physicsassets.pearsonschool.com/asset_mgr/current/201623/A01...physics for scientists and engineers a strategic approach 4/e randall d.knight California Polytechnic State University

physicsfor scientists and engineers a strategic approach 4/e

randall d. knightCalifornia Polytechnic State University San Luis Obispo

with modern physics

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About the Author

Randy Knight taught introductory physics for 32 years at Ohio State University and California Polytechnic State University, where he is Professor Emeritus of Physics. Professor Knight received a Ph.D. in physics from the University of California, Berkeley and was a post-doctoral fellow at the Harvard-Smithsonian Center for Astrophysics before joining the faculty at Ohio State University. It was at Ohio State that he began to learn about the research in physics education that, many years later, led to Five Easy Lessons: Strategies for Successful Physics Teaching and this book, as well as College Physics: A Strategic Approach, co-authored with Brian Jones and Stuart Field. Professor Knight’s research interests are in the fields of laser spectroscopy and environmental science. When he’s not in front of a computer, you can find Randy hiking, sea kayaking, playing the piano, or spending time with his wife Sally and their five cats.


Built from the ground up on physics education research and crafted using key ideas from learning theory, Knight has set the standard for eff ective and accessible pedagogical materials in physics. In this fourth edition, Knight continues to refi ne and expand the instructional techniques to take students further.

NEW AND UPDATED LEARNING TOOLS PROMOTE DEEPER AND BETTER-CONNECTED UNDERSTANDING

NEW! MODEL BOXES enhance the text’s emphasis on modeling—analyzing a complex, real-world situation in terms of simple but reasonable idealizations that can be applied over and over in solving problems. These fun-damental simplifications are developed in the text and then deployed more explicitly in the worked examples, helping students to recog-nize when and how to use recurring models, a key critical-thinking skill.

REVISED! ENHANCED CHAPTER PREVIEWS, based on the educational psychology concept of an “advance organizer,” have been reconceived to address the questions students are most likely to ask themselves while studying the material for the first time. Questions cover the important ideas, and provide a big-picture overview of the chapter’s key principles. Each chapter con-cludes with the visual Chapter Summary, consolidating and structuring understanding.

46 CHAPTER 2 Kinematics in One Dimension

au

Mathematically:

Limitations: Model fails if the particle’sacceleration changes.

Model the object as a particle movingin a straight line with constant acceleration.

For motion with constant acceleration.

vu

Parabola

s

si t

The slope is vs.

Horizontal lineas

0 t

The acceleration is constant.

Straight linevs

vis t

The slope is as.vfs = vis + as∆t

vfs2 = vis

2 + 2as∆s

sf = si + vis∆t + as1∆t2212

Constant acceleration

MODEL 2.2

Exercise 16

M03_KNIG2651_04_SE_C02.indd 46 9/13/15 8:41 PM

142 CHAPTER 6 Dynamics I: Motion Along a Line

MODEL 6.3

FrictionThe friction force is parallel to the surface.

■ Static friction: Acts as needed to prevent motion. Can have any magnitude up to fs max = ms n.

■ Kinetic friction: Opposes motion with fk = mk n.

■ Rolling friction: Opposes motion with fr = mr n.

■ Graphically:

Push orpull

Friction

Motion is relativeto the surface.

f

Push or pull force

Static frictionincreases to matchthe push or pull.

Kinetic friction is constantas the object moves.

KineticStatic

The object slips when staticfriction reaches fs max.

Rest Moving

fs max = msn

mkn

0

M07_KNIG2651_04_SE_C06.indd 142 9/13/15 8:39 PM


SUMMARY

The goal of Chapter 6 has been to learn to solve linear force-and-motion problems.

GENERAL PRINCIPLES

Two Explanatory ModelsAn object on which there is no net force is in mechanical equilibrium.• Objects at rest.• Objects moving with constant

velocity.• Newton’s second law applies

with au = 0u.

An object on which the net force is constant undergoes dynamics with constant force.• The object accelerates.• The kinematic model is that of

constant acceleration.• Newton’s second law applies.

A Problem-Solving StrategyA four-part strategy applies to both equilibrium and dynamics problems.

MODEL Make simplifying assumptions.

VISUALIZE

• Translate words into symbols.• Draw a sketch to define the situation.• Draw a motion diagram.• Identify forces.• Draw a free-body diagram.

SOLVE Use Newton’s second law:

Fu

net = ai

Fu

i = mau

“Read” the vectors from the free-body diagram. Use kinematics to find velocities and positions.

ASSESS Is the result reasonable? Does it have correct units and significant figures?

equilibrium modelconstant-force modelflat-earth approximation

weightcoefficient of static friction, ms

coefficient of kinetic friction, mk

rolling frictioncoefficient of rolling friction, mr

drag coefficient, Cterminal speed, vterm

TERMS AND NOTATION

A falling object reaches terminal speed

vterm = B2mg

CrA

APPLICATIONS

Mass is an intrinsic property of an object that describes the object’s inertia and, loosely speaking, its quantity of matter.

The weight of an object is the reading of a spring scale when the object is at rest relative to the scale. Weight is the result of weigh-ing. An object’s weight depends on its mass, its acceleration, and the strength of gravity. An object in free fall is weightless.

IMPORTANT CONCEPTS

Specific information about three important descriptive models:

Gravity Fu

G = 1mg, downward2Friction f

u

s = 10 to ms n, direction as necessary to prevent motion2 f

u

k = 1mk n, direction opposite the motion2 f

u

r = 1mr n, direction opposite the motion2Drag F

u

drag = 112 CrAv2, direction opposite the motion2

Newton’s laws are vector expressions. You must write them out by components:

1Fnet2x = aFx = max

1Fnet2y = aFy = may

The acceleration is zero in equi-librium and also along an axis perpendicular to the motion.

Fnet = 0u u

au

Go back and forthbetween thesesteps as needed.

d

y

x

Fnet

u

F1

u

F3

u

F2

u

FG

Terminal speed is reached when the drag force exactly balances the gravitational force: a = 0.

u

u

u

Fdrag

u

M07_KNIG2651_04_SE_C06.indd 152 9/13/15 8:12 PM

6 The powerful thrust of the jet engines accelerates this enormous plane to a speed of over 150 mph in less than a mile.

Dynamics I: Motion Along a Line

IN THIS CHAPTER, you will learn to solve linear force-and-motion problems.

How are Newton’s laws used to solve problems?Newton’s first and second laws are vector equations. To use them,

■ Draw a free-body diagram.■ Read the x- and y-components of the

forces directly off the free-body diagram.■ Use aFx = max and aFy = may.

How are dynamics problems solved?A net force on an object causes the object to accelerate.

■ Identify the forces and draw a free-body diagram.

■ Use Newton’s second law to find the object’s acceleration.

■ Use kinematics for velocity and position.

❮❮ LOOKING BACK Sections 2.4–2.6 Kinematics

How are equilibrium problems solved?An object at rest or moving with constant velocity is in equilibrium with no net force.


■ Use Newton’s second law with a = 0 to solve for unknown forces.

❮❮ LOOKING BACK Sections 5.1–5.2 Forces

What are mass and weight?Mass and weight are not the same.

■ Mass describes an object’s inertia. Loosely speaking, it is the amount of matter in an object. It is the same everywhere.

■ Gravity is a force.■ Weight is the result of weighing an object

on a scale. It depends on mass, gravity, and acceleration.

How do we model friction and drag?Friction and drag are complex forces, but we will develop simple models of each.

■ Static, kinetic, and rolling friction depend on the coefficients of friction but not on the object’s speed.

■ Drag depends on the square of an object’s speed and on its cross-section area.

■ Falling objects reach terminal speed when drag and gravity are balanced.

How do we solve problems?We will develop and use a four-part problem-solving strategy:

■ Model the problem, using information about objects and forces.■ Visualize the situation with a pictorial representation.■ Set up and solve the problem with Newton’s laws.■ Assess the result to see if it is reasonable.

Fnet

u

y

x

au

Friction fs

uNormal n

u

Gravity FG

u

FG

u

Fsp

u

vu

Kinetic friction

M07_KNIG2651_04_SE_C06.indd 131 9/13/15 8:09 PM

A research-driven approach, fine-tuned for even greater ease-of-use and student success

REVISED COVERAGE AND ORGANIZATION GIVE INSTRUCTORS GREATER CHOICE AND FLEXIBILITY

NEW! CHAPTER ORGANIZATION allows instructors to more easily present material as needed to complement labs, course schedules, and different teaching styles. Work and energy are now covered before momentum, oscillations are grouped with mechan-ical waves, and optics appears after electricity and magnetism. Unchanged is Knight’s unique approach of working from concrete to abstract, using multiple representations, balancing qualitative with quantitative, and addressing misconceptions.

NEW! MORE CALCULUS-BASED PROBLEMS have been added, along with an icon to make these easy to identify. The sig-nificantly revised end-of-chapter problem sets, extensively class-tested and both calibrated and improved using MasteringPhysics® data, expand the range of physics and math skills students will use to solve problems.

Exercises and Problems 259

55. ||| Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons—hence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is

U = U031 - e-x/x04where x is the distance between the centers of the two nucle-ons, x0 is a constant having the value x0 = 2.0 * 10-15 m, and U0 = 6.0 * 10-11 J.

Quantum effects are essential for a proper understand-ing of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass 1.67 * 10-27 kg and diameter 1.0 * 10-15 m. Suppose you hold two neutrons 5.0 * 10-15 m apart, measured between their centers, then release them. What is the speed of each neutron as they crash together? Keep in mind that both neutrons are moving.

56. || A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx = 120 - 5x2 N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially the block is at rest at x = 0 m. What is the block’s speed when it has been pulled to x = 4.0 m?

57. || A system has potential energy

U1x2 = x + sin112 rad/m2x2as a particle moves over the range 0 m … x … p m.a. Where are the equilibrium positions in this range?b. For each, is it a point of stable or unstable equilibrium?

58. || A particle that can move along the x-axis is part of a system with potential energy

U1x2 = A

x2 -Bx

where A and B are positive constants.a. Where are the particle’s equilibrium positions?b. For each, is it a point of stable or unstable equilibrium?

59. Suppose the particle is shot to the right from x = 1.0 m with a speed of 25 m/s. Where is its turning point?FIGURE P10.59

60. || A clever engineer designs a “sprong” that obeys the force law Fx = -q1x - xeq23, where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we’ll let xeq = 0 m. Then Fx = -qx3.a. What are the units of q?b. Find an expression for the potential energy of a stretched or

compressed sprong.c. A sprong-loaded toy gun shoots a 20 g plastic ball. What

is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.

61. || The potential energy for a particle that can move along the x-axis is U = Ax2 + B sin1px/L2, where A, B, and L are constants. What is the force on the particle at (a) x = 0, (b) x = L/2, and (c) x = L?

62. || A particle that can move along the x-axis experiences an interaction force Fx = 13x2 - 5x2 N, where x is in m. Find an expression for the system’s potential energy.

63. || An object moving in the xy-plane is subjected to the force Fu= 12xy in + x2 jn2 N, where x and y are in m.

a. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the x-axis to 1a, 02, then parallel to the y-axis. How much work does the force do?

b. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the y-axis to 10, b2, then parallel to the x-axis. How much work does the force do?

c. Is this a conservative force?64. || An object moving in the xy-plane is subjected to the force

Fu= 12xy in + 3y jn2 N, where x and y are in m.



c. Is this a conservative force?65. Write a realistic problem for which the energy bar chart shown in

FIGURE P10.65 correctly shows the energy at the beginning and end of the problem.

In Problems 66 through 68 you are given the equation used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial representation.c. Finish the solution of the problem.

