartificially. Such rainbows can be produced, forinstance, in the spiral of small water dropletsemerging from a water hose, viewed when one’sback is to the Sun.

Perception of Light and Color

People literally live and die for colors: the colorsof a flag, for instance, present a rallying point forsoldiers, and different colors are assigned specif-ic political meanings. Blue, both in the Americanand French flags, typically stands for liberty. Redcan symbolize the blood shed by patriots, or itcan mean some version of fraternity or brother-hood. Such is the case with the red of the Frenchtricolor (red-white-blue); likewise, the red in theflag of the former Soviet Union and other Com-munist countries stood for the alleged interna-tional brotherhood of all working peoples. InIslamic countries, by contrast, green stands forthe unity of all Muslims.

These are just a few examples, drawn from aspecific realm—politics—illustrating the mean-ings that people ascribe to colors. Similarly, peo-ple find meanings in images presented to themby light itself. In his Republic, the ancient Greekphilosopher Plato (c. 427-347 B.C.) offered acomplex parable, intended to illustrate the differ-ence between reality and illusion, concerning agroup of slaves who do not recognize the differ-ence between sunlight and the light of a torch ina cave. Modern writers have noted the similari-ties between Plato’s cave and a phenomenonwhich the ancient philosopher could hardly haveimagined: a movie theatre, in which an artificiallight projects images—images that people some-times perceive as being all too real—onto ascreen.

People refer to “tricks of the light,” as, forinstance, when one seems to see an image in afire. One particularly well-known “trick of thelight,” a mirage, is discussed below, but there arealso manmade illusions created by light, shapes,and images. An optical illusion is something thatproduces a false impression in the brain, causing

one to believe that something is as it appears,when, in fact, it is not. When two lines of equallength are placed side by side, but one has arrowspointed outward at either end while the otherline has arrows pointing inward, it appears thatthe line with the inward-pointing arrows areshorter.

This is an example of the ways in whichhuman perception plays a role in what peoplesee. That topic, of course, goes far beyond physicsand into the realms of psychology and the socialsciences. Nonetheless, it is worthwhile to consid-er, from a physical standpoint, how humans seewhat they see—and sometimes see things thatare not there.

A MIRAGE. Because they can bedemonstrated in light waves as well as in soundwaves, diffraction and interference are discussedin separate essays. As for refraction, or the bend-ing of light waves, this phenomenon can be seenin the familiar example of a mirage. While driv-ing down a road on a hot day, one may observethat there are pools of water up ahead, but by thetime one approaches them, they disappear.

Of course, the pools were never there; lightitself has created an optical illusion of sorts. Aslight moves from one material to another, itbends with a different angle of refraction, and,though, in this instance, it is traveling entirelythrough air, it is moving through regions of dif-fering temperature. Light waves travel fasterthrough warm air than through cool air, and,thus, when the light enters the area over the heat-ed surface of the asphalt, it experiences refrac-tion. The waves are thus bent, creating theimpression of a reflection, which suggests to theobserver that there is water up ahead.

HOW THE EYE SEES COLOR.

White, as noted earlier, is the combination of allcolors; black is the absence of color. Where ink,dye, or other forms of artificial pigmentation areconcerned, of course, black is a “real” color, butin terms of light, it is not. In the same way, theexperience of coldness is real, yet “cold” does notexist as a physical phenomenon: it is simply theabsence of heat.

The mixture of pigmentation is an entirelydifferent matter from the mixture of light. Inartificial pigmentation, the primary colors—thethree colors which, when mixed, yield theremainder of the shades on the rainbow—arered, blue, and yellow. Red mixed with blue creates



Light purple, blue mixed with yellow makes green, andred mixed with yellow yields orange. Black andwhite are usually created by using natural sub-stances of that color—chalk for white, forinstance, or various oxides for black. For light, onthe other hand, blue and red are primary colors,but the third primary color is green, not yellow.From these three primary colors, all other shadesof the visible spectrum can be made.

The mechanism of the human eye respondsto the three primary colors of the visible lightspectrum: thus, the eye’s retina is equipped withtiny cones that respond to red, blue, and greenlight. The cones respond to bright light; otherstructures called rods respond to dim light, andthe pupil regulates the amount of light thatenters the eye.

The eye responds with maximum sensitivityto light at the middle of the visible color spec-trum—specifically, green light with a wavelengthof about 555 nm. The optimal wavelength formaximum sensitivity in dim light is around 510nm, on the blue end. It is difficult for the eye torecognize red light, at the far end of the spec-trum, against a dark background. However, thiscan be an advantage in situations of relativedarkness, which is why red light is often used tomaintain vision for sailors, amateur astronomers,and the military on night maneuvers. Becausethere is not much difference between the dark-ness and the red light, the eye adjusts and is ableto see beyond the red light into the darkness. Abright yellow or white light in such situations, onthe other hand, would minimize visibility inareas beyond the light.

