College physics reasoning and relationships

COLLEGE PHYSICS
Reasoning and Relationships


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COLLEGE PHYSICS
Reasoning and Relationships

Nicholas J. Giordano
PURDU E U N I VE RS I TY

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College Physics: Reasoning and
Relationships, First Edition

© 2010 Brooks/Cole, Cengage Learning

Nicholas J. Giordano

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Brief Table of Contents
VOLUME I

VOLUME 2

Mechanics, Waves & Thermal
Physics

Electromagnetism, Optics &
Modern Physics

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Introduction 1
Motion, Forces, and Newton’s Laws 26
Forces and Motion in One Dimension 54
Forces and Motion in Two and Three
Dimensions 91
Circular Motion and Gravitation 130
Work and Energy 165
Momentum, Impulse, and Collisions 205
Rotational Motion 240
Energy and Momentum of Rotational
Motion 279
Fluids 309
Harmonic Motion and Elasticity 348

Waves 378
Sound 406
Temperature and Heat 433
Gases and Kinetic Theory 468
Thermodynamics 492

17
18
19
20
21
22
23
24
25
26
27
28
29
30
31

Electric Forces and Fields 529
Electric Potential 564
Electric Currents and Circuits 601
Magnetic Fields and Forces 644
Magnetic Induction 687
Alternating-Current Circuits and
Machines 723
Electromagnetic Waves 761

Geometrical Optics 795
Wave Optics 840
Applications of Optics 880
Relativity 917
Quantum Theory 954
Atomic Theory 986
Nuclear Physics 1021
Physics in the 21st Century 1059

Appendix A: Reference Tables A-1
Appendix B: Mathematical Review A-9
Answers to Concept Checks and OddNumbered Problems A-15
Index I-1

BRIEF CONTENTS

v


Table of Contents
PREFACE

xiii

Chapter 1

Introduction
1.1
1.2
1.3

1.4
1.5
1.6
1.7
1.8

1

THE PURPOSE OF PHYSICS

2

PROBLEM SOLVING IN PHYSICS: REASONING AND RELATIONSHIPS
DEALING WITH NUMBERS

9

PHYSICAL QUANTITIES AND UNITS OF MEASURE
DIMENSIONS AND UNITS

12

ALGEBR A AND SIMULTANEOUS EQUATIONS
TRIGONOMETRY
VECTORS

3

4

14

15

17

Chapter 2

© comstock Images/Jupiterimages

Motion, Forces, and Newton’s Laws

vi

CONTENTS

2.1
2.2
2.3
2.4
2.5
2.6

ARISTOTLE’S MECHANICS
WHAT IS MOTION?

26

27

29

38
NEWTON’S LAWS OF MOTION 40
THE PRINCIPLE OF INERTIA

WHY DID IT TAKE NEWTON TO DISCOVER NEWTON’S LAWS?
THINKING ABOUT THE LAWS OF NATURE

45

46

Chapter 3

Forces and Motion in One Dimension

54

3.1
3.2
3.3
3.4
3.5

MOTION OF A SPACECR AF T IN INTERSTELLAR SPACE

3.6
3.7
3.8

REASONING AND RELATIONSHIPS: FINDING THE MISSING PIECE

NORMAL FORCES AND WEIGHT
ADDING FRICTION TO THE MIX
FREE FALL

55

59
63

68

CABLES, STRINGS, AND PULLEYS: TR ANSMIT TING FORCES FROM HERE
TO THERE 72
PAR ACHUTES, AIR DR AG, AND TERMINAL VELOCIT Y
LIFE AS A BACTERIUM

82

79

75


Chapter 4

Forces and Motion in Two and Three Dimensions

91

4.1
4.2
4.3
4.4
4.5

107

STATICS

92
99

PROJECTILE MOTION

A FIRST LOOK AT REFERENCE FR AMES AND RELATIVE VELOCIT Y

110

FURTHER APPLICATIONS OF NEWTON’S LAWS

DETECTING ACCELER ATION: REFERENCE FR AMES AND THE WORKINGS
OF THE EAR 117

4.6

PROJECTILE MOTION REVISITED: THE EFFECT OF AIR DR AG

119

Chapter 5

Circular Motion and Gravitation
UNIFORM CIRCULAR MOTION

131

E X AMPLES OF CIRCULAR MOTION
NEWTON’S LAW OF GR AVITATION

138
145

PLANETARY MOTION AND KEPLER’S LAWS

© Joseph Van Os/Getty Images

5.1
5.2
5.3
5.4
5.5
5.6

130

150

155

MOONS AND TIDES

DEEP NOTIONS CONTAINED IN NEWTON’S LAW
OF GR AVITATION 156

Chapter 6

Work and Energy

165

6.1
6.2
6.3
6.4
6.5

FORCE, DISPLACEMENT, AND WORK

6.6
6.7
6.8

THE NATURE OF NONCONSERVATIVE FORCES: WHAT IS FRICTION ANY WAY?