=

=

40

20

0

-20Ki UGi USp i UGf

+ + + +

+ + + +USp fKf

E (J)

FIGURE P10.65

66. 1211500 kg215.0 m/s22 + 11500 kg219.80 m/s22110 m2 = 12 11500 kg2vi

2 + 11500 kg219.80 m/s2210 m267. 1

210.20 kg212.0 m/s22 + 12 k10 m22

= 12 10.20 kg210 m/s22 + 12 k1-0.15 m22

68. 1210.50 kg2vf

2 + 10.50 kg219.80 m/s2210 m2 + 12 1400 N/m210 m22 = 1

2 10.50 kg210 m/s22 + 10.50 kg219.80 m/s2211-0.10 m2 sin 30°2 + 12 1400 N/m21-0.10 m22

Challenge Problems

69. ||| A pendulum is formed from a small ball of mass m on a string of length L. As FIGURE CP10.69 shows, a peg is height h = L /3

M12_KNIG2651_04_SE_C10.indd 259 9/28/15 5:29 PM

NEW! ADVANCED TOPICS as optional sections add even more flexibility for instructors’ individual courses. Topics include rocket propulsion, gyroscopes and precession, the wave equation (including for electromagnetic waves), the speed of sound in gases, and more details on the interference of light.

STOP TO THINK 11.6 An object trav-eling to the right with pu = 2 in kg m/s suddenly explodes into two pieces. Piece 1 has the momentum pu1 shown in the figure. What is the momentum pu2 of the second piece?

11.6 advanced topic Rocket Propulsion Newton’s second law F

u= mau applies to objects whose mass does not change. That’s

an excellent assumption for balls and bicycles, but what about something like a rocket that loses a significant amount of mass as its fuel is burned? Problems of varying mass are solved with momentum rather than acceleration. We’ll look at one important example.

FIGURE 11.29 shows a rocket being propelled by the thrust of burning fuel but not influenced by gravity or drag. Perhaps it is a rocket in deep space where gravity is very weak in comparison to the rocket’s thrust. This may not be highly realistic, but ignoring gravity allows us to understand the essentials of rocket propulsion without making the mathematics too complicated. Rocket propulsion with gravity is a Challenge Problem in the end-of-chapter problems.

The system rocket + exhaust gases is an isolated system, so its total momentum is conserved. The basic idea is simple: As exhaust gases are shot out the back, the rocket “recoils” in the opposite direction. Putting this idea on a mathematical footing is fairly straightforward—it’s basically the same as analyzing an explosion—but we have to be extremely careful with signs.

We’ll use a before-and-after approach, as we do with all momentum problems. The Before state is a rocket of mass m (including all onboard fuel) moving with velocity vx and having initial momentum Pix = mvx. During a small interval of time dt, the rocket burns a small mass of fuel mfuel and expels the resulting gases from the back of the rocket at an exhaust speed vex relative to the rocket. That is, a space cadet on the rocket sees the gases leaving the rocket at speed vex regardless of how fast the rocket is traveling through space.

After this little packet of burned fuel has been ejected, the rocket has new velocity vx + dvx and new mass m + dm. Now you’re probably thinking that this can’t be right; the rocket loses mass rather than gaining mass. But that’s our understanding of the physical situation. The mathematical analysis knows only that the mass changes, not whether it increases or decreases. Saying that the mass is m + dm at time t + dt is a formal statement that the mass has changed, and that’s how analysis of change is done in calculus. The fact that the rocket’s mass is decreasing means that dm has a negative value. That is, the minus goes with the value of dm, not with the statement that the mass has changed.

After the gas has been ejected, both the rocket and the gas have momentum. Conservation of momentum tells us that

Pfx = mrocket1vx2rocket + mfuel1vx2fuel = Pix = mvx (11.35)

The mass of this little packet of burned fuel is the mass lost by the rocket: mfuel = -dm. Mathematically, the minus sign tells us that the mass of the burned fuel (the gases) and the rocket mass are changing in opposite directions. Physically, we know that dm 6 0, so the exhaust gases have a positive mass.

a

b

c

e

d0

2

-2

py (kg m/s)

px (kg m/s)2

f. p2 = 0u u

p1u

0

2

-2

py (kg m/s)

FIGURE 11.29 A before-and-after pictorial representation of a rocket burning a small amount of fuel.

Before:

After:

Relative to rocket

m + dmvex

mfuel vx + dvx

mvx

11.6 Advanced Topic: Rocket Propulsion 281

M13_KNIG2651_04_SE_C11.indd 281 9/28/15 5:23 PM

9.1 Energy Overview 207

9.1 Energy Overview Energy. It’s a word you hear all the time, and everyone has some sense of what energy means. Moving objects have energy; energy is the ability to make things happen; energy is associated with heat and with electricity; we’re constantly told to conserve energy; living organisms need energy; and engineers harness energy to do useful things. Some scientists consider the law of conservation of energy to be the most important of all the laws of nature. But all that in due time—first we have to start with the basic ideas.

Just what is energy? The concept of energy has grown and changed with time, and it is not easy to define in a general way just what energy is. Rather than starting with a formal definition, we’re going to let the concept of energy expand slowly over the course of several chapters. Our goal is to understand the characteristics of energy, how energy is used, and how energy is transformed from one form into another. It’s a complex story, so we’ll take it step by step until all the pieces are in place.

The Energy Principle❮❮ Section 7.1 introduced interaction diagrams and the very important distinction between the system, those objects whose motion and interactions we wish to analyze, and the environment, objects external to the system but exerting forces on the system. The most important step in an energy analysis is to clearly define the system. Why? Because energy is not some disembodied, ethereal substance; it’s the energy of something. Specifically, it’s the energy of a system.

FIGURE 9.1 illustrates the idea pictorially. The system has energy, the system energy, which we’ll designate Esys. There are many kinds or forms of energy: kinetic energy K, potential energy U, thermal energy Eth, chemical energy, and so on. We’ll introduce these one by one as we go along. Within the system, energy can be transformed without loss. Chemical energy can be transformed into kinetic energy, which is then transformed into thermal energy. As long as the system is not interacting with the environment, the total energy of the system is unchanged. You’ll recognize this idea as an initial statement of the law of conservation of energy.

But systems often do interact with their environment. Those interactions change the energy of the system, either increasing it (energy added) or decreasing it (energy removed). We say that interactions with the environment transfer energy into or out of the system. Interestingly, there are only two ways to transfer energy. One is by mechanical means, using forces to push and pull on the system. A process that

Some important forms of energy

Kinetic energy K Potential energy U Thermal energy Eth

Kinetic energy is the energy of motion. All moving objects have kinetic energy. The more massive an object or the faster it moves, the larger its kinetic energy.

Potential energy is stored energy associated with an object’s position. The roller coaster’s gravitational potential energy depends on its height above the ground.

Thermal energy is the sum of the micro-scopic kinetic and potential energies of all the atoms and bonds that make up the object. An object has more thermal energy when hot than when cold.

FIGURE 9.1 A system-environment perspective on energy.

System

Environment

EnvironmentHeat Work

Heat

Kinetic Potential

Thermal Chemical

WorkEnergy removed

Energy added

Energy can be transformed

The system has energy Esys

M11_KNIG2651_04_SE_C09.indd 207 9/28/15 5:35 PM


Built from the ground up on physics education research and crafted using key ideas from learning theory, Knight has set the standard for eff ective and accessible pedagogical materials in physics. In this fourth edition, Knight continues to refi ne and expand the instructional techniques to take students further.

NEW AND UPDATED LEARNING TOOLS PROMOTE DEEPER AND BETTER-CONNECTED UNDERSTANDING

NEW! MODEL BOXES enhance the text’s emphasis on modeling—analyzing a complex, real-world situation in terms of simple but reasonable idealizations that can be applied over and over in solving problems. These fun-damental simplifications are developed in the text and then deployed more explicitly in the worked examples, helping students to recog-nize when and how to use recurring models, a key critical-thinking skill.

REVISED! ENHANCED CHAPTER PREVIEWS, based on the educational psychology concept of an “advance organizer,” have been reconceived to address the questions students are most likely to ask themselves while studying the material for the first time. Questions cover the important ideas, and provide a big-picture overview of the chapter’s key principles. Each chapter con-cludes with the visual Chapter Summary, consolidating and structuring understanding.

46 CHAPTER 2 Kinematics in One Dimension

au

Mathematically:

Limitations: Model fails if the particle’sacceleration changes.

Model the object as a particle movingin a straight line with constant acceleration.

For motion with constant acceleration.

vu

Parabola

s

si t

The slope is vs.

Horizontal lineas

0 t

The acceleration is constant.

Straight linevs

vis t

The slope is as.vfs = vis + as∆t

vfs2 = vis

2 + 2as∆s

sf = si + vis∆t + as1∆t2212

Constant acceleration

MODEL 2.2

Exercise 16

M03_KNIG2651_04_SE_C02.indd 46 9/13/15 8:41 PM


MODEL 6.3

FrictionThe friction force is parallel to the surface.

■ Static friction: Acts as needed to prevent motion. Can have any magnitude up to fs max = ms n.

■ Kinetic friction: Opposes motion with fk = mk n.

■ Rolling friction: Opposes motion with fr = mr n.

■ Graphically:

Push orpull

Friction

Motion is relativeto the surface.

f

Push or pull force

Static frictionincreases to matchthe push or pull.

Kinetic friction is constantas the object moves.

KineticStatic

The object slips when staticfriction reaches fs max.

Rest Moving

fs max = msn

mkn

0

M07_KNIG2651_04_SE_C06.indd 142 9/13/15 8:39 PM


SUMMARY

The goal of Chapter 6 has been to learn to solve linear force-and-motion problems.

GENERAL PRINCIPLES

Two Explanatory ModelsAn object on which there is no net force is in mechanical equilibrium.• Objects at rest.• Objects moving with constant

velocity.• Newton’s second law applies

with au = 0u.

An object on which the net force is constant undergoes dynamics with constant force.• The object accelerates.• The kinematic model is that of

constant acceleration.• Newton’s second law applies.

A Problem-Solving StrategyA four-part strategy applies to both equilibrium and dynamics problems.

MODEL Make simplifying assumptions.

VISUALIZE

• Translate words into symbols.• Draw a sketch to define the situation.• Draw a motion diagram.• Identify forces.• Draw a free-body diagram.

SOLVE Use Newton’s second law:

Fu

net = ai

Fu

i = mau

“Read” the vectors from the free-body diagram. Use kinematics to find velocities and positions.

ASSESS Is the result reasonable? Does it have correct units and significant figures?

equilibrium modelconstant-force modelflat-earth approximation

weightcoefficient of static friction, ms

coefficient of kinetic friction, mk

rolling frictioncoefficient of rolling friction, mr

drag coefficient, Cterminal speed, vterm

TERMS AND NOTATION

A falling object reaches terminal speed

vterm = B2mg

CrA

APPLICATIONS

Mass is an intrinsic property of an object that describes the object’s inertia and, loosely speaking, its quantity of matter.

The weight of an object is the reading of a spring scale when the object is at rest relative to the scale. Weight is the result of weigh-ing. An object’s weight depends on its mass, its acceleration, and the strength of gravity. An object in free fall is weightless.

IMPORTANT CONCEPTS

Specific information about three important descriptive models:

Gravity Fu

G = 1mg, downward2Friction f

u

s = 10 to ms n, direction as necessary to prevent motion2 f

u

k = 1mk n, direction opposite the motion2 f

u

r = 1mr n, direction opposite the motion2Drag F

u

drag = 112 CrAv2, direction opposite the motion2

Newton’s laws are vector expressions. You must write them out by components:

1Fnet2x = aFx = max

1Fnet2y = aFy = may

The acceleration is zero in equi-librium and also along an axis perpendicular to the motion.