Artificial Light

PREHISTORIC LIGHTING TECH-

NOLOGY. Prehistoric humans did not knowit, but they were making use of electromagneticradiation when they lit and warmed their caveswith light from a fire. Though it would seem thatwarmth was more essential to human survivalthan artificial light, in fact, it is likely that bothfunctions emerged at about the same time: oncehumans began using fire for warmth, it wouldhave been a relatively short time before theycomprehended the power of fire to drive outboth darkness and the fierce creatures (forinstance, bears) that came with it.

These distant forebears advanced to thefashioning of portable lighting technology in the

form of torches or rudimentary lamps. Torcheswere probably made by binding togetherresinous material from trees, while lamps weremade either from stones with natural depres-sions, or from soft rocks—for example, soap-stone or steatite—into which depressions werecarved by using harder material. Most of themany hundreds of lamps found by archaeologistsat sites in southwestern France are made of eitherlimestone or sandstone. Limestone was a partic-ularly good choice, since it conducts heat poorly;lamps made of sandstone, a good conductor ofheat, usually had carved handles to protect thehands of the user.

ARTIFICIAL LIGHT IN PRE-

MODERN TIMES. The history of lightingis generally divided into four periods, each ofwhich overlap, and which together illustrate theslow pace of change in illumination technology.First was the primitive, a period encompassingthe torches and lamps of prehistoric humanbeings—though, in fact, French peasants usedthe same lighting methods depicted in nearbycave paintings until World War I.

Next came the classical stage, the world ofGreece and Rome. Earlier civilizations, such asthat of Egypt, belong to the primitive era in light-ing—before the relatively widespread adoptionof the candle and of vegetable oil as fuel. Thirdwas the medieval stage, which saw the develop-ment of metal lamps. Last came the modern orinvention stage, which began with the creation ofthe glass lantern chimney by Leonardo da Vinci(1452-1519) in 1490, culminated with ThomasEdison’s (1847-1931) first practical incandescentbulb in 1879, and continues today.

At various times, ancient peoples used thefat of seals, horses, cattle, and fish as fuel forlamps. (Whale oil, by contrast, entered wide-spread use only during the nineteenth century.)Primitive humans sometimes used entire ani-mals—for example, the storm petrel, a bird heavyin fat—to provide light. Even without such cruelexcesses, however, animal fat made for a smoky,dangerous, foul-smelling fire.

The use of vegetable oils, a much more effi-cient medium for lighting, did not take hold untilGreek, and especially, Roman times. Animal oilsremained in use, however, among the poor,whose homes often reeked with the odor of cas-tor oil or fish oil. Because virtually all fuels came



Lightfrom edible sources, times of famine usuallymeant times of darkness as well.

The candle, as well as the use of vegetableoils, dates back to earliest antiquity, but the use ofcandles only became common among the richestcitizens of Rome. Because it used animal fat, thecandle was apparently a return to an earlier stage,but its hardened tallow actually represented amuch safer, more stable fuel than lamp oil.

INCANDESCENT LIGHT. Lightingtechnology in the period from about 1500 to thelate nineteenth century involved a number ofimprovements, but in one respect, little had pro-gressed since prehistoric times: people were stillburning fuel to provide illumination. This allchanged with the invention of the incandescentbulb, which, though it is credited to Edison, wasthe product of experimentation that took placethroughout the nineteenth century. As early as1802, British scientist Sir Humphry Davy (1778-1829) showed that electricity running throughthin strips of metal could heat them enough tocause them to give off light—that is, electromag-netic radiation.

Edison, in fact, was just one of several inven-tors in the 1870s attempting to develop a practi-cal incandescent lamp. His innovation lay in hisunderstanding of the parameters necessary fordeveloping such a lamp—in particular, decreas-ing the electrical resistance in the lamp filament(the part that is heated) so that less energy wouldbe required to light it. On October 19, 1879,using low-resistance filaments of carbon or plat-inum, combined with a high-resistance carbonfilament in a vacuum-sealed glass container, Edi-son produced the first practical lightbulb.

Much has changed in the design of light-bulbs during the decades following Edison’singenious invention, of course, but his designprovided the foundation. There is just one prob-lem with incandescent light, however—a prob-lem inherent in the definition and derivation ofthe word incandescent, which comes from aLatin root meaning “to become hot.” The effi-ciency of a light is determined by the ratio oflight, or usable energy, to heat—which, except inthe case of a campfire, is typically not a desirableform of energy where lighting is concerned.