166

KINETIC ENERGY AND THE WORK–ENERGY THEOREM

170

174

POTENTIAL ENERGY

MORE POTENTIAL ENERGY FUNCTIONS

182

CONSERVATIVE VERSUS NONCONSERVATIVE FORCES
AND CONSERVATION OF ENERGY 189
POWER

192

193

WORK, ENERGY, AND MOLECULAR MOTORS

195

Chapter 7

Momentum, Impulse, and Collisions
7.1
7.2
7.3
7.4

7.5
7.6
7.7
7.8

MOMENTUM

206

FORCE AND IMPULSE

208

CONSERVATION OF MOMENTUM
COLLISIONS

205

211

213

USING MOMENTUM CONSERVATION TO ANALYZE INELASTIC EVENTS
CENTER OF MASS

223

226

A BOUNCING BALL AND MOMENTUM CONSERVATION

231

THE IMPORTANCE OF CONSERVATION PRINCIPLES IN PHYSICS

232

CONTENTS

vii


Chapter 8

Rotational Motion
8.1
8.2
8.3
8.4
8.5
8.6

240
241

DESCRIBING ROTATIONAL MOTION

TORQUE AND NEWTON’S LAWS FOR ROTATIONAL MOTION
MOMENT OF INERTIA

247

252

ROTATIONAL EQUILIBRIUM

260
263

ROTATIONAL DYNAMICS

COMBINED ROTATIONAL AND TR ANSLATIONAL MOTION

267

Chapter 9

Energy and Momentum of Rotational Motion
9.1
9.2
9.3
9.4

KINETIC ENERGY OF ROTATION

9.5
9.6

THE VECTOR NATURE OF ROTATIONAL MOTION: GYROSCOPES

280

CONSERVATION OF ENERGY AND ROTATIONAL MOTION
ANGULAR MOMENTUM

ANGULAR MOMENTUM AND KEPLER’S SECOND LAW
OF PLANETARY MOTION 293
CATS AND OTHER ROTATING OBJECTS

© Corbis/Jupiterimages

Fluids

297

309

10.1
10.2
10.3
10.4
10.5

PRESSURE AND DENSIT Y

10.6
10.7

REAL FLUIDS: A MOLECULAR VIEW

310

314
HYDR AULICS AND PASCAL’S PRINCIPLE 321
FLUIDS AND THE EFFECT OF GR AVIT Y

BUOYANCY AND ARCHIMEDES’S PRINCIPLE

324

FLUIDS IN MOTION: CONTINUIT Y
AND BERNOULLI’S EQUATION 328
TURBULENCE

334

339

Chapter 11

Harmonic Motion and Elasticity
11.1
11.2
11.3
11.4
11.5
11.6

CONTENTS

284

287

Chapter 10

viii

279

348

GENER AL FEATURES OF HARMONIC MOTION
E X AMPLES OF SIMPLE HARMONIC MOTION

360
STRESS, STR AIN, AND HOOKE’S LAW 362
DAMPING AND RESONANCE 366
DETECTING SMALL FORCES 368
HARMONIC MOTION AND ENERGY

348
352

294


Chapter 12

Waves

12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9

378

379
381
E X AMPLES OF WAVES 385
WHAT IS A WAVE?

