Physics for Scientists and EngineersIntroduction and Chapter 1 Physics and Measurements

PhysicsFundamental ScienceConcerned with the fundamental principles of the UniverseFoundation of other physical sciencesHas simplicity of fundamental conceptsIntroduction

Physics, cont.Divided into six major areas:Classical MechanicsRelativityThermodynamicsElectromagnetismOpticsQuantum Mechanics

Introduction

Classical PhysicsMechanics and electromagnetism are basic to all other branches of classical and modern physics.Classical physicsDeveloped before 1900First part of text deals with Classical MechanicsAlso called Newtonian Mechanics or MechanicsModern physicsFrom about 1900 to the present

Introduction

Objectives of PhysicsTo find the limited number of fundamental laws that govern natural phenomenaTo use these laws to develop theories that can predict the results of future experimentsExpress the laws in the language of mathematicsMathematics provides the bridge between theory and experiment.Introduction

Theory and ExperimentsShould complement each otherWhen a discrepancy occurs, theory may be modified or new theories formulated.A theory may apply to limited conditions.Example: Newtonian Mechanics is confined to objects traveling slowly with respect to the speed of light.Try to develop a more general theoryIntroduction

Classical Physics OverviewClassical physics includes principles in many branches developed before 1900.MechanicsMajor developments by Newton, and continuing through the 18th centuryThermodynamics, optics and electromagnetismDeveloped in the latter part of the 19th centuryApparatus for controlled experiments became availableIntroduction

Modern PhysicsBegan near the end of the 19th centuryPhenomena that could not be explained by classical physicsIncludes theories of relativity and quantum mechanicsIntroduction

Special RelativityCorrectly describes motion of objects moving near the speed of lightModifies the traditional concepts of space, time, and energyShows the speed of light is the upper limit for the speed of an objectShows mass and energy are relatedIntroduction

Quantum MechanicsFormulated to describe physical phenomena at the atomic levelLed to the development of many practical devicesIntroduction

MeasurementsUsed to describe natural phenomenaEach measurement is associated with a physical quantityNeed defined standardsCharacteristics of standards for measurementsReadily accessible Possess some property that can be measured reliablyMust yield the same results when used by anyone anywhereCannot change with timeSection 1.1

Standards of Fundamental QuantitiesStandardized systemsAgreed upon by some authority, usually a governmental bodySI Systme InternationalAgreed to in 1960 by an international committeeMain system used in this textSection 1.1

Fundamental Quantities and Their UnitsSection 1.1

QuantitySI UnitLengthmeterMasskilogramTimesecondTemperatureKelvinElectric CurrentAmpereLuminous IntensityCandelaAmount of Substancemole

Quantities Used in MechanicsIn mechanics, three fundamental quantities are used:LengthMassTimeAll other quantities in mechanics can be expressed in terms of the three fundamental quantities.Section 1.1

LengthLength is the distance between two points in space.UnitsSI meter, mDefined in terms of a meter the distance traveled by light in a vacuum during a given timeSee Table 1.1 for some examples of lengths.

Section 1.1

MassUnitsSI kilogram, kgDefined in terms of a kilogram, based on a specific cylinder kept at the International Bureau of StandardsSee Table 1.2 for masses of various objects.Section 1.1

Standard KilogramSection 1.1

TimeUnitsseconds, sDefined in terms of the oscillation of radiation from a cesium atomSee Table 1.3 for some approximate time intervals.Section 1.1

Reasonableness of ResultsWhen solving a problem, you need to check your answer to see if it seems reasonable.Reviewing the tables of approximate values for length, mass, and time will help you test for reasonableness.Section 1.1

Number NotationWhen writing out numbers with many digits, spacing in groups of three will be used.No commasStandard international notationExamples:25 100 5.123 456 789 12

Section 1.1

US Customary SystemStill used in the US, but text will use SI

Section 1.1

QuantityUnitLengthfootMassslugTimesecond

PrefixesPrefixes correspond to powers of 10.Each prefix has a specific name.Each prefix has a specific abbreviation.The prefixes can be used with any basic units.They are multipliers of the basic unit.Examples:1 mm = 10-3 m1 mg = 10-3 g

Section 1.1

Prefixes, cont.Section 1.1

Fundamental and Derived UnitsDerived quantities can be expressed as a mathematical combination of fundamental quantities.Examples:AreaA product of two lengthsSpeedA ratio of a length to a time intervalDensityA ratio of mass to volumeSection 1.1

Model BuildingA model is a system of physical components.Useful when you cannot interact directly with the phenomenonIdentifies the physical componentsMakes predictions about the behavior of the systemThe predictions will be based on interactions among the components and/orBased on the interactions between the components and the environmentSection 1.2

Models of MatterSome Greeks thought matter is made of atoms.No additional structureJJ Thomson (1897) found electrons and showed atoms had structure.Rutherford (1911) determined a central nucleus surrounded by electrons.Section 1.2

Models of Matter, cont.Nucleus has structure, containing protons and neutronsNumber of protons gives atomic numberNumber of protons and neutrons gives mass numberProtons and neutrons are made up of quarks.Section 1.2

Models of Matter, finalQuarksSix varietiesUp, down, strange, charmed, bottom, topFractional electric charges+ of a protonUp, charmed, top of a protonDown, strange, bottomSection 1.2