Fnet = 0u u

au

Go back and forthbetween thesesteps as needed.

d

y

x

Fnet

u

F1

u

F3

u

F2

u

FG

Terminal speed is reached when the drag force exactly balances the gravitational force: a = 0.

u

u

u

Fdrag

u

M07_KNIG2651_04_SE_C06.indd 152 9/13/15 8:12 PM

6 The powerful thrust of the jet engines accelerates this enormous plane to a speed of over 150 mph in less than a mile.

Dynamics I: Motion Along a Line

IN THIS CHAPTER, you will learn to solve linear force-and-motion problems.

How are Newton’s laws used to solve problems?Newton’s first and second laws are vector equations. To use them,

■ Draw a free-body diagram.■ Read the x- and y-components of the

forces directly off the free-body diagram.■ Use aFx = max and aFy = may.

How are dynamics problems solved?A net force on an object causes the object to accelerate.


■ Use Newton’s second law to find the object’s acceleration.

■ Use kinematics for velocity and position.

❮❮ LOOKING BACK Sections 2.4–2.6 Kinematics

How are equilibrium problems solved?An object at rest or moving with constant velocity is in equilibrium with no net force.


■ Use Newton’s second law with a = 0 to solve for unknown forces.

❮❮ LOOKING BACK Sections 5.1–5.2 Forces

What are mass and weight?Mass and weight are not the same.

■ Mass describes an object’s inertia. Loosely speaking, it is the amount of matter in an object. It is the same everywhere.

■ Gravity is a force.■ Weight is the result of weighing an object

on a scale. It depends on mass, gravity, and acceleration.

How do we model friction and drag?Friction and drag are complex forces, but we will develop simple models of each.

■ Static, kinetic, and rolling friction depend on the coefficients of friction but not on the object’s speed.

■ Drag depends on the square of an object’s speed and on its cross-section area.

■ Falling objects reach terminal speed when drag and gravity are balanced.

How do we solve problems?We will develop and use a four-part problem-solving strategy:

■ Model the problem, using information about objects and forces.■ Visualize the situation with a pictorial representation.■ Set up and solve the problem with Newton’s laws.■ Assess the result to see if it is reasonable.

Fnet

u

y

x

au

Friction fs

uNormal n

u

Gravity FG

u

FG

u

Fsp

u

vu

Kinetic friction

M07_KNIG2651_04_SE_C06.indd 131 9/13/15 8:09 PM

A research-driven approach, fine-tuned for even greater ease-of-use and student success

REVISED COVERAGE AND ORGANIZATION GIVE INSTRUCTORS GREATER CHOICE AND FLEXIBILITY

NEW! CHAPTER ORGANIZATION allows instructors to more easily present material as needed to complement labs, course schedules, and different teaching styles. Work and energy are now covered before momentum, oscillations are grouped with mechan-ical waves, and optics appears after electricity and magnetism. Unchanged is Knight’s unique approach of working from concrete to abstract, using multiple representations, balancing qualitative with quantitative, and addressing misconceptions.

NEW! MORE CALCULUS-BASED PROBLEMS have been added, along with an icon to make these easy to identify. The sig-nificantly revised end-of-chapter problem sets, extensively class-tested and both calibrated and improved using MasteringPhysics® data, expand the range of physics and math skills students will use to solve problems.

Exercises and Problems 259

55. ||| Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons—hence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is

U = U031 - e-x/x04where x is the distance between the centers of the two nucle-ons, x0 is a constant having the value x0 = 2.0 * 10-15 m, and U0 = 6.0 * 10-11 J.

Quantum effects are essential for a proper understand-ing of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass 1.67 * 10-27 kg and diameter 1.0 * 10-15 m. Suppose you hold two neutrons 5.0 * 10-15 m apart, measured between their centers, then release them. What is the speed of each neutron as they crash together? Keep in mind that both neutrons are moving.

56. || A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx = 120 - 5x2 N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially the block is at rest at x = 0 m. What is the block’s speed when it has been pulled to x = 4.0 m?

57. || A system has potential energy

U1x2 = x + sin112 rad/m2x2as a particle moves over the range 0 m … x … p m.a. Where are the equilibrium positions in this range?b. For each, is it a point of stable or unstable equilibrium?

58. || A particle that can move along the x-axis is part of a system with potential energy

U1x2 = A

x2 -Bx

where A and B are positive constants.a. Where are the particle’s equilibrium positions?b. For each, is it a point of stable or unstable equilibrium?

59. Suppose the particle is shot to the right from x = 1.0 m with a speed of 25 m/s. Where is its turning point?FIGURE P10.59

60. || A clever engineer designs a “sprong” that obeys the force law Fx = -q1x - xeq23, where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we’ll let xeq = 0 m. Then Fx = -qx3.a. What are the units of q?b. Find an expression for the potential energy of a stretched or

compressed sprong.c. A sprong-loaded toy gun shoots a 20 g plastic ball. What

is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.

61. || The potential energy for a particle that can move along the x-axis is U = Ax2 + B sin1px/L2, where A, B, and L are constants. What is the force on the particle at (a) x = 0, (b) x = L/2, and (c) x = L?

62. || A particle that can move along the x-axis experiences an interaction force Fx = 13x2 - 5x2 N, where x is in m. Find an expression for the system’s potential energy.

63. || An object moving in the xy-plane is subjected to the force Fu= 12xy in + x2 jn2 N, where x and y are in m.



c. Is this a conservative force?64. || An object moving in the xy-plane is subjected to the force

Fu= 12xy in + 3y jn2 N, where x and y are in m.



c. Is this a conservative force?65. Write a realistic problem for which the energy bar chart shown in

FIGURE P10.65 correctly shows the energy at the beginning and end of the problem.

In Problems 66 through 68 you are given the equation used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation.b. Draw the before-and-after pictorial representation.c. Finish the solution of the problem.

=

=

40

20

0

-20Ki UGi USp i UGf

+ + + +

+ + + +USp fKf

E (J)

FIGURE P10.65

66. 1211500 kg215.0 m/s22 + 11500 kg219.80 m/s22110 m2 = 12 11500 kg2vi

2 + 11500 kg219.80 m/s2210 m267. 1

210.20 kg212.0 m/s22 + 12 k10 m22

= 12 10.20 kg210 m/s22 + 12 k1-0.15 m22

68. 1210.50 kg2vf

2 + 10.50 kg219.80 m/s2210 m2 + 12 1400 N/m210 m22 = 1

2 10.50 kg210 m/s22 + 10.50 kg219.80 m/s2211-0.10 m2 sin 30°2 + 12 1400 N/m21-0.10 m22

Challenge Problems

69. ||| A pendulum is formed from a small ball of mass m on a string of length L. As FIGURE CP10.69 shows, a peg is height h = L /3

M12_KNIG2651_04_SE_C10.indd 259 9/28/15 5:29 PM

NEW! ADVANCED TOPICS as optional sections add even more flexibility for instructors’ individual courses. Topics include rocket propulsion, gyroscopes and precession, the wave equation (including for electromagnetic waves), the speed of sound in gases, and more details on the interference of light.

STOP TO THINK 11.6 An object trav-eling to the right with pu = 2 in kg m/s suddenly explodes into two pieces. Piece 1 has the momentum pu1 shown in the figure. What is the momentum pu2 of the second piece?

11.6 advanced topic Rocket Propulsion Newton’s second law F

u= mau applies to objects whose mass does not change. That’s

an excellent assumption for balls and bicycles, but what about something like a rocket that loses a significant amount of mass as its fuel is burned? Problems of varying mass are solved with momentum rather than acceleration. We’ll look at one important example.

FIGURE 11.29 shows a rocket being propelled by the thrust of burning fuel but not influenced by gravity or drag. Perhaps it is a rocket in deep space where gravity is very weak in comparison to the rocket’s thrust. This may not be highly realistic, but ignoring gravity allows us to understand the essentials of rocket propulsion without making the mathematics too complicated. Rocket propulsion with gravity is a Challenge Problem in the end-of-chapter problems.

The system rocket + exhaust gases is an isolated system, so its total momentum is conserved. The basic idea is simple: As exhaust gases are shot out the back, the rocket “recoils” in the opposite direction. Putting this idea on a mathematical footing is fairly straightforward—it’s basically the same as analyzing an explosion—but we have to be extremely careful with signs.

We’ll use a before-and-after approach, as we do with all momentum problems. The Before state is a rocket of mass m (including all onboard fuel) moving with velocity vx and having initial momentum Pix = mvx. During a small interval of time dt, the rocket burns a small mass of fuel mfuel and expels the resulting gases from the back of the rocket at an exhaust speed vex relative to the rocket. That is, a space cadet on the rocket sees the gases leaving the rocket at speed vex regardless of how fast the rocket is traveling through space.

After this little packet of burned fuel has been ejected, the rocket has new velocity vx + dvx and new mass m + dm. Now you’re probably thinking that this can’t be right; the rocket loses mass rather than gaining mass. But that’s our understanding of the physical situation. The mathematical analysis knows only that the mass changes, not whether it increases or decreases. Saying that the mass is m + dm at time t + dt is a formal statement that the mass has changed, and that’s how analysis of change is done in calculus. The fact that the rocket’s mass is decreasing means that dm has a negative value. That is, the minus goes with the value of dm, not with the statement that the mass has changed.

After the gas has been ejected, both the rocket and the gas have momentum. Conservation of momentum tells us that

Pfx = mrocket1vx2rocket + mfuel1vx2fuel = Pix = mvx (11.35)

The mass of this little packet of burned fuel is the mass lost by the rocket: mfuel = -dm. Mathematically, the minus sign tells us that the mass of the burned fuel (the gases) and the rocket mass are changing in opposite directions. Physically, we know that dm 6 0, so the exhaust gases have a positive mass.

a

b

c

e

d0

2

-2

py (kg m/s)

px (kg m/s)2

f. p2 = 0u u

p1u

0

2

-2

py (kg m/s)

FIGURE 11.29 A before-and-after pictorial representation of a rocket burning a small amount of fuel.

Before:

After:

Relative to rocket

m + dmvex

mfuel vx + dvx

mvx

11.6 Advanced Topic: Rocket Propulsion 281

M13_KNIG2651_04_SE_C11.indd 281 9/28/15 5:23 PM

9.1 Energy Overview 207

9.1 Energy Overview Energy. It’s a word you hear all the time, and everyone has some sense of what energy means. Moving objects have energy; energy is the ability to make things happen; energy is associated with heat and with electricity; we’re constantly told to conserve energy; living organisms need energy; and engineers harness energy to do useful things. Some scientists consider the law of conservation of energy to be the most important of all the laws of nature. But all that in due time—first we have to start with the basic ideas.

Just what is energy? The concept of energy has grown and changed with time, and it is not easy to define in a general way just what energy is. Rather than starting with a formal definition, we’re going to let the concept of energy expand slowly over the course of several chapters. Our goal is to understand the characteristics of energy, how energy is used, and how energy is transformed from one form into another. It’s a complex story, so we’ll take it step by step until all the pieces are in place.

The Energy Principle❮❮ Section 7.1 introduced interaction diagrams and the very important distinction between the system, those objects whose motion and interactions we wish to analyze, and the environment, objects external to the system but exerting forces on the system. The most important step in an energy analysis is to clearly define the system. Why? Because energy is not some disembodied, ethereal substance; it’s the energy of something. Specifically, it’s the energy of a system.