DESCRIBING WAVES

THE GEOMETRY OF A WAVE: WAVE FRONTS

389

390

SUPERPOSITION AND INTERFERENCE

392
REFR ACTION 394
REFLECTION

394

STANDING WAVES

SEISMIC WAVES AND THE STRUCTURE OF THE EARTH

396

Chapter 13

Sound
13.1
13.2
13.3
13.4
13.5
13.6
13.7

406

SOUND IS A LONGITUDINAL WAVE

406

AMPLITUDE AND INTENSIT Y OF A SOUND WAVE

414

STANDING SOUND WAVES
BEATS

410

418

REFLECTION AND SCAT TERING OF SOUND

420

420

THE DOPPLER EFFECT

425

APPLICATIONS

Chapter 14

Temperature and Heat
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8

433

THERMODYNAMICS: APPLYING PHYSICS TO A “SYSTEM”
TEMPER ATURE AND HEAT

434

434

THERMAL EQUILIBRIUM AND THE ZEROTH LAW OF THERMODYNAMICS
PHASES OF MAT TER AND PHASE CHANGES

438

439

448
452

THERMAL E XPANSION
HEAT CONDUCTION
CONVECTION

455

HEAT FLOW BY R ADIATION

456

Chapter 15

15.1
15.2
15.3
15.4
15.5
15.6

MOLECULAR PICTURE OF A GAS

468
469

IDEAL GASES: AN E XPERIMENTAL PERSPECTIVE
IDEAL GASES AND NEWTON’S LAWS
KINETIC THEORY
DIFFUSION

476

478

483

DEEP PUZZLES IN KINETIC THEORY

487

470

© Radius Images/Jupiterimages

Gases and Kinetic Theory

CONTENTS

ix


Chapter 16

© Andy Moore/photolibrary/Jupiterimages

Thermodynamics

492

16.1

THERMODYNAMICS IS ABOUT THE WAY A SYSTEM E XCHANGES ENERGY
WITH ITS ENVIRONMENT 493

16.2

THE ZEROTH LAW OF THERMODYNAMICS AND
THE MEANING OF TEMPER ATURE 494

16.3

THE FIRST LAW OF THERMODYNAMICS AND
THE CONSERVATION OF ENERGY 494

16.4
16.5

THERMODYNAMIC PROCESSES

16.6
16.7
16.8
16.9
16.10

HEAT ENGINES AND OTHER THERMODYNAMIC DEVICES

499

REVERSIBLE AND IRREVERSIBLE PROCESSES AND
THE SECOND LAW OF THERMODYNAMICS 508
ENTROPY

509

516

THE THIRD LAW OF THERMODYNAMICS AND ABSOLUTE ZERO
THERMODYNAMICS AND PHOTOSYNTHESIS

519

520

CONVERTING HEAT ENERGY TO MECHANICAL ENERGY AND THE ORIGIN
OF THE SECOND LAW OF THERMODYNAMICS 521

Chapter 17

Electric Forces and Fields
17.1
17.2
17.3
17.4
17.5
17.6
17.7

529

EVIDENCE FOR ELECTRIC FORCES: THE OBSERVATIONAL FACTS

531

ELECTRIC FORCES AND COULOMB’S LAW
THE ELECTRIC FIELD

530

537

CONDUCTORS, INSULATORS, AND THE MOTION OF ELECTRIC CHARGE
ELECTRIC FLUX AND GAUSS’S LAW

541

546

APPLICATIONS: DNA FINGERPRINTING

553

“WHY IS CHARGE QUANTIZED?” AND OTHER DEEP QUESTIONS

554

Chapter 18

Electric Potential
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8

564

565

ELECTRIC POTENTIAL: VOLTAGE 570
ELECTRIC POTENTIAL ENERGY

EQUIPOTENTIAL LINES AND SURFACES

579

581
DIELECTRICS 588
CAPACITORS

ELECTRICIT Y IN THE ATMOSPHERE

590

BIOLOGICAL E X AMPLES AND APPLICATIONS

592

ELECTRIC POTENTIAL ENERGY REVISITED: WHERE IS THE ENERGY?

592

Chapter 19

Electric Currents and Circuits
19.1
19.2
19.3
19.4

x

CONTENTS

601

ELECTRIC CURRENT: THE FLOW OF CHARGE
BAT TERIES

602

604

CURRENT AND VOLTAGE IN A RESISTOR CIRCUIT

606

DC CIRCUITS: BAT TERIES, RESISTORS, AND KIRCHHOFF’S RULES

612


19.5
19.6
19.7
19.8
19.9
19.10

DC CIRCUITS: ADDING CAPACITORS

625

MAKING ELECTRICAL MEASUREMENTS: AMMETERS AND VOLTMETERS
RC CIRCUITS AS FILTERS

629

630

ELECTRIC CURRENTS IN THE HUMAN BODY 632
HOUSEHOLD CIRCUITS 632
T E M P E R AT U R E D E P E N D E N C E O F R E S I S TA N C E AND
SUPERCONDUCTIVIT Y 634

Chapter 20

Magnetic Fields and Forces

644

20.1
20.2
20.3
20.4
20.5
20.6

SOURCES OF MAGNETIC FIELDS

645

20.7
20.8
20.9
20.10
20.11

CALCULATING THE MAGNETIC FIELD: AMPÈRE’S LAW

MAGNETIC FORCES INVOLVING BAR MAGNETS

649

651

MAGNETIC FORCE ON A MOVING CHARGE

656

MAGNETIC FORCE ON AN ELECTRIC CURRENT

TORQUE ON A CURRENT LOOP AND MAGNETIC MOMENTS

658

MOTION OF CHARGED PARTICLES IN THE PRESENCE OF ELECTRIC AND MAGNETIC
FIELDS 659

662

© Cengage Learning/Charles D. Winters

MAGNETIC MATERIALS: WHAT GOES ON INSIDE?