Amazingly, only about 10% of the energyoutput from a typical incandescent light bulb isin the form of visible light; the rest comesthrough the infrared region of the spectrum,

producing heat rather than light that people canuse. The visible light tends to be in the red andyellow end of the spectrum—closer to infrared—but a blue-tinted bulb helps to absorb some ofthe red and yellow, providing a color balance.This, however, only further diminishes the totallight output, and, hence, in many applicationstoday, fluorescent light takes the place of incan-descent light.

Lasers

A laser is an extremely focused, extremely nar-row, and extremely powerful beam of light. Actu-ally, the term laser is an acronym, standing forLight Amplification by Simulated Emission ofRadiation. Simulated emission involves bringinga large number of atoms into what is called an“excited state.” Generally, most atoms are in aground state, and are less active in their move-ments, but the energy source that activates a laserbrings about population inversion, a reversal ofthe ratios, such that the majority of atoms with-in the active medium are in an excited ratherthan a ground state. To visualize this, picture apopcorn popper, with the excited atoms beingthe popping kernels, and the ground-state atomsthe ones remaining unpopped. As the atomsbecome excited, and the excited atoms outnum-ber the ground ones, they start to cause a multi-plication of the resident photons. This is simulat-ed emission.

A laser consists of three components: anoptical cavity, an energy source, and an activemedium. To continue the popcorn analogy, the“popper” itself—the chamber which holds thelaser—is the optical cavity, which, in the case of alaser, involves two mirrors facing one another.One of these mirrors fully reflects light, whereasthe other is a partly reflecting mirror. The lightnot reflected by the second mirror escapes as ahighly focused beam. As with the popcorn pop-per, the power source involves electricity, and theactive medium is analogous to the oil in a con-ventional popper.

TYPES OF LASERS. There are fourtypes of lasers: solid-state, semiconductor, gas,and dye. Solid-state lasers are generally very largeand extremely powerful. Having a crystal or glasshousing, they have been implemented in nuclearenergy research, and in various areas of industry.Whereas solid-state lasers can be as long as a cityblock, semiconductor lasers can be smaller than



Light

the head of a pin. Semiconductor lasers (involv-

ing materials such as arsenic that conduct elec-

tricity, but do not do so as efficiently as the met-

als typically used as conductors) are applied for

the intricate work of making compact discs and

computer microchips.

Gas lasers contain carbon dioxide or other

gases, activated by electricity in much the same

way the gas in a neon sign is activated. Among

their applications are eye surgery, printing, and

scanning. Finally, dye lasers, as their name sug-

gests, use different colored dyes. (Laser light

itself, unlike ordinary light, is monochromatic.)

Dye lasers can be used for medical research, or

for fun—as in the case of laser light shows held at

parks in the summertime.

LASER APPLICATIONS. Laser

beams have a number of other useful functions,

for instance, the production of compact discs

(CDs). Lasers etch information onto a surface,

and because of the light beam’s qualities, can

record far more information in much less space


THE BEAM OF A MODE LOCKED, FREQUENCY DOUBLED ND YLF LASER IS REFLECTED OFF MIRRORS AND THROUGH

FILTERS AT COLORADO STATE UNIVERSITY. (Photograph by Chris/RogersBikderberg. The Stock Market. Reproduced by permission.)


Light


APERTURE: An opening.

DIFFRACTION: The bending of waves

around obstacles, or the spreading of waves

by passing them through an aperture.

DIFFUSION: A process by which the

concentration or density of something is

decreased.












gamma rays.


transverse wave with electric and magnetic

fields that emanate from it. The directions

of these fields are perpendicular to one

another, and both are perpendicular to the

line of propagation for the wave itself.






cy, named after nineteenth—century Ger-


(1857-1894).

INCIDENCE: Contact between a ray—

for example, a light ray—and a surface.

Types of incidence include reflection and

refraction.

MEDIUM: A substance through which

light travels, such as air, water, or glass.

Because light moves by radiation, it does

not require a medium, and, in fact, move-

ment through a medium slows the speed of

light somewhat.

OPTICS: An area of physics that studies

the production and propagation of light.

PHOTOELECTRIC EFFECT: The

phenomenon whereby certain metals

acquire an electrical potential when

exposed to light.

PHOTON: A particle of electromagnet-

ic radiation—for example, light—carrying

a specific amount of energy, measured in

electron volts (eV).