FIGURE 9.1 illustrates the idea pictorially. The system has energy, the system energy, which we’ll designate Esys. There are many kinds or forms of energy: kinetic energy K, potential energy U, thermal energy Eth, chemical energy, and so on. We’ll introduce these one by one as we go along. Within the system, energy can be transformed without loss. Chemical energy can be transformed into kinetic energy, which is then transformed into thermal energy. As long as the system is not interacting with the environment, the total energy of the system is unchanged. You’ll recognize this idea as an initial statement of the law of conservation of energy.

But systems often do interact with their environment. Those interactions change the energy of the system, either increasing it (energy added) or decreasing it (energy removed). We say that interactions with the environment transfer energy into or out of the system. Interestingly, there are only two ways to transfer energy. One is by mechanical means, using forces to push and pull on the system. A process that

Some important forms of energy

Kinetic energy K Potential energy U Thermal energy Eth

Kinetic energy is the energy of motion. All moving objects have kinetic energy. The more massive an object or the faster it moves, the larger its kinetic energy.

Potential energy is stored energy associated with an object’s position. The roller coaster’s gravitational potential energy depends on its height above the ground.

Thermal energy is the sum of the micro-scopic kinetic and potential energies of all the atoms and bonds that make up the object. An object has more thermal energy when hot than when cold.

FIGURE 9.1 A system-environment perspective on energy.

System

Environment

EnvironmentHeat Work

Heat

Kinetic Potential

Thermal Chemical

WorkEnergy removed

Energy added

Energy can be transformed

The system has energy Esys

M11_KNIG2651_04_SE_C09.indd 207 9/28/15 5:35 PM


A STRUCTURED AND CONSISTENT APPROACH BUILDS PROBLEM-SOLVING SKILLS AND CONFIDENCE

With a research-based 4-step problem-solving framework used throughout the text, students learn the importance of making assumptions (in the MODEL step) and gathering informa-tion and making sketches (in the VISUALIZE step) before treating the problem mathemati-cally (SOLVE) and then analyzing their results (ASSESS).

The REVISED STUDENT WORKBOOK is tightly integrated with the main text–allowing students to practice skills from the text’s Tactics Boxes, work through the steps of Problem-Solv-ing Strategies, and assess the applicability of the Models. The workbook is referenced throughout the text with the icon . This workbook is avail-able for purchase.

Detailed PROBLEM-SOLVING STRATEGIES for different topics and categories of problems (circular-motion problems, calorimetry problems, etc.) are developed throughout, each one built on the 4-step framework and carefully illustrated in worked examples.

TACTICS BOXES give step-by-step procedures for developing specific skills (drawing free-body diagrams, using ray tracing, etc.).

10.4 Conservation of Energy 243

PROBLEM-SOLVING STRATEGY 10.1

Energy-conservation problemsMODEL Define the system so that there are no external forces or so that any external forces do no work on the system. If there’s friction, bring both surfaces into the system. Model objects as particles and springs as ideal.VISUALIZE Draw a before-and-after pictorial representation and an energy bar chart. A free-body diagram may be needed to visualize forces.SOLVE If the system is both isolated and nondissipative, then the mechanical energy is conserved:

Ki + Ui = Kf + Uf

where K is the total kinetic energy of all moving objects and U is the total potential energy of all interactions within the system. If there’s friction, then

Ki + Ui = Kf + Uf + ∆Eth

where the thermal energy increase due to friction is ∆Eth = fk ∆s.ASSESS Check that your result has correct units and significant figures, is reasonable, and answers the question.

Exercise 14

M12_KNIG2651_04_SE_C10.indd 243 10/6/15 9:28 AM

716 CHAPTER 26 Potential and Field

TACTICS BOX 26.1

Finding the potential from the electric field

●1 Draw a picture and identify the point at which you wish to find the potential. Call this position f.

●2 Choose the zero point of the potential, often at infinity. Call this position i. ●3 Establish a coordinate axis from i to f along which you already know or can

easily determine the electric field component Es. ●4 Carry out the integration of Equation 26.3 to find the potential.

Exercise 1

M32_KNIG2651_04_SE_C26.indd 716 10/6/15 9:29 AM

30-8 chapter 30 • Electromagnetic Induction

© 2

017

Pear

son

Edu

catio

n.

18. The graph shows how the magnetic field changes through a rectangular loop of wire with resistance R. Draw a graph of the current in the loop as a function of time. Let a counterclockwise current be positive, a clockwise current be negative.

a. What is the magnetic flux through the loop at t = 0?

b. Does this flux change between t = 0 and t = t1?

c. Is there an induced current in the loop between t = 0 and t = t1?

d. What is the magnetic flux through the loop at t = t2?

e. What is the change in flux through the loop between t1 and t2?

f. What is the time interval between t1 and t2?

g. What is the magnitude of the induced emf between t1 and t2?

h. What is the magnitude of the induced current between t1 and t2?

i. Does the magnetic field point out of or into the loop?

j. Between t1 and t2, is the magnetic flux increasing or decreasing?

k. To oppose the change in the flux between t1 and t2, should the magnetic field of the induced current point out of or into the loop?

l. Is the induced current between t1 and t2 positive or negative?

m. Does the flux through the loop change after t2?

n. Is there an induced current in the loop after t2?

o. Use all this information to draw a graph of the induced current. Add appropriate labels on the vertical axis.

PSS30.1

M30_KNIG3162_04_SE_C30.indd 8 09/25/15 4:07 PM

THE ULTIMATE RESOURCE BEFORE, DURING, AND AFTER CLASS

BEFORE CLASS

DURING CLASS

AFTER CLASS

NEW! INTERACTIVE PRELECTURE VIDEOS address the rapidly growing movement toward pre-lecture teaching and flipped classrooms. These whiteboard-style animations provide an introduction to key topics with embedded assessment to help students prepare and profes-sors identify student misconceptions before lecture.

NEW! LEARNING CATALYTICS™ is an interactive classroom tool that uses students’ devices to engage them in more sophisticated tasks and thinking. Learning Catalytics enables instructors to generate classroom discussion and promote peer-to-peer learning to help students develop critical-thinking skills. Instructors can take advantage of real-time analytics to find out where students are struggling and adjust their instructional strategy.

NEW! ENHANCED END-OF-CHAPTER QUESTIONS offer stu-dents instructional support when and where they need it, including links to the eText, math remediation, and wrong-answer feedback for homework assignments.

ADAPTIVE FOLLOW-UPS are personalized assignments that pair Mastering’s powerful content with Knewton’s adaptive learning engine to provide individualized help to students before misconceptions take hold. These adaptive follow-ups address topics students struggled with on assigned homework, including core prerequisite topics.

NEW! DYNAMIC STUDY MODULES (DSMs) con-tinuously assess students’ performance in real time to provide personalized question and explanation content until students master the module with confidence. The DSMs cover basic math skills and key definitions and relationships for topics across all of mechanics and electricity and magnetism.

MasteringPhysics


A STRUCTURED AND CONSISTENT APPROACH BUILDS PROBLEM-SOLVING SKILLS AND CONFIDENCE

With a research-based 4-step problem-solving framework used throughout the text, students learn the importance of making assumptions (in the MODEL step) and gathering informa-tion and making sketches (in the VISUALIZE step) before treating the problem mathemati-cally (SOLVE) and then analyzing their results (ASSESS).

The REVISED STUDENT WORKBOOK is tightly integrated with the main text–allowing students to practice skills from the text’s Tactics Boxes, work through the steps of Problem-Solv-ing Strategies, and assess the applicability of the Models. The workbook is referenced throughout the text with the icon . This workbook is avail-able for purchase.

Detailed PROBLEM-SOLVING STRATEGIES for different topics and categories of problems (circular-motion problems, calorimetry problems, etc.) are developed throughout, each one built on the 4-step framework and carefully illustrated in worked examples.

TACTICS BOXES give step-by-step procedures for developing specific skills (drawing free-body diagrams, using ray tracing, etc.).

10.4 Conservation of Energy 243

PROBLEM-SOLVING STRATEGY 10.1

Energy-conservation problemsMODEL Define the system so that there are no external forces or so that any external forces do no work on the system. If there’s friction, bring both surfaces into the system. Model objects as particles and springs as ideal.VISUALIZE Draw a before-and-after pictorial representation and an energy bar chart. A free-body diagram may be needed to visualize forces.SOLVE If the system is both isolated and nondissipative, then the mechanical energy is conserved:

Ki + Ui = Kf + Uf

where K is the total kinetic energy of all moving objects and U is the total potential energy of all interactions within the system. If there’s friction, then

Ki + Ui = Kf + Uf + ∆Eth

where the thermal energy increase due to friction is ∆Eth = fk ∆s.ASSESS Check that your result has correct units and significant figures, is reasonable, and answers the question.

Exercise 14

M12_KNIG2651_04_SE_C10.indd 243 10/6/15 9:28 AM

716 CHAPTER 26 Potential and Field

TACTICS BOX 26.1

Finding the potential from the electric field

●1 Draw a picture and identify the point at which you wish to find the potential. Call this position f.

●2 Choose the zero point of the potential, often at infinity. Call this position i. ●3 Establish a coordinate axis from i to f along which you already know or can

easily determine the electric field component Es. ●4 Carry out the integration of Equation 26.3 to find the potential.

Exercise 1

M32_KNIG2651_04_SE_C26.indd 716 10/6/15 9:29 AM

30-8 chapter 30 • Electromagnetic Induction

© 2

017

Pear

son

Edu

catio

n.

18. The graph shows how the magnetic field changes through a rectangular loop of wire with resistance R. Draw a graph of the current in the loop as a function of time. Let a counterclockwise current be positive, a clockwise current be negative.

a. What is the magnetic flux through the loop at t = 0?

b. Does this flux change between t = 0 and t = t1?

c. Is there an induced current in the loop between t = 0 and t = t1?

d. What is the magnetic flux through the loop at t = t2?

e. What is the change in flux through the loop between t1 and t2?

f. What is the time interval between t1 and t2?

g. What is the magnitude of the induced emf between t1 and t2?

h. What is the magnitude of the induced current between t1 and t2?

i. Does the magnetic field point out of or into the loop?

j. Between t1 and t2, is the magnetic flux increasing or decreasing?

k. To oppose the change in the flux between t1 and t2, should the magnetic field of the induced current point out of or into the loop?

l. Is the induced current between t1 and t2 positive or negative?

m. Does the flux through the loop change after t2?

n. Is there an induced current in the loop after t2?

o. Use all this information to draw a graph of the induced current. Add appropriate labels on the vertical axis.

PSS30.1

M30_KNIG3162_04_SE_C30.indd 8 09/25/15 4:07 PM

THE ULTIMATE RESOURCE BEFORE, DURING, AND AFTER CLASS

BEFORE CLASS

DURING CLASS

AFTER CLASS

NEW! INTERACTIVE PRELECTURE VIDEOS address the rapidly growing movement toward pre-lecture teaching and flipped classrooms. These whiteboard-style animations provide an introduction to key topics with embedded assessment to help students prepare and profes-sors identify student misconceptions before lecture.

NEW! LEARNING CATALYTICS™ is an interactive classroom tool that uses students’ devices to engage them in more sophisticated tasks and thinking. Learning Catalytics enables instructors to generate classroom discussion and promote peer-to-peer learning to help students develop critical-thinking skills. Instructors can take advantage of real-time analytics to find out where students are struggling and adjust their instructional strategy.

NEW! ENHANCED END-OF-CHAPTER QUESTIONS offer stu-dents instructional support when and where they need it, including links to the eText, math remediation, and wrong-answer feedback for homework assignments.