Modeling TechniqueAn important problem-solving technique is to build a model for a problem.Identify a system of physical components for the problemMake predictions of the behavior of the system based on the interactions among the components and/or the components and the environment

Section 1.2

Basic Quantities and Their DimensionDimension has a specific meaning it denotes the physical nature of a quantity.Dimensions are often denoted with square brackets.Length [L]Mass [M]Time [T]Section 1.3

Dimensions and UnitsEach dimension can have many actual units.Table 1.5 for the dimensions and units of some derived quantities

Section 1.3

Dimensional AnalysisTechnique to check the correctness of an equation or to assist in deriving an equationDimensions (length, mass, time, combinations) can be treated as algebraic quantities. Add, subtract, multiply, divideBoth sides of equation must have the same dimensions.Any relationship can be correct only if the dimensions on both sides of the equation are the same.Cannot give numerical factors: this is its limitationSection 1.3

Dimensional Analysis, exampleGiven the equation: x = at 2Check dimensions on each side:

The T2s cancel, leaving L for the dimensions of each side.The equation is dimensionally correct.There are no dimensions for the constant.Section 1.3

Dimensional Analysis to Determine a Power LawDetermine powers in a proportionalityExample: find the exponents in the expression

You must have lengths on both sides.Acceleration has dimensions of L/T2Time has dimensions of T.Analysis gives

Section 1.3

SymbolsThe symbol used in an equation is not necessarily the symbol used for its dimension.Some quantities have one symbol used consistently.For example, time is t virtually all the time.Some quantities have many symbols used, depending upon the specific situation.For example, lengths may be x, y, z, r, d, h, etc.The dimensions will be given with a capitalized, non-italic letter.The algebraic symbol will be italicized.Section 1.3

Conversion of UnitsWhen units are not consistent, you may need to convert to appropriate ones.See Appendix A for an extensive list of conversion factors.Units can be treated like algebraic quantities that can cancel each other out.

Section 1.4

ConversionAlways include units for every quantity, you can carry the units through the entire calculation.Will help detect possible errorsMultiply original value by a ratio equal to one.Example:

Note the value inside the parentheses is equal to 1, since 1 inch is defined as 2.54 cm.Section 1.4

Order of MagnitudeApproximation based on a number of assumptionsMay need to modify assumptions if more precise results are neededThe order of magnitude is the power of 10 that applies.Section 1.5

Order of Magnitude ProcessEstimate a number and express it in scientific notation.The multiplier of the power of 10 needs to be between 1 and 10.Compare the multiplier to 3.162 ( )If the remainder is less than 3.162, the order of magnitude is the power of 10 in the scientific notation.If the remainder is greater than 3.162, the order of magnitude is one more than the power of 10 in the scientific notation.Section 1.5

Using Order of MagnitudeEstimating too high for one number is often canceled by estimating too low for another number.The resulting order of magnitude is generally reliable within about a factor of 10.Working the problem allows you to drop digits, make reasonable approximations and simplify approximations.With practice, your results will become better and better.Section 1.5

Uncertainty in MeasurementsThere is uncertainty in every measurement this uncertainty carries over through the calculations.May be due to the apparatus, the experimenter, and/or the number of measurements madeNeed a technique to account for this uncertaintyWe will use rules for significant figures to approximate the uncertainty in results of calculations.Section 1.6

Significant FiguresA significant figure is one that is reliably known.Zeros may or may not be significant.Those used to position the decimal point are not significant.To remove ambiguity, use scientific notation.In a measurement, the significant figures include the first estimated digit.

Section 1.6

Significant Figures, examples0.0075 m has 2 significant figuresThe leading zeros are placeholders only.Write the value in scientific notation to show more clearly: 7.5 x 10-3 m for 2 significant figures10.0 m has 3 significant figuresThe decimal point gives information about the reliability of the measurement.1500 m is ambiguousUse 1.5 x 103 m for 2 significant figuresUse 1.50 x 103 m for 3 significant figuresUse 1.500 x 103 m for 4 significant figuresSection 1.6

Operations with Significant Figures Multiplying or DividingWhen multiplying or dividing several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the smallest number of significant figures.Example: 25.57 m x 2.45 m = 62.6 m2The 2.45 m limits your result to 3 significant figures.Section 1.6

Operations with Significant Figures Adding or SubtractingWhen adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum or difference.Example: 135 cm + 3.25 cm = 138 cmThe 135 cm limits your answer to the units decimal value.

Section 1.6

Operations With Significant Figures Summary The rule for addition and subtraction are different than the rule for multiplication and division.For adding and subtracting, the number of decimal places is the important consideration.For multiplying and dividing, the number of significant figures is the important consideration.Section 1.6

Significant Figures in the TextMost of the numerical examples and end-of-chapter problems will yield answers having three significant figures.When estimating a calculation, typically work with one significant figure.Section 1.6

RoundingLast retained digit is increased by 1 if the last digit dropped is greater than 5.Last retained digit remains as it is if the last digit dropped is less than 5. If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number.Saving rounding until the final result will help eliminate accumulation of errors.It is useful to perform the solution in algebraic form and wait until the end to enter numerical values.This saves keystrokes as well as minimizes rounding.Section 1.6