PRISM: A three-dimensional glass

shape used for the diffusion of light rays.



RADIATION: The transfer of energy by




the Sun’s energy (including its light), via

the electromagnetic spectrum, by means of

radiation.

RAY: In geometry, a ray is that part of a

straight line that extends in one direction

only. The term “ray” is used to describe the

directed line made by light as it moves

through space.

REFLECTION: A type of incidence

whereby a light ray is returned toward its

source rather than being absorbed at the

interface.

REFRACTION: The bending of a light

ray that occurs when it passes through a

dense medium, such as water or glass.

KEY TERMS


Light


than the old-fashioned ways of producingphonograph records.

Lasers used in the production of CD-ROM(Read-Only Memory) disks are able to condensehuge amounts of information—a set of encyclo-pedias or the New York metropolitan phonebook—onto a disk one can hold in the palm ofone’s hand. Laser etching is also used to createdigital videodiscs (DVDs) and holograms.Another way that lasers affect everyday life is inthe field of fiber optics, which uses pulses of laserlight to send information on glass strands.

Before the advent of fiber-optic communi-cations, telephone calls were relayed on thickbundles of copper wire; with the appearance ofthis new technology, a glass wire no thicker thana human hair now carries thousands of conversa-tions. Lasers are also used in scanners, such as theprice-code checkers at supermarkets and variouskinds of tags that prevent thefts of books fromlibraries or clothing items from stores. In anindustrial setting, heating lasers can drill throughsolid metal, or in an operating room, lasers canremove gallstones or cataracts. Lasers are alsoused for guiding missiles, and to help building

contractors ensure that walls and floors and ceil-ings are in proper alignment.

WHERE TO LEARN MORE

Burton, Jane and Kim Taylor. The Nature and Science ofColors. Milwaukee, WI: Gareth Stevens Publishing,1998.

Glover, David. Color and Light. New York: DorlingKindersley Publishing, 2001.

Kalman, Bobbie and April Fast. Cosmic Light Shows. NewYork: Crabtree Publishing, 1999.

Kurtus, Ron. “Visible Light” (Web site). <http://www.school-for-champions.com/science/light.html> (May 2, 2001).

“Light Waves and Color.” The Physics Classroom (Website). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/lighttoc.html> (May 2, 2001).

Miller-Schroeder, Patricia. The Science and Light of Color.Milwaukee, WI: Gareth Stevens Publishing, 2000.

Nassau, Kurt. Experimenting with Color. New York: F.Watts, 1997.

Riley, Peter D. Light and Color. New York: F. Watts, 1999.

Taylor, Helen Suzanne. A Rainbow Is a Circle: And OtherFacts About Color. Brookfield, CT: Copper BeechBooks, 1999.

“Visible Light Waves” NASA: National Aeronautics andSpace Administration (Web site). <http://imagers.gsfc.nasa.gov/ems/visible.html> (May 2, 2001).





include the colors of visible light, or the

electromagnetic spectrum of which visible

light is a part.




moving.

VACUUM: An area of space devoid of





shorter the wavelength, the higher the fre-

quency.




LUM INESCENCELuminescence

CONCEPTLuminescence is the generation of light withoutheat. There are two principal varieties of lumi-nescence, fluorescence and phosphorescence, dis-tinguished by the delay in reaction to externalelectromagnetic radiation. The ancients observedphosphorescence in the form of a glow emittedby the oceans at night, and confused this phe-nomenon with the burning of the chemicalphosphor, but, in fact, phosphorescence hasnothing at all to do with burning. Likewise, fluo-rescence, as applied today in fluorescent lighting,involves no heat—thus creating a form of light-ing more efficient than that which comes fromincandescent bulbs.

HOW IT WORKS

Radiation

Elsewhere in this volume, the term “radiation”has been used to describe the transfer of energyin the form of heat. In fact, radiation can also bedescribed, in a more general sense, as anythingthat travels in a stream, whether that stream becomposed of subatomic particles or electromag-netic waves.

Many people think of radiation purely interms of the harmful effects produced byradioactive materials—those subject to a form ofdecay brought about by the emission of high-energy particles or radiation, including alphaparticles, beta particles, or gamma rays. Thesehigh-energy forms of radiation are called ioniz-ing radiation, because they are capable of literal-ly ripping through some types of atoms, remov-ing electrons and leaving behind a string of ions.

Ionizing radiation can indeed cause a greatdeal of damage to matter—including the matterin a human body. Even radiation produced byparts of the electromagnetic spectrum possessingfar less energy than gamma rays can be detri-mental, as will be discussed below. In general,however, there is nothing inherently dangerousabout radiation: indeed, without the radiationtransmitted to Earth via the Sun’s electromagnet-ic spectrum, life simply could not exist.