ADAPTIVE FOLLOW-UPS are personalized assignments that pair Mastering’s powerful content with Knewton’s adaptive learning engine to provide individualized help to students before misconceptions take hold. These adaptive follow-ups address topics students struggled with on assigned homework, including core prerequisite topics.

NEW! DYNAMIC STUDY MODULES (DSMs) con-tinuously assess students’ performance in real time to provide personalized question and explanation content until students master the module with confidence. The DSMs cover basic math skills and key definitions and relationships for topics across all of mechanics and electricity and magnetism.

MasteringPhysics


viii

Preface to the Instructor

This fourth edition of Physics for Scientists and Engineers: A Strategic Approach continues to build on the research-driven instructional techniques introduced in the first edition and the extensive feedback from thousands of users. From the begin-ning, the objectives have been:

■ To produce a textbook that is more focused and coherent, less encyclopedic.

■ To move key results from physics education research into the classroom in a way that allows instructors to use a range of teaching styles.

■ To provide a balance of quantitative reasoning and con-ceptual understanding, with special attention to concepts known to cause student difficulties.

■ To develop students’ problem-solving skills in a systematic manner.

These goals and the rationale behind them are discussed at length in the Instructor’s Guide.

What’s New to This EditionFor this fourth edition, we continue to apply the best results from educational research and to tailor them for this course and its students. At the same time, the extensive feedback we’ve received from both instructors and students has led to many changes and improvements to the text, the figures, and the end-of-chapter problems. These include:

■ Chapter ordering changes allow instructors to more easily organize content as needed to accommodate labs, schedules, and different teaching styles. Work and energy are now covered before momentum, oscillations are grouped with mechanical waves, and optics appears after electricity and magnetism.

■ Addition of advanced topics as optional sections further expands instructors’ options. Topics include rocket propul-sion, gyroscopes, the wave equation (for mechanical and electromagnetic waves), the speed of sound in gases, and more details on the interference of light.

■ Model boxes enhance the text’s emphasis on modeling—analyzing a complex, real-world situation in terms of simple but reasonable idealizations that can be applied over and over in solving problems. These fundamental simplifications are developed in the text and then deployed more explicitly in the worked examples, helping students to recognize when and how to use recurring models.

■ Enhanced chapter previews have been redesigned, with student input, to address the questions students are most likely to ask themselves while studying the material for the first time. The previews provide a big-picture overview of the chapter’s key principles.

■ Looking Back pointers enable students to look back at a previous chapter when it’s important to review concepts. Pointers provide the specific section to consult at the exact point in the text where they need to use this material.

■ Focused Part Overviews and Knowledge Structures con-solidate understanding of groups of chapters and give a tighter structure to the book as a whole. Reworked Knowledge Struc-tures provide more targeted detail on overarching themes.

■ Updated visual program that has been enhanced by revis-ing over 500 pieces of art to increase the focus on key ideas.

■ Significantly revised end-of-chapter problem sets in-clude more challenging problems to expand the range of physics and math skills students will use to solve problems. A new icon for calculus-based problems has been added.

At the front of this book, you’ll find an illustrated walkthrough of the new pedagogical features in this fourth edition.

Textbook OrganizationThe full textbook is divided into eight parts: Part I: Newton’s Laws, Part II: Conservation Laws, Part III: Applications of Newtonian Mechanics, Part IV: Oscillations and Waves, Part V: Thermodynamics, Part VI: Electricity and Magnetism, Part VII: Optics, and Part VIII: Relativity and Quantum Physics. Note that covering the parts in this order is by no means essential. Each topic is self-contained, and Parts III–VII can be rear-ranged to suit an instructor’s needs. Part VII: Optics does need to follow Part IV: Oscillations and Waves, but optics can be taught either before or after electricity and magnetism.

There’s a growing sentiment that quantum physics is quick-ly becoming the province of engineers, not just scientists, and that even a two-semester course should include a reasonable introduction to quantum ideas. The Instructor’s Guide out-lines a couple of routes through the book that allow most of the quantum physics chapters to be included in a two-semester course.

MasteringPhysics® and Program Components

The Mastering platform is the most effec-tive and widely used online homework, tutorial, and assess-ment system for physics. It delivers self-paced tutorials that focus on teachers’ course objectives, provides individual-ized coaching, and responds to each student’s progress. The Mastering system helps educators maximize class time with easy-to-assign, customizable, and automatically graded as-sessments that motivate students to learn outside of class and arrive prepared.


Preface to the Instructor ix

This product features all of the resources of MasteringPhys-ics in addition to the NEW! Pearson eText 2.0. Now avail-able on smartphones and tablets, Pearson eText 2.0 comprises the full text, including videos and other rich media. Students can configure reading settings, including resizeable type and night-reading mode, take notes, and highlight, bookmark, and search the text.

Mastering Preview and Adoption Access Upon textbook purchase, students and teachers are granted access to MasteringPhysics with Pearson eText. High school teachers can obtain preview or adoption access to Mastering-Physics in one of the following ways:

Preview Access

■ Teachers can request preview access online by visiting www.PearsonSchool.com/Access_Request. Select Science, choose Initial Access, and complete the form under Option 2. Preview Access information will be sent to the teacher via e-mail.

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■ With the purchase of this program, a Pearson Adoption Access Card with Instructor Manual will be delivered with your textbook purchase. (ISBN: 978-0-13-353986-8)

■ Ask your Account General Manger for a Pearson Adoption Access Card with Instructor Manual. (ISBN: 978-0-13-353986-8)

OR

■ Visit PearsonSchool.com/Access_Request, select Science, choose initial Access, and complete the form under Option 3—MyLab/Mastering Class Adoption Access. Teacher and Student access information will be sent to the teacher via e-mail.

Students, ask your teacher for access.Pearson reserves the right to change and/or update technology plat-forms, including possible edition updates to customers during the term of access. This will allow Pearson to continue to deliver the most up-to-date content and technology to customers. Customer will be notified of any change prior to the beginning of the new school year.

For the InstructorPhysics for Scientists and Engineers: A Strategic Approach, fourth edition, provides an integrated teaching and learning package of support material for students and instructors.

Most of the teacher supplements and resources for this text are available electronically to qualified adopters within Mas-tering and on the Instructor Resource Center (IRC). Upon adoption or to preview, please go to www.pearsonschool.com/ access_request and select Instructor Resource Center. You will be required to complete a brief one-time registration subject

to verification of educator status. Upon verification, access information and instructions will be sent to you via e-mail. Once logged into the IRC, enter 978-0-13-439178-6 in the “Search our Catalog” box to locate resources.

Instructor’s Solutions Manual

This comprehensive solutions manual contains complete solutions to all end-of-chapter questions and problems. All problem solutions follow the Model/Visualize/Solve/Assess problem-solving strategy used in the text.

Instructor’s Guide

Written by Randy Knight, this resource provides chapter-by-chapter creative ideas and teaching tips for use in your class. It also contains an extensive review of results of what has been learned from physics education research and provides guide-lines for using active-learning techniques in your classroom.

TestGen Test Bank

The Test Bank contains over 2,000 high-quality conceptual and multiple-choice questions. Test files are provided in both Test-Gen® and Word format.

Instructor’s Resource DVD

This cross-platform DVD includes an Image Library; editable content for Key Equations, Problem-Solving Strategies, Math Relationship Boxes, Model Boxes, and Tactic Boxes; Power Point Lecture Slides and Clicker Questions; Instructor’s Guide, Instructor’s Solutions Manual; Solutions to Student Workbook exercises; and PhET simulations.

For the StudentThe following resources are available for purchase.

The Student WorkbookA key component of Physics for Scientists and Engineers: A Strategic Approach is the accompanying Student Workbook.

The workbook bridges the gap between textbook and home-work problems by providing students the opportunity to learn and practice skills prior to using those skills in quantitative end-of-chapter problems, much as a musician practices technique separately from performance pieces. The workbook exercises, which are keyed to each section of the textbook, focus on de-veloping specific skills, ranging from identifying forces and drawing free-body diagrams to interpreting wave functions.

The workbook exercises, which are generally qualitative and/or graphical, draw heavily upon the physics education re-search literature. The exercises deal with issues known to cause student difficulties and employ techniques that have proven to be effective at overcoming those difficulties. New to the fourth edition workbook are exercises that provide guided practice for the textbook’s Model boxes. The workbook exercises can be used in class as part of an active learning teaching strategy, in recitation sections, or as assigned homework. More informa-tion about effective use of the Student Workbook can be found in the Instructor’s Guide.


x Preface to the Instructor

AcknowledgmentsI have relied upon conversations with and, especially, the written publications of many members of the physics education research community. Those whose influence can be seen in these pages include Wendy Adams, the late Arnold Arons, Stuart Field, Uri Ganiel, Ibrahim Halloun, Richard Hake, Ken Heller, Paula Heron, David Hestenes, Brian Jones, the late Leonard Jossem, Jill Larkin, Priscilla Laws, John Mallinckrodt, Kandiah Manivannan, Richard Mayer, Lillian McDermott and members of the Physics Education Research Group at the University of Washington, David Meltzer, Edward “Joe” Redish, Fred Reif, Jeffery Saul, Rachel Scherr, Bruce Sherwood, Josip Slisko, David Sokoloff, Richard Steinberg, Ronald Thornton, Sheila Tobias, Alan Van Heuleven, Carl Wieman, and Michael Wittmann. John Rigden, founder and director of the Introductory University Physics Project, provided the impetus that got me started down this path. Early development of the materials was supported by the National Science Foundation as the Physics for the Year 2000 project; their support is gratefully acknowledged.

I especially want to thank my editors, Jeanne Zalesky and Becky Ruden, development editor Alice Houston, project manager Martha Steele, art development editors Kim Brucker and Margot Otway, and all the other staff at Pearson for their enthusiasm and hard work on this project. Rose Kernan and the team at Cenveo along with photo researcher Eric Schrader get a good deal of the credit for making this complex project all come together. Larry Smith, Larry Stookey, and Michael Ottinger have done an outstanding job of checking the solutions to every end-of-chapter problem and updating the Instructor’s Solutions Manual. John Filaseta must be thanked for carefully writing out the solutions to the Student Workbook exercises, and Jason Harlow for putting together the Lecture Slides. In addition to the reviewers and classroom testers listed below, who gave invaluable feedback, I am particularly grateful to Charlie Hibbard for his close scrutiny of every word and figure.

Finally, I am endlessly grateful to my wife Sally for her love, encouragement, and patience, and to our many cats, past and present, who are always ready to suggest “Dinner time?” when I’m in need of a phrase.