666

669
APPLICATIONS OF MAGNETISM 672
THE EARTH’S MAGNETIC FIELD

THE PUZZLE OF A VELOCIT Y-DEPENDENT FORCE

675

Chapter 21

Magnetic Induction
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8

687
688

689

WHY IS IT CALLED ELECTROMAGNETISM?
MAGNETIC FLUX AND FAR ADAY’S LAW

LENZ’S LAW AND WORK–ENERGY PRINCIPLES
INDUCTANCE
RL CIRCUITS

696

701
704

ENERGY STORED IN A MAGNETIC FIELD
APPLICATIONS

707

710

THE PUZZLE OF INDUCTION FROM A DISTANCE

714

Chapter 22

Alternating-Current Circuits and Machines
22.1
22.2

22.3
22.4
22.5
22.6
22.7
22.8
22.9
22.10
22.11

GENER ATION OF AC VOLTAGES

724

ANALYSIS OF AC RESISTOR CIRCUITS
AC CIRCUITS WITH CAPACITORS
AC CIRCUITS WITH INDUCTORS
LC CIRCUITS
RESONANCE

723

726

731
734

736
738

AC CIRCUITS AND IMPEDANCE

740

FREQUENCY-DEPENDENT BEHAVIOR OF AC CIRCUITS: A CONCEPTUAL RECAP
TR ANSFORMERS
MOTORS

743

746

748

WHAT CAN AC CIRCUITS DO THAT DC CIRCUITS CANNOT?

750

CONTENTS

xi


Chapter 23

Electromagnetic Waves

761

23.1

23.2
23.3
23.4

THE DISCOVERY OF ELECTROMAGNETIC WAVES

23.5
23.6
23.7
23.8

GENER ATION AND PROPAGATION OF ELECTROMAGNETIC WAVES

PROPERTIES OF ELECTROMAGNETIC WAVES

762
763

ELECTROMAGNETIC WAVES CARRY ENERGY AND MOMENTUM

765

T YPES OF ELECTROMAGNETIC R ADIATION: THE ELECTROMAGNETIC
SPECTRUM 770

775

779
DOPPLER EFFECT 783
POLARIZATION

DEEP CONCEPTS AND PUZZLES CONNECTED WITH ELECTROMAGNETIC
WAVES 786

Chapter 24

Geometrical Optics

© Charles Gupton/Stone/Getty Images

24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8

795

R AY (GEOMETRICAL) OPTICS

796

REFLECTION FROM A PLANE MIRROR: THE LAW OF REFLECTION
REFLECTIONS AND IMAGES PRODUCED BY CURVED MIRRORS
LENSES

797

800

REFR ACTION

808

817
822

HOW THE EYE WORKS

OPTICS IN THE ATMOSPHERE
ABERR ATIONS

826

828

Chapter 25

Wave Optics
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8

25.9
25.10

840

COHERENCE AND CONDITIONS FOR INTERFERENCE
THE MICHELSON INTERFEROMETER
THIN-FILM INTERFERENCE

841

844

847

LIGHT THROUGH A SINGLE SLIT: QUALITATIVE BEHAVIOR
DOUBLE-SLIT INTERFERENCE: YOUNG’S E XPERIMENT

854

855

SINGLE-SLIT DIFFR ACTION: INTERFERENCE OF LIGHT FROM A SINGLE SLIT
DIFFR ACTION GR ATINGS

OPTICAL RESOLUTION AND THE R AYLEIGH CRITERION
WHY IS THE SK Y BLUE?

858

861
864

869

T H E N AT U R E O F L I G H T: W A V E O R PA R T I C L E ?