The electromagnetic spectrum is the completerange of electromagnetic waves on a continuousdistribution from those with very low frequen-cies and energy levels, along with corresponding-ly long wavelengths, to those with very high fre-quencies and energy levels, with correspondinglyshort wavelengths.

An electromagnetic wave is transverse,meaning that even as it moves forward, it oscil-lates in a direction perpendicular to the line ofpropagation. An electromagnetic wave can thusbe defined as a transverse wave with mutuallyperpendicular electrical and magnetic fields thatemanate from it. Though their shape is akin tothat of waves on the ocean, electromagneticwaves travel much, much faster than any wavesthat human eyes can see. Their speed of propaga-tion in a vacuum is equal to that of light: 186,000mi (299,339 km) per second.

PARTS OF THE ELECTROMAG-

NETIC SPECTRUM. Included on theelectromagnetic spectrum are radio waves andmicrowaves; infrared, visible, and ultravioletlight; x rays, and gamma rays. Though each occu-


Luminescence trary about the order in which the different typesof electromagnetic waves are listed above: this istheir order in terms of frequency (measured inHertz, or Hz) and energy levels, which are direct-ly related. This ordering also represents thereverse order (that is, from longer to shorter) forwavelength, which is inversely related to fre-quency.

Extremely low-energy, long-wavelengthradio waves have frequencies of around 102 Hz,while the highest-energy, shortest-wavelengthgamma rays can have frequencies of up to 1025

Hz. This means that these gamma rays are oscillating at the rate of 10 trillion trillion timesa second!

The wavelengths of very low-energy, low-frequency radio waves can be extremely long: 108

centimeters, equal to 1 million meters or about621 miles. Precisely because these wavelengthsare so very long, they are hard to apply for anypractical use: ordinary radio waves of the kindused for actual radio broadcasts are closer to 105

cm (about 328 ft).

At the opposite end of the spectrum aregamma rays with wavelengths of less than 10-15

centimeters—in other words, a decimal pointfollowed by 14 zeroes and a 1. There is literallynothing in the observable world that can becompared to this figure, equal to one-trillionth ofa centimeter. Even the angstrom—a unit so smallit is used to measure the diameter of an atom—is 10 million times as large.

Emission and Absorption

The electromagnetic spectrum is not the onlyspectrum: physicists, as well as people who arenot scientifically trained, often speak of the colorspectrum for visible light. The reader is encour-aged to study the essays on both subjects to gaina greater understanding of each. In the presentcontext, however, two other types of spectra (theplural of “spectrum”) are of interest: emissionand absorption spectra.

Emission occurs when internal energy fromone system is transformed into energy that is car-ried away from that system by electromagneticradiation. An emission spectrum for any givensystem shows the range of electromagnetic radi-ation it emits. When an atom has energy trans-ferred to it, either by collisions or as a result ofexposure to radiation, it is said to be experienc-ing excitation, or to be “excited.” Excited atoms


pies a definite place on the spectrum, the divi-sions between them are not firm: as befits thenature of a spectrum, one simply “blurs” intoanother.

Though the Sun sends its energy to Earth inthe form of light and heat from the electromag-netic spectrum, not everything within the spec-trum is either “bright.” The “bright” area of thespectrum—that is, the band of visible light—isincredibly small, equal to about 3.2 parts in 100billion. This is like comparing a distance of 16 ft(4.8 m) to the distance between Earth and theSun: 93 million miles (1.497 • 109 km).

When electromagnetic waves of almost anyfrequency are asborbed in matter, their energycan be converted to heat. Whether or not thishappens depends on the absorption mechanism.However, the realm of “heat” as it is most experi-enced in daily life is much smaller, encompassinginfrared, visible, and ultraviolet light. Below thisfrequency range are various types of radio waves,and above it are ultra high-energy x rays andgamma rays. Some of the heat experienced in anuclear explosion comes from the absorption ofgamma rays emitted in the nuclear reaction.

FREQUENCY AND WAVE-

LENGTH RANGE. There is nothing arbi-

MODERN UNDERSTANDING OF LUMINESCENCE OWES

MUCH TO MARIE CURIE.



will emit light of a given frequency as they relaxback to their normal state. Atoms of neon, forinstance, can be excited in such a way that theyemit light at wavelengths corresponding to thecolor red, a property that finds application inneon signs.