Randy Knight, September [email protected]

Reviewers and Classroom TestersGary B. Adams, Arizona State UniversityEd Adelson, Ohio State UniversityKyle Altmann, Elon UniversityWayne R. Anderson, Sacramento City CollegeJames H. Andrews, Youngstown State UniversityKevin Ankoviak, Las Positas CollegeDavid Balogh, Fresno City CollegeDewayne Beery, Buffalo State College

Joseph Bellina, Saint Mary’s CollegeJames R. Benbrook, University of HoustonDavid Besson, University of KansasMatthew Block, California State University, SacramentoRandy Bohn, University of ToledoRichard A. Bone, Florida International UniversityGregory Boutis, York CollegeArt Braundmeier, University of Southern Illinois, EdwardsvilleCarl Bromberg, Michigan State UniversityMeade Brooks, Collin CollegeDouglas Brown, Cabrillo CollegeRonald Brown, California Polytechnic State University, San Luis ObispoMike Broyles, Collin County Community CollegeDebra Burris, University of Central ArkansasJames Carolan, University of British ColumbiaMichael Chapman, Georgia Tech UniversityNorbert Chencinski, College of Staten IslandTonya Coffey, Appalachian State UniversityKristi Concannon, King’s CollegeDesmond Cook, Old Dominion UniversitySean Cordry, Northwestern College of IowaRobert L. Corey, South Dakota School of MinesMichael Crescimanno, Youngstown State UniversityDennis Crossley, University of Wisconsin–SheboyganWei Cui, Purdue UniversityRobert J. Culbertson, Arizona State UniversityDanielle Dalafave, The College of New JerseyPurna C. Das, Purdue University North CentralChad Davies, Gordon CollegeWilliam DeGraffenreid, California State University–SacramentoDwain Desbien, Estrella Mountain Community CollegeJohn F. Devlin, University of Michigan, DearbornJohn DiBartolo, Polytechnic UniversityAlex Dickison, Seminole Community CollegeChaden Djalali, University of South CarolinaMargaret Dobrowolska, University of Notre DameSandra Doty, Denison UniversityMiles J. Dresser, Washington State UniversityTaner Edis, Truman State UniversityCharlotte Elster, Ohio UniversityRobert J. Endorf, University of CincinnatiTilahun Eneyew, Embry-Riddle Aeronautical UniversityF. Paul Esposito, University of CincinnatiJohn Evans, Lee UniversityHarold T. Evensen, University of Wisconsin–PlattevilleMichael R. Falvo, University of North CarolinaAbbas Faridi, Orange Coast CollegeNail Fazleev, University of Texas–ArlingtonStuart Field, Colorado State UniversityDaniel Finley, University of New MexicoJane D. Flood, Muhlenberg CollegeMichael Franklin, Northwestern Michigan College


Preface to the Instructor xi

Jonathan Friedman, Amherst CollegeThomas Furtak, Colorado School of MinesAlina Gabryszewska-Kukawa, Delta State UniversityLev Gasparov, University of North FloridaRichard Gass, University of CincinnatiDelena Gatch, Georgia Southern UniversityJ. David Gavenda, University of Texas, AustinStuart Gazes, University of ChicagoKatherine M. Gietzen, Southwest Missouri State UniversityRobert Glosser, University of Texas, DallasWilliam Golightly, University of California, BerkeleyPaul Gresser, University of MarylandC. Frank Griffin, University of AkronJohn B. Gruber, San Jose State UniversityThomas D. Gutierrez, California Polytechnic State University, San Luis ObispoStephen Haas, University of Southern CaliforniaJohn Hamilton, University of Hawaii at HiloJason Harlow, University of TorontoRandy Harris, University of California, DavisNathan Harshman, American UniversityJ. E. Hasbun, University of West GeorgiaNicole Herbots, Arizona State UniversityJim Hetrick, University of Michigan–DearbornScott Hildreth, Chabot CollegeDavid Hobbs, South Plains CollegeLaurent Hodges, Iowa State UniversityMark Hollabaugh, Normandale Community CollegeSteven Hubbard, Lorain County Community CollegeJohn L. Hubisz, North Carolina State UniversityShane Hutson, Vanderbilt UniversityGeorge Igo, University of California, Los AngelesDavid C. Ingram, Ohio UniversityBob Jacobsen, University of California, BerkeleyRong-Sheng Jin, Florida Institute of TechnologyMarty Johnston, University of St. ThomasStanley T. Jones, University of AlabamaDarrell Judge, University of Southern CaliforniaPawan Kahol, Missouri State UniversityTeruki Kamon, Texas A&M UniversityRichard Karas, California State University, San MarcosDeborah Katz, U.S. Naval AcademyMiron Kaufman, Cleveland State UniversityKatherine Keilty, Kingwood CollegeRoman Kezerashvili, New York City College of TechnologyPeter Kjeer, Bethany Lutheran CollegeM. Kotlarchyk, Rochester Institute of TechnologyFred Krauss, Delta CollegeCagliyan Kurdak, University of MichiganFred Kuttner, University of California, Santa CruzH. Sarma Lakkaraju, San Jose State UniversityDarrell R. Lamm, Georgia Institute of TechnologyRobert LaMontagne, Providence CollegeEric T. Lane, University of Tennessee–Chattanooga

Alessandra Lanzara, University of California, BerkeleyLee H. LaRue, Paris Junior CollegeSen-Ben Liao, Massachusetts Institute of TechnologyDean Livelybrooks, University of OregonChun-Min Lo, University of South FloridaOlga Lobban, Saint Mary’s UniversityRamon Lopez, Florida Institute of TechnologyVaman M. Naik, University of Michigan, DearbornKevin Mackay, Grove City CollegeCarl Maes, University of ArizonaRizwan Mahmood, Slippery Rock UniversityMani Manivannan, Missouri State UniversityMark E. Mattson, James Madison UniversityRichard McCorkle, University of Rhode IslandJames McDonald, University of HartfordJames McGuire, Tulane UniversityStephen R. McNeil, Brigham Young University–IdahoTheresa Moreau, Amherst CollegeGary Morris, Rice UniversityMichael A. Morrison, University of OklahomaRichard Mowat, North Carolina State UniversityEric Murray, Georgia Institute of TechnologyMichael Murray, University of KansasTaha Mzoughi, Mississippi State UniversityScott Nutter, Northern Kentucky UniversityCraig Ogilvie, Iowa State UniversityBenedict Y. Oh, University of WisconsinMartin Okafor, Georgia Perimeter CollegeHalina Opyrchal, New Jersey Institute of TechnologyDerek Padilla, Santa Rosa Junior CollegeYibin Pan, University of Wisconsin–MadisonGeorgia Papaefthymiou, Villanova UniversityPeggy Perozzo, Mary Baldwin CollegeBrian K. Pickett, Purdue University, CalumetJoe Pifer, Rutgers UniversityDale Pleticha, Gordon CollegeMarie Plumb, Jamestown Community CollegeRobert Pompi, SUNY-BinghamtonDavid Potter, Austin Community College–Rio Grande CampusChandra Prayaga, University of West FloridaKenneth M. Purcell, University of Southern IndianaDidarul Qadir, Central Michigan UniversitySteve Quon, Ventura CollegeMichael Read, College of the SiskiyousLawrence Rees, Brigham Young UniversityRichard J. Reimann, Boise State UniversityMichael Rodman, Spokane Falls Community CollegeSharon Rosell, Central Washington UniversityAnthony Russo, Northwest Florida State CollegeFreddie Salsbury, Wake Forest UniversityOtto F. Sankey, Arizona State UniversityJeff Sanny, Loyola Marymount UniversityRachel E. Scherr, University of MarylandCarl Schneider, U.S. Naval Academy


xii Preface to the Instructor

Bruce Schumm, University of California, Santa CruzBartlett M. Sheinberg, Houston Community CollegeDouglas Sherman, San Jose State UniversityElizabeth H. Simmons, Boston UniversityMarlina Slamet, Sacred Heart UniversityAlan Slavin, Trent CollegeAlexander Raymond Small, California State Polytechnic University, PomonaLarry Smith, Snow CollegeWilliam S. Smith, Boise State UniversityPaul Sokol, Pennsylvania State UniversityLTC Bryndol Sones, United States Military AcademyChris Sorensen, Kansas State UniversityBrian Steinkamp, University of Southern IndianaAnna and Ivan Stern, AW Tutor CenterGay B. Stewart, University of ArkansasMichael Strauss, University of OklahomaChin-Che Tin, Auburn UniversityChristos Valiotis, Antelope Valley CollegeAndrew Vanture, Everett Community CollegeArthur Viescas, Pennsylvania State UniversityErnst D. Von Meerwall, University of AkronChris Vuille, Embry-Riddle Aeronautical UniversityJerry Wagner, Rochester Institute of TechnologyRobert Webb, Texas A&M UniversityZodiac Webster, California State University, San BernardinoRobert Weidman, Michigan Technical UniversityFred Weitfeldt, Tulane UniversityGary Williams, University of California, Los AngelesLynda Williams, Santa Rosa Junior CollegeJeff Allen Winger, Mississippi State UniversityCarey Witkov, Broward Community CollegeRonald Zammit, California Polytechnic State University, San Luis ObispoDarin T. Zimmerman, Pennsylvania State University, AltoonaFredy Zypman, Yeshiva University

Student Focus GroupsCalifornia Polytechnic State University, San Luis ObispoMatthew BaileyJames CaudillAndres GonzalezMytch Johnson

California State University, SacramentoLogan AllenAndrew FujikawaSagar GuptaMarlene JuarezCraig KovacAlissa McKownKenneth MercadoDouglas OstheimerIan TabbadaJames Womack

Santa Rosa Junior CollegeKyle DoughtyTacho GardinerErik GonzalezJoseph GoodwinChelsea IrmerVatsal PandyaParth ParikhAndrew ProsserDavid ReynoldsBrian SwainGrace Woods

Stanford UniversityMontserrat CorderoRylan EdlinMichael Goodemote IIStewart IsaacsDavid LaFehrSergio RebelesJack Takahashi


The most incomprehensible thing about the universe is that it is comprehensible.

—Albert Einstein

The day I went into physics class it was death.—Sylvia Plath, The Bell Jar

Let’s have a little chat before we start. A rather one-sided chat, admittedly, because you can’t respond, but that’s OK. I’ve talked with many of your fellow students over the years, so I have a pretty good idea of what’s on your mind.

What’s your reaction to taking physics? Fear and loathing? Uncertainty? Excitement? All the above? Let’s face it, physics has a bit of an image problem on campus. You’ve probably heard that it’s difficult, maybe impossible unless you’re an Einstein. Things that you’ve heard, your experiences in other science courses, and many other factors all color your expectations about what this course is going to be like.

It’s true that there are many new ideas to be learned in physics and that the course, like college courses in general, is going to be much faster paced than other science courses you had in high school. I think it’s fair to say that it will be an intense course. But we can avoid many potential problems and difficulties if we can establish, here at the beginning, what this course is about and what is expected of you—and of me!

Just what is physics, anyway? Physics is a way of think-ing about the physical aspects of nature. Physics is not better than art or biology or poetry or religion, which are also ways to think about nature; it’s simply different. One of the things this course will emphasize is that physics is a human endeavor. The ideas presented in this book were not found in a cave or conveyed to us by aliens; they were discovered and developed by real people engaged in a struggle with real issues.

You might be surprised to hear that physics is not about “facts.” Oh, not that facts are unimportant, but physics is far more focused on discovering relationships and patterns than on learning facts for their own sake.

For example, the colors of the rainbow appear both when white light passes through a prism and—as in this photo—when white light reflects from a thin film of oil on water. What does this pattern tell us about the nature of light?

Our emphasis on relationships and patterns means that there’s not a lot of memorization when you

study physics. Some—there are still definitions and equations to learn—but less than in many other courses. Our emphasis, instead, will be on thinking and reasoning. This is important to factor into your expectations for the course.

Perhaps most important of all, physics is not math! Physics is much broader. We’re going to look for patterns and relationships in nature, develop the logic that relates different ideas, and search for the reasons why things hap-pen as they do. In doing so, we’re going to stress qualitative reasoning, pictorial and graphical reasoning, and reasoning by analogy. And yes, we will use math, but it’s just one tool among many.

It will save you much frustration if you’re aware of this physics–math distinction up front. Many of you, I know, want to find a formula and plug numbers into it—that is, to do a math problem.