As its name suggests, absorption has a recip-rocal relationship with emission: it is the result ofany process wherein the energy transmitted to asystem via electromagnetic radiation is added tothe internal energy of that system. Each materialhas a unique absorption spectrum, which makesit possible to identify that material using a devicecalled a spectrometer. In the phenomenon ofluminescence, certain materials absorb electro-magnetic radiation and proceed to emit thatradiation in ways that distinguish the materials aseither fluorescent or phosphorescent.


Early Observations of Luminescence

For the most part, prior to the nineteenth centu-ry, scientists had little concept of light without

heat. Even what premodern observers called“phosphorescence” was not phosphorescence asthe term is used in modern science. Instead, theword was used to describe light given off in afiery reaction that occurs when the elementphosphorus is exposed to air.

There are, however, examples of lumines-cence in nature that had been observed fromancient times onward—for instance, the phos-phorescent glow of the ocean, visible at nightunder certain conditions. At one time this, too,was mistakenly associated with phosphorus,which was supposedly burning in the water. Infact, the ocean’s phosphorescence comes neitherfrom phosphorus nor water, but from living crea-tures called dinoflagellates. This is an example ofa phenomenon known as bioluminescence—fireflies are another example—discussed below.

Modern understanding of luminescenceowes much to Polish-French physicist andchemist Marie Curie (1867-1934). Operating infields that had been dominated by men since thebirth of the physical sciences, Curie distinguishedherself with a number of achievements, becom-ing the first scientist in history to receive twoNobel prizes (physics in 1903 and chemistry in1911). While working on her doctoral thesis,

COMPARED TO STANDARD INCANDESCENT LIGHT BULBS (SHOWN ON THE LEFT), NEWER FLUORESCENT BULBS (SHOWN

ON THE RIGHT) USE FAR LESS ELECTRICITY AND LAST MUCH LONGER. (Photograph by Roger Ressmeyer/Corbis. Reproduced by per-

mission.)

Luminescence


Luminescence


Curie noted that calcium fluoride glows whenexposed to a radioactive material known as radium.

Curie—who also coined the term “radioac-tivity”—helped spark a revolution in science andtechnology. As a result of her work and the dis-coveries of others who followed, interest in lumi-nescence and luminescent devices grew. Today,luminescence is applied in a number of devicesaround the household, most notably in televisionscreens and fluorescent lights.

Fluorescence

As indicated in the introduction to this essay, thedifference between the two principal types ofluminescence relates to the timing of their reac-tions to electromagnetic radiation. Fluorescenceis a type of luminescence whereby a substanceabsorbs radiation and almost instantly begins tore-emit the radiation. (Actually, the delay is 10-6

seconds, or a millionth of a second.) Fluorescentluminescence stops within 10-5 seconds after theenergy source is removed; thus, it comes to anend almost as quickly as it begins.

Usually, the wavelength of the re-emittedradiation is longer than the wavelength of theradiation the substance absorbed. British mathe-

matician and physicist George Gabriel Stokes(1819-1903), who coined the term “fluores-cence,” first discovered this difference in wave-length. However, in a special type of fluorescenceknown as resonance fluorescence, the wave-lengths are the same. Applications of resonanceinclude its use in analyzing the flow of gases in awind tunnel.

BLACK LIGHTS AND FLUO-

RESCENCE. A “black light,” so calledbecause it emits an eerie bluish-purple glow, isactually an ultraviolet lamp, and it brings outvibrant colors in fluorescent materials. For thisreason, it is useful in detecting art forgeries:newer paint tends to fluoresce when exposed toultraviolet light, whereas older paint does not.Thus, if a forger is trying to pass off a painting asthe work of an Old Master, the ultraviolet lampwill prove whether the artwork is genuine or not.

Another example of ultraviolet light and flu-orescent materials is the “black-light” poster,commonly associated with the psychedelic rockmusic of the late 1960s and early 1970s. Underordinary visible light, a black-light poster doesnot look particularly remarkable, but whenexposed to ultraviolet light in an environment inwhich visible light rays are not propagated (thatis, a darkened room), it presents a dazzling array

LIKE MANY MARINE CREATURES, JELLYFISH PRODUCE THEIR OWN LIGHT THROUGH PHOSPHORESCENCE. (Photograph by

Mark A. Johnson. The Stock Market. Reproduced by permission.)


Luminescenceof colors. Yet, because they are fluorescent, themoment the black light is turned off, the colorsof the poster cease to glow. Thus, the poster, likethe light itself, can be turned “on” and “off,” sim-ply by activating or deactivating the ultravioletlamp.

RUBIES AND LASERS. Fluores-cence has applications far beyond catching artforgers or enhancing the experience of hearing aJimi Hendrix album. In 1960, American physicistTheodore Harold Maiman developed the firstlaser using a ruby, a gem that exhibits fluorescentcharacteristics. A laser is a very narrow, highlyfocused, and extremely powerful beam of lightused for everything from etching data on a sur-face to performing eye surgery.

Crystalline in structure, a ruby is a solid thatincludes the element chromium, which gives thegem its characteristic reddish color. A rubyexposed to blue light will absorb the radiationand go into an excited state. After losing some ofthe absorbed energy to internal vibrations, theruby passes through a state known as metastablebefore dropping to what is known as the groundstate, the lowest energy level for an atom or mol-ecule. At that point, it begins emitting radiationon the red end of the spectrum.

The ratio between the intensity of a ruby’semitted fluorescence and that of its absorbedradiation is very high, and, thus, a ruby isdescribed as having a high level of fluorescentefficiency. This made it an ideal material forMaiman’s purposes. In building his laser, he useda ruby cylinder which emitted radiation that wasboth coherent, or all in a single direction, andmonochromatic, or all of a single wavelength.The laser beam, as Maiman discovered, couldtravel for thousands of miles with very little dis-persion—and its intensity could be concentratedon a small, highly energized pinpoint of space.

FLUORESCENT LIGHTS. By farthe most common application of fluorescence indaily life is in the fluorescent light bulb, of whichthere are more than 1.5 billion operating in theUnited States. Fluorescent light stands in contrastto incandescent, or heat-producing, electricallight. First developed successfully by ThomasEdison (1847-1931) in 1879, the incandescentlamp quite literally transformed human life,making possible a degree of activity after darkthat would have been impractical in the age ofgas lamps. Yet, incandescent lighting is highly

inefficient compared to fluorescent light: in anincandescent bulb, fully 90% of the energy out-put is wasted on heat, which comes through theinfrared region.

A fluorescent bulb consuming the sameamount of power as an incandescent bulb willproduce three to five times more light, and itdoes this by using a phosphor, a chemical thatglows when exposed to electromagnetic energy.(The term “phosphor” should not be confusedwith phosphorescence: phosphors are used inboth fluorescent and phosphorescent applica-tions.) The phosphor, which coats the inside sur-face of a fluorescent lamp, absorbs ultravioletlight emitted by excited mercury atoms. It thenre-emits the ultraviolet light, but at longer wave-lengths—as visible light. Thanks to the phos-phor, a fluorescent lamp gives off much morelight than an incandescent one, and does so with-out producing heat.

PHOSPHORESCENCE. In contrastto the nearly instantaneous “on-off” of fluores-cence, phosphorescence involves a delayed emis-sion of radiation following absorption. The delaymay take as much as several minutes, but phos-phorescence continues to appear after the energysource has been removed. The hands and num-bers of a watch that glows in the dark, as well asany number of other items, are coated with phos-phorescent materials.

Television tubes also use phosphorescence.The tube itself is coated with phosphor, and anarrow beam of electrons causes excitation in asmall portion of the phosphor. The phosphorthen emits red, green, or blue light—the primarycolors of light—and continues to do so even afterthe electron beam has moved on to anotherregion of phosphor on the tube. As it scans acrossthe tube, the electron beam is turned rapidly onand off, creating an image made up of thousandsof glowing, colored dots.

PHOSPHORESCENCE IN SEA

CREATURES. As noted above, one of thefirst examples of luminescence ever observed wasthe phosphorescent effect sometimes visible onthe surface of the ocean at night—an effect thatscientists now know is caused by materials in thebodies of organisms known as dinoflagellates.Inside the body of a dinoflagellate are the sub-stances luciferase and luciferin, which chemicallyreact with oxygen in the air above the water toproduce light with minimal heat levels. Though



Luminescence


dinoflagellates are microscopic creatures, in largenumbers they produce a visible glow.

Nor are dinoflagellates the only biolumines-cent organisms in the ocean. Jellyfish, as well asvarious species of worms, shrimp, and squid, allproduce their own light through phosphores-cence. This is particularly useful for creatures liv-ing in what is known as the mesopelagic zone, arange of depth from about 650 to 3,000 ft (200-1,000 m) below the ocean surface, where littlelight can penetrate.

One interesting bioluminescent sea creatureis the cypridina. Resembling a clam, the cypridi-na mixes its luciferin and luciferase with seawater to create a bright bluish glow. When dried

to a powder, a dead cypridina can continue to

produce light, if mixed with water. Japanese sol-

diers in World War II used the powder of cyprid-

ina to illuminate maps at night, providing them-

selves with sufficient reading light without

exposing themselves to enemy fire.