As you study, you’ll sometimes be baffled, puzzled, and confused. That’s perfectly normal and to be expected. Making mistakes is OK too if you’re willing to learn from the experience. No one is born knowing how to do physics any more than he or she is born knowing how to play the piano or shoot basketballs. The ability to do physics comes from practice, repetition, and struggling with the ideas until you “own” them and can apply them yourself in new situations. There’s no way to make learning effortless, at least for anything worth learning, so expect to have some difficult moments ahead. But also expect to have some moments of excitement at the joy of discovery. There will be instants at which the pieces suddenly click into place and you know that you understand a powerful idea. There will be times when you’ll surprise yourself by successfully working a difficult problem that you didn’t think you could solve. My hope, as an author, is that the excitement and sense of adventure will far outweigh the difficulties and frustrations.

Getting the Most Out of Your CourseMany of you, I suspect, would like to know the “best” way to study for this course. There is no best way. People are different, and what works for one student is less effective for another. But I do want to stress that reading the text is vitally important. The basic knowledge for this course is written down on these pages, and your instructor’s number-one expectation is that you will read carefully to find and learn that knowledge.

Despite there being no best way to study, I will suggest one way that is successful for many students.

1. Read each chapter before it is discussed in class. I can-not stress too strongly how important this step is. Class attendance is much more effective if you are prepared. When you first read a chapter, focus on learning new vo-cabulary, definitions, and notation. There’s a list of terms and notations at the end of each chapter. Learn them! You won’t understand what’s being discussed or how the

Preface to the StudentFrom Me to You

xiii


xiv Preface to the Student

ideas are being used if you don’t know what the terms and symbols mean.

2. Participate actively in class. Take notes, ask and answer questions, and participate in discussion groups. There is ample scientific evidence that active participation is much more effective for learning science than passive listening.

3. After class, go back for a careful re-reading of the chapter. In your second reading, pay closer attention to the details and the worked examples. Look for the logic behind each example (I’ve highlighted this to make it clear), not just at what formula is being used. And use the textbook tools that are designed to help your learning, such as the problem-solving strategies, the chapter summaries, and the exercises in the Student Workbook.

4. Finally, apply what you have learned to the home-work problems at the end of each chapter. I strongly encourage you to form a study group with two or three classmates. There’s good evidence that students who study regularly with a group do better than the rugged individualists who try to go it alone.

Did someone mention a workbook? The companion Stu-dent Workbook (available for purchase) is a vital part of the course. Its questions and exer-cises ask you to reason qualita-tively, to use graphical informa-tion, and to give explanations. It is through these exercises that you will learn what the concepts mean and will practice the rea-soning skills appropriate to the chapter. You will then have ac-

quired the baseline knowledge and confidence you need before turning to the end-of-chapter homework problems. In sports or in music, you would never think of performing before you practice, so why would you want to do so in physics? The workbook is where you practice and work on basic skills.

Many of you, I know, will be tempted to go straight to the homework problems and then thumb through the text looking for a formula that seems like it will work. That approach will not succeed in this course, and it’s guaranteed to make you frustrated and discouraged. Very few homework problems are of the “plug and chug” variety where you simply put numbers into a formula. To work the homework problems successfully, you need a better study strategy—either the one outlined above or your own—that helps you learn the concepts and the rela-tionships between the ideas.

Getting the Most Out of Your TextbookYour textbook provides many features designed to help you learn the concepts of physics and solve problems more effectively.

■ TACTICS BOXES give step-by-step procedures for particu-lar skills, such as interpreting graphs or drawing special

diagrams. Tactics Box steps are explicitly illustrated in sub-sequent worked examples, and these are often the starting point of a full Problem-Solving Strategy.

■ PROBLEM-SOLVING STRATEGIES are provided for each broad class of problems—problems characteristic of a chapter or group of chapters. The strategies follow a con-sistent four-step approach to help you develop confidence and proficient problem-solving skills: MODEL, VISUALIZE,

SOLVE, ASSESS.■ Worked EXAMPLES illustrate good problem-solving practices

through the consistent use of the four-step problem-solving approach The worked examples are often very detailed and carefully lead you through the reasoning behind the solution as well as the numerical calculations.

■ STOP TO THINK questions embedded in the chapter allow you to quickly assess whether you’ve understood the main idea of a section. A correct answer will give you confidence to move on to the next section. An incorrect answer will alert you to re-read the previous section.

■ Blue annotations on figures help you better understand what the figure is showing. They will help you to in-terpret graphs; translate between graphs, math, and pictures; grasp dif-ficult concepts through a visual analogy; and de-velop many other impor-tant skills.

■ Schematic Chapter Summaries help you organize what you have learned into a hierarchy, from general principles (top) to applications (bottom). Side-by-side pictorial, graphical, tex-tual, and mathematical representations are used to help you translate between these key representations.

■ Each part of the book ends with a KNOWLEDGE STRUCTURE

designed to help you see the forest rather than just the trees.

Now that you know more about what is expected of you, what can you expect of me? That’s a little trickier because the book is already written! Nonetheless, the book was prepared on the basis of what I think my students throughout the years have expected—and wanted—from their physics textbook. Further, I’ve listened to the extensive feedback I have received from thousands of students like you, and their instructors, who used the first three editions of this book.

You should know that these course materials—the text and the workbook—are based on extensive research about how stu-dents learn physics and the challenges they face. The effective-ness of many of the exercises has been demonstrated through extensive class testing. I’ve written the book in an informal style that I hope you will find appealing and that will encour-age you to do the reading. And, finally, I have endeavored to make clear not only that physics, as a technical body of knowl-edge, is relevant to your profession but also that physics is an exciting adventure of the human mind.

I hope you’ll enjoy the time we’re going to spend together.

I

The current in a wire isthe same at all points.

I = constant


xv

Detailed Contents

Chapter 4 Kinematics in Two Dimensions 80 4.1 Motion in Two Dimensions 81 4.2 Projectile Motion 85 4.3 Relative Motion 90 4.4 Uniform Circular Motion 92 4.5 Centripetal Acceleration 96 4.6 Nonuniform Circular Motion 98 SUMMARY 103

QUESTIONS AND PROBLEMS 104

Chapter 5 Force and Motion 110 5.1 Force 111 5.2 A Short Catalog of Forces 113 5.3 Identifying Forces 115 5.4 What Do Forces Do? 117 5.5 Newton’s Second Law 120 5.6 Newton’s First Law 121 5.7 Free-Body Diagrams 123 SUMMARY 126


Chapter 6 Dynamics I: Motion Along a Line 131

6.1 The Equilibrium Model 132 6.2 Using Newton’s Second Law 134 6.3 Mass, Weight, and Gravity 137 6.4 Friction 141 6.5 Drag 145 6.6 More Examples of Newton’s Second

Law 148 SUMMARY 152


Chapter 7 Newton’s Third Law 159 7.1 Interacting Objects 160 7.2 Analyzing Interacting Objects 161 7.3 Newton’s Third Law 164 7.4 Ropes and Pulleys 169 7.5 Examples of Interacting-Object

Problems 172 SUMMARY 175


Part I Newton’s Laws OVERVIEW Why Things Change 1

Chapter 1 Concepts of Motion 2 1.1 Motion Diagrams 3 1.2 Models and Modeling 4 1.3 Position, Time, and Displacement 5 1.4 Velocity 9 1.5 Linear Acceleration 11 1.6 Motion in One Dimension 15 1.7 Solving Problems in Physics 18 1.8 Unit and Significant Figures 22 SUMMARY 27


Chapter 2 Kinematics in One Dimension 32 2.1 Uniform Motion 33 2.2 Instantaneous Velocity 37 2.3 Finding Position from Velocity 40 2.4 Motion with Constant Acceleration 43 2.5 Free Fall 49 2.6 Motion on an Inclined Plane 51 2.7 ADVANCED TOPIC Instantaneous

Acceleration 54 SUMMARY 57


Chapter 3 Vectors and Coordinate Systems 65 3.1 Scalars and Vectors 66 3.2 Using Vectors 66 3.3 Coordinate Systems and Vector

Components 69 3.4 Unit Vectors and Vector Algebra 72 SUMMARY 76



xvi Detailed Contents

Chapter 8 Dynamics II: Motion in a Plane 182 8.1 Dynamics in Two Dimensions 183 8.2 Uniform Circular Motion 184 8.3 Circular Orbits 189 8.4 Reasoning About Circular Motion 191 8.5 Nonuniform Circular Motion 194 SUMMARY 197


Part I Newton’s Laws 204

Part II Conservation Laws OVERVIEW Why Some Things Don’t Change 205

Chapter 9 Work and Kinetic Energy 206 9.1 Energy Overview 207 9.2 Work and Kinetic Energy for a Single

Particle 209 9.3 Calculating the Work Done 213 9.4 Restoring Forces and the Work Done by

a Spring 219 9.5 Dissipative Forces and Thermal

Energy 221 9.6 Power 224 SUMMARY 226


Chapter 10 Interactions and Potential Energy 231

10.1 Potential Energy 232 10.2 Gravitational Potential Energy 233 10.3 Elastic Potential Energy 239 10.4 Conservation of Energy 242 10.5 Energy Diagrams 244 10.6 Force and Potential Energy 247 10.7 Conservative and Nonconservative

Forces 249 10.8 The Energy Principle Revisited 251 SUMMARY 254


KNOWLEDGE STRUCTURE

Chapter 11 Impulse and Momentum 261 11.1 Momentum and Impulse 262 11.2 Conservation of Momentum 266 11.3 Collisions 272 11.4 Explosions 277 11.5 Momentum in Two Dimensions 279 11.6 ADVANCED TOPIC Rocket Propulsion 281 SUMMARY 285


Part II Conservation Laws 292

Part III Applications of Newtonian Mechanics

OVERVIEW Power Over Our Environment 293

KNOWLEDGE STRUCTURE

Chapter 12 Rotation of a Rigid Body 294 12.1 Rotational Motion 295 12.2 Rotation About the Center of Mass 296 12.3 Rotational Energy 299 12.4 Calculating Moment of Inertia 301 12.5 Torque 303 12.6 Rotational Dynamics 307 12.7 Rotation About a Fixed Axis 309 12.8 Static Equilibrium 311 12.9 Rolling Motion 314 12.10 The Vector Description of Rotational

Motion 317 12.11 Angular Momentum 320 12.12 ADVANCED TOPIC Precession of a

Gyroscope 324 SUMMARY 328



Detailed Contents xvii

Chapter 16 Traveling Waves 420 16.1 The Wave Model 421 16.2 One-Dimensional Waves 423 16.3 Sinusoidal Waves 426 16.4 ADVANCED TOPIC The Wave Equation

on a String 430 16.5 Sound and Light 434 16.6 ADVANCED TOPIC The Wave Equation

in a Fluid 438 16.7 Waves in Two and Three

Dimensions 441 16.8 Power, Intensity, and Decibels 443 16.9 The Doppler Effect 445 SUMMARY 449


Chapter 17 Superposition 455 17.1 The Principle of Superposition 456 17.2 Standing Waves 457 17.3 Standing Waves on a String 459 17.4 Standing Sound Waves and Musical

Acoustics 463 17.5 Interference in One Dimension 467 17.6 The Mathematics of Interference 471 17.7 Interference in Two and Three

Dimensions 474 17.8 Beats 477 SUMMARY 481


Part IV Oscillations and Waves 488

Part V Thermodynamics OVERVIEW It’s All About Energy 489

Chapter 18 A Macroscopic Description of Matter 490

18.1 Solids, Liquids, and Gases 491 18.2 Atoms and Moles 492 18.3 Temperature 494 18.4 Thermal Expansion 496 18.5 Phase Changes 497 18.6 Ideal Gases 499 18.7 Ideal-Gas Processes 503 SUMMARY 509