Processes that Create Luminescence

The phenomenon of bioluminescence actually

goes beyond the frontiers of physics, into chem-

istry and biology. In fact, it is a subset of chemi-

luminescence, or luminescence produced by

chemical reactions. Chemiluminescence is, in

ABSORPTION: The result of any

process wherein the energy transmitted to

a system via electromagnetic radiation is

added to the internal energy of that system.

Each material has a unique absorption

spectrum, which makes it possible to iden-

tify that material using a device called a

spectrometer. (Compare absorption to

emission.)












gamma rays.


transverse wave with electric and magnetic

fields that emanate from it. These waves are

propagated by means of radiation.

EMISSION: The result of a process that

occurs when internal energy from one sys-

tem is transformed into energy that is car-

ried away from it by electromagnetic radi-

ation. An emission spectrum for any given

system shows the range of electromagnetic

radiation it emits. (Compare emission to

absorption.)

EXCITATION: The transfer of energy to

an atom, either by collisions or due to

radiation.

FLUORESCENCE: A type of lumines-

cence whereby a substance absorbs radia-

tion and begins to re-emit the radiation

10-6 seconds after absorption. Usually the

wavelength of emission is longer than the

wavelength of the radiation the substance

absorbed. Fluorescent luminescence stops

within 10-5 seconds after the energy source

is removed.





KEY TERMS


Luminescence


turn, one of several processes that can create

luminescence.

Many of the types of luminescence discussed

above are described under the heading of elec-

troluminescence, or luminescence involving elec-

tromagnetic energy. Another process is tribolu-

minescence, in which friction creates light.

Though this type of friction can produce a fire, it

is not to be confused with the heat-causing fric-

tion that occurs when flint and steel are struck

together.

Yet another physical process used to create

luminescence is sonoluminescence, in which

light is produced from the energy transmitted by

sound waves. Sonoluminescence is one of the

fields at the cutting edge in physics today, andresearch in this area reveals that extremely highlevels of energy may be produced in small areasfor very short periods of time.

WHERE TO LEARN MORE

Birch, Beverley. Marie Curie: Pioneer in the Study ofRadiation. Milwaukee, WI: Gareth Stevens Children’sBooks, 1990.

Evans, Neville. The Science of a Light Bulb. Austin, TX:Raintree Steck-Vaughn Publishers, 2000.

“Luminescence.” Slider.com (Web site). <http://www.slid-er.com/enc/32000/luminescence.html> (May 5,2001).

“Luminescence.” Xrefer (Web site).<http://www.xrefer.com/entry/642646> (May 5,2001).


cy, named after ninetenth-century German

physicist Heinrich Rudolf Hertz (1857-

1894).

LUMINESCENCE: The generation of

light without heat. There are two principal

varieties of luminescence, fluorescence and

phosphorescence.

PHOSPHORESCENCE: A type of

luminescence involving a delayed emission

of radiation following absorption. The

delay may take as much as several minutes,

but phosphorescence continues to appear

after the energy source has been removed.


travelling from one place to another.

RADIATION: In a general sense, radia-

tion can refer to anything that travels in a

stream, whether that stream be composed

of subatomic particles or electromagnetic

waves.

RADIOACTIVE: A term describing

materials which are subject to a form of

decay brought about by the emission of

high-energy particles or radiation, includ-

ing alpha particles, beta particles, or

gamma rays.





include the colors of visible light, the elec-

tromagnetic spectrum of which visible

light is a part, as well as emission and

absorption spectra.




moving.

VACUUM: An area of space devoid of





shorter the wavelength, the higher the fre-

quency.



Luminescence Macaulay, David. The New Way Things Work. Boston:

Houghton Mifflin, 1998.

Pettigrew, Mark. Radiation. New York: Gloucester Press,

1986.

Simon, Hilda. Living Lanterns: Luminescence in Animals.

Illustrated by the author. New York: Viking Press,

1971.

Skurzynski, Gloria. Waves: The Electromagnetic Universe.Washington, D.C.: National Geographic Society,1996.


“UV-Vis Luminescence Spectroscopy” (Web site).<http://www.shu.ac.uk/virtual_campus/courses/241/lumin1.html> (May 5, 2001).



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EVERYDAY SCIENCE THINGS - Higher Intellect · SCIENCE EVERYDAY THINGS OF volume 2: REAL-LIFE PHYSICS A SCHLAGER INFORMATION GROUP BOOK edited by NEIL SCHLAGER written by JUDSON KNIGHT