KNOWLEDGE STRUCTURE

Chapter 13 Newton’s Theory of Gravity 336 13.1 A Little History 337 13.2 Isaac Newton 338 13.3 Newton’s Law of Gravity 339 13.4 Little g and Big G 341 13.5 Gravitational Potential Energy 343 13.6 Satellite Orbits and Energies 347 SUMMARY 352


Chapter 14 Fluids and Elasticity 357 14.1 Fluids 358 14.2 Pressure 359 14.3 Measuring and Using Pressure 365 14.4 Buoyancy 369 14.5 Fluid Dynamics 373 14.6 Elasticity 378 SUMMARY 382


Part III Applications of Newtonian Mechanics 388

Part IV Oscillations and Waves OVERVIEW The Wave Model 389

KNOWLEDGE STRUCTURE

Chapter 15 Oscillations 390 15.1 Simple Harmonic Motion 391 15.2 SHM and Circular Motion 394 15.3 Energy in SHM 397 15.4 The Dynamics of SHM 399 15.5 Vertical Oscillations 402 15.6 The Pendulum 404 15.7 Damped Oscillations 408 15.8 Driven Oscillations and Resonance 411 SUMMARY 413



xviii Detailed Contents

Chapter 19 Work, Heat, and the First Law of Thermodynamics 515

19.1 It’s All About Energy 516 19.2 Work in Ideal-Gas Processes 517 19.3 Heat 521 19.4 The First Law of Thermodynamics 524 19.5 Thermal Properties of Matter 526 19.6 Calorimetry 529 19.7 The Specific Heats of Gases 531 19.8 Heat-Transfer Mechanisms 537 SUMMARY 541


Chapter 20 The Micro/Macro Connection 548 20.1 Molecular Speeds and Collisions 549 20.2 Pressure in a Gas 550 20.3 Temperature 553 20.4 Thermal Energy and Specific Heat 555 20.5 Thermal Interactions and Heat 558 20.6 Irreversible Processes and the Second

Law of Thermodynamics 561 SUMMARY 565


Chapter 21 Heat Engines and Refrigerators 570

21.1 Turning Heat into Work 571 21.2 Heat Engines and Refrigerators 573 21.3 Ideal-Gas Heat Engines 578 21.4 Ideal-Gas Refrigerators 582 21.5 The Limits of Efficiency 584 21.6 The Carnot Cycle 587 SUMMARY 592


Part V Thermodynamics 600

Part VI Electricity and Magnetism OVERVIEW Forces and Fields 601

Chapter 22 Electric Charges and Forces 602 22.1 The Charge Model 603 22.2 Charge 606 22.3 Insulators and Conductors 608 22.4 Coulomb’s Law 612 22.5 The Electric Field 616 SUMMARY 622


KNOWLEDGE STRUCTURE

Chapter 23 The Electric Field 629 23.1 Electric Field Models 630 23.2 The Electric Field of Point Charges 630 23.3 The Electric Field of a Continuous

Charge Distribution 635 23.4 The Electric Fields of Rings, Disks,

Planes, and Spheres 639 23.5 The Parallel-Plate Capacitor 643 23.6 Motion of a Charged Particle in an

Electric Field 645 23.7 Motion of a Dipole in an Electric

Field 648 SUMMARY 651


Chapter 24 Gauss’s Law 658 24.1 Symmetry 659 24.2 The Concept of Flux 661 24.3 Calculating Electric Flux 663 24.4 Gauss’s Law 669 24.5 Using Gauss’s Law 672 24.6 Conductors in Electrostatic

Equilibrium 676 SUMMARY 680


Chapter 25 The Electric Potential 687 25.1 Electric Potential Energy 688 25.2 The Potential Energy of Point

Charges 691 25.3 The Potential Energy of a Dipole 694 25.4 The Electric Potential 695 25.5 The Electric Potential Inside a Parallel-

Plate Capacitor 698 25.6 The Electric Potential of a Point

Charge 702 25.7 The Electric Potential of Many

Charges 704 SUMMARY 707



Detailed Contents xix

Chapter 26 Potential and Field 714 26.1 Connecting Potential and Field 715 26.2 Finding the Electric Field from the

Potential 717 26.3 A Conductor in Electrostatic

Equilibrium 720 26.4 Sources of Electric Potential 722 26.5 Capacitance and Capacitors 724 26.6 The Energy Stored in a Capacitor 729 26.7 Dielectrics 730 SUMMARY 735


Chapter 27 Current and Resistance 742 27.1 The Electron Current 743 27.2 Creating a Current 745 27.3 Current and Current Density 749 27.4 Conductivity and Resistivity 753 27.5 Resistance and Ohm’s Law 755 SUMMARY 760


Chapter 28 Fundamentals of Circuits 766 28.1 Circuit Elements and Diagrams 767 28.2 Kirchhoff’s Laws and the Basic Circuit 768 28.3 Energy and Power 771 28.4 Series Resistors 773 28.5 Real Batteries 775 28.6 Parallel Resistors 777 28.7 Resistor Circuits 780 28.8 Getting Grounded 782 28.9 RC Circuits 784 SUMMARY 788


Chapter 29 The Magnetic Field 796 29.1 Magnetism 797 29.2 The Discovery of the Magnetic Field 798 29.3 The Source of the Magnetic Field: Moving

Charges 800 29.4 The Magnetic Field of a Current 802 29.5 Magnetic Dipoles 806 29.6 Ampère’s Law and Solenoids 809 29.7 The Magnetic Force on a Moving

Charge 815 29.8 Magnetic Forces on Current-Carrying

Wires 820 29.9 Forces and Torques on Current Loops 823 29.10 Magnetic Properties of Matter 824 SUMMARY 828


Chapter 30 Electromagnetic Induction 836 30.1 Induced Currents 837 30.2 Motional emf 838 30.3 Magnetic Flux 842 30.4 Lenz’s Law 845 30.5 Faraday’s Law 848 30.6 Induced Fields 852 30.7 Induced Currents: Three

Applications 855 30.8 Inductors 857 30.9 LC Circuits 861 30.10 LR Circuits 863 SUMMARY 867


Chapter 31 Electromagnetic Fields and Waves 876

31.1 E or B? It Depends on Your Perspective 877

31.2 The Field Laws Thus Far 882 31.3 The Displacement Current 883 31.4 Maxwell’s Equations 886 31.5 ADVANCED TOPIC Electromagnetic

Waves 888 31.6 Properties of Electromagnetic

Waves 893 31.7 Polarization 896 SUMMARY 899


Chapter 32 AC Circuits 905 32.1 AC Sources and Phasors 906 32.2 Capacitor Circuits 908 32.3 RC Filter Circuits 910 32.4 Inductor Circuits 913 32.5 The Series RLC Circuit 914 32.6 Power in AC Circuits 918 SUMMARY 922


Part VI Electricity and Magnetism 928KNOWLEDGE STRUCTURE


xx Detailed Contents

Part VII Optics OVERVIEW The Story of Light 929

Part VIII Relativity and Quantum Physics

OVERVIEW Contemporary Physics 1021

Chapter 36 Relativity 1022 36.1 Relativity: What’s It All About? 1023 36.2 Galilean Relativity 1023 36.3 Einstein’s Principle of Relativity 1026 36.4 Events and Measurements 1029 36.5 The Relativity of Simultaneity 1032 36.6 Time Dilation 1035 36.7 Length Contraction 1039 36.8 The Lorentz Transformations 1043 36.9 Relativistic Momentum 1048 36.10 Relativistic Energy 1051 SUMMARY 1057


Chapter 37 The Foundations of Modern Physics 1063

37.1 Matter and Light 1064 37.2 The Emission and Absorption of

Light 1064 37.3 Cathode Rays and X Rays 1067 37.4 The Discovery of the Electron 1069 37.5 The Fundamental Unit of Charge 1072 37.6 The Discovery of the Nucleus 1073 37.7 Into the Nucleus 1077 37.8 Classical Physics at the Limit 1079 SUMMARY 1080


Chapter 38 Quantization 1085 38.1 The Photoelectric Effect 1086 38.2 Einstein’s Explanation 1089 38.3 Photons 1092 38.4 Matter Waves and Energy

Quantization 1096 38.5 Bohr’s Model of Atomic

Quantization 1099 38.6 The Bohr Hydrogen Atom 1103 38.7 The Hydrogen Spectrum 1108 SUMMARY 1112


Chapter 33 Wave Optics 930 33.1 Models of Light 931 33.2 The Interference of Light 932 33.3 The Diffraction Grating 937 33.4 Single-Slit Diffraction 940 33.5 ADVANCED TOPIC A Closer Look at

Diffraction 944 33.6 Circular-Aperture Diffraction 947 33.7 The Wave Model of Light 948 33.8 Interferometers 950 SUMMARY 953


Chapter 34 Ray Optics 960 34.1 The Ray Model of Light 961 34.2 Reflection 963 34.3 Refraction 966 34.4 Image Formation by Refraction at a Plane

Surface 971 34.5 Thin Lenses: Ray Tracing 972 34.6 Thin Lenses: Refraction Theory 978 34.7 Image Formation with Spherical

Mirrors 983 SUMMARY 988


Chapter 35 Optical Instruments 995 35.1 Lenses in Combination 996 35.2 The Camera 997 35.3 Vision 1001 35.4 Optical Systems That Magnify 1004 35.5 Color and Dispersion 1008 35.6 The Resolution of Optical

Instruments 1010 SUMMARY 1015


Part VII Optics 1020KNOWLEDGE STRUCTURE


Detailed Contents xxi

Chapter 39 Wave Functions and Uncertainty 1118

39.1 Waves, Particles, and the Double-Slit Experiment 1119

39.2 Connecting the Wave and Photon Views 1122

39.3 The Wave Function 1124 39.4 Normalization 1126 39.5 Wave Packets 1128 39.6 The Heisenberg Uncertainty

Principle 1131 SUMMARY 1135


Chapter 40 One-Dimensional Quantum Mechanics 1141

40.1 The Schrödinger Equation 1142 40.2 Solving the Schrödinger Equation 1145 40.3 A Particle in a Rigid Box: Energies and

Wave Functions 1147 40.4 A Particle in a Rigid Box: Interpreting

the Solution 1150 40.5 The Correspondence Principle 1153 40.6 Finite Potential Wells 1155 40.7 Wave-Function Shapes 1160 40.8 The Quantum Harmonic

Oscillator 1162 40.9 More Quantum Models 1165 40.10 Quantum-Mechanical Tunneling 1168 SUMMARY 1173


Chapter 41 Atomic Physics 1178 41.1 The Hydrogen Atom: Angular

Momentum and Energy 1179 41.2 The Hydrogen Atom: Wave Functions

and Probabilities 1182 41.3 The Electron’s Spin 1185 41.4 Multielectron Atoms 187 41.5 The Periodic Table of the Elements 1190 41.6 Excited States and Spectra 1193 41.7 Lifetimes of Excited States 1198 41.8 Stimulated Emission and Lasers 1200 SUMMARY 1205


Chapter 42 Nuclear Physics 1210 42.1 Nuclear Structure 1211 42.2 Nuclear Stability 1214 42.3 The Strong Force 1217 42.4 The Shell Model 1218 42.5 Radiation and Radioactivity 1220 42.6 Nuclear Decay Mechanisms 1225 42.7 Biological Applications of Nuclear

Physics 1230 SUMMARY 1234


Part VIII Relativity and Quantum Physics 1240

Appendix A Mathematics Review A-1 Appendix B Periodic Table of Elements A-4 Appendix C Atomic and Nuclear Data A-5 Answers to Stop to Think Questions and

Odd-Numbered Problems A-9

Credits C-1 Index I-1

KNOWLEDGE STRUCTURE



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