870

Chapter 26

Applications of Optics
26.1

APPLICATIONS OF A SINGLE LENS: CONTACT LENSES, EYEGLASSES, AND THE
MAGNIF YING GLASS 880

26.2
MICROSCOPES 888
26.3 TELESCOPES 892

xii

CONTENTS

880


26.4
26.5

26.6
26.7

CAMER AS

899

905
OPTICAL FIBERS 908
CDS AND DVDS

910

MICROSCOPY WITH OPTICAL FIBERS

Chapter 27

27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.12

917

NASA/JPL-Caltech/University of Arizona/STScI

Relativity

918
THE POSTULATES OF SPECIAL RELATIVIT Y 919
TIME DILATION 921
SIMULTANEIT Y IS NOT ABSOLUTE 927
LENGTH CONTR ACTION 928
ADDITION OF VELOCITIES 932
RELATIVISTIC MOMENTUM 935
WHAT IS “MASS”? 937
MASS AND ENERGY 938
NEWTON’S MECHANICS AND RELATIVIT Y

THE EQUIVALENCE PRINCIPLE AND GENER AL RELATIVIT Y
RELATIVIT Y AND ELECTROMAGNETISM
WHY RELATIVIT Y IS IMPORTANT

942

945

946

Chapter 28

Quantum Theory

28.1
28.2
28.3
28.4
28.5
28.6
28.7
28.8

954
955

PARTICLES, WAVES, AND “PARTICLE-WAVES”
PHOTONS

957

WAVELIKE PROPERTIES OF CLASSICAL PARTICLES
THE MEANING OF THE WAVE FUNCTION
TUNNELING

965

968

ELECTRON SPIN

970

976

DETECTION OF PHOTONS BY THE EYE
THE NATURE OF QUANTA: A FEW PUZZLES

978
979

Chapter 29

Atomic Theory
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8

986

STRUCTURE OF THE ATOM: WHAT’S INSIDE?
ATOMIC SPECTR A

987

991

BOHR’S MODEL OF THE ATOM

994

WAVE MECHANICS AND THE HYDROGEN ATOM
MULTIELECTRON ATOMS

1002

1004

CHEMICAL PROPERTIES OF THE ELEMENTS AND THE PERIODIC TABLE
APPLICATIONS

1007

1010

QUANTUM MECHANICS AND NEWTON’S MECHANICS: SOME PHILOSOPHICAL
ISSUES 1015

CONTENTS

xiii


Chapter 30

Nuclear Physics
30.1
30.2
30.3

30.4
30.5
30.6

1021

STRUCTURE OF THE NUCLEUS: WHAT’S INSIDE?

1022

NUCLEAR REACTIONS: SPONTANEOUS DECAY OF A NUCLEUS
STABILIT Y OF THE NUCLEUS: FISSION AND FUSION

1026

1037

1044

BIOLOGICAL EFFECTS OF R ADIOACTIVIT Y

APPLICATIONS OF NUCLEAR PHYSICS IN MEDICINE AND OTHER FIELDS

1051

QUESTIONS ABOUT THE NUCLEUS

© Photo Researchers/Alamy

Chapter 31

Physics in the 21st Century
31.1
31.2
31.3
31.4
31.5
31.6
31.7
31.8

COSMIC R AYS

1059

1060

MAT TER AND ANTIMAT TER

1061
1064

QUANTUM ELECTRODYNAMICS

ELEMENTARY PARTICLE PHYSICS: THE STANDARD MODEL
THE FUNDAMENTAL FORCES OF NATURE

1065

1070

ELEMENTARY PARTICLE PHYSICS: IS THIS THE FINAL ANSWER?
ASTROPHYSICS AND THE UNIVERSE

PHYSICS AND INTERDISCIPLINARY SCIENCE
APPENDIX A: REFERENCE TABLES

1074

1074
1078

A-1

APPENDIX B: MATHEMATICAL REVIEW

A-9

ANSWERS TO CONCEPT CHECKS AND ODD-NUMBERED PROBLEMS
INDE X

xiv

CONTENTS

I-1

A-15

1048

Preface

College Physics: Reasoning and Relationships is designed for the many students
who take a college physics course. The majority of these students are not physics
majors (and don’t want to be) and their college physics course is the only physics class they will ever take. The topics covered in a typical college physics course
have changed little in recent years, and even decades. Indeed, except for many of
the applications, much of the physics covered here was well established more than
a century ago. Although the basic material covered may not be changing much,
the way it is taught should not necessarily stay the same.

GOALS OF THIS BOOK
Reasoning and Relationships
Students often view physics as merely a collection of loosely related equations.
We who teach physics work hard to overcome this perception and help students
understand how our subject is part of a broader science context. But what does
“understanding” in this context really mean?
Many physics textbooks assume understanding will result if a solid problemsolving methodology is introduced early and followed strictly. Students in this
model can be viewed as successful if they deal with a representative collection of
quantitative problems. However, physics education research has shown that students can succeed in such narrow problem-solving tasks and at the same time have
fundamentally flawed notions of the basic principles of physics. For these students,
physics is simply a collection of equations and facts without a fi rm connection
to the way the world works. Although students do need a solid problem-solving
framework, I believe such a framework is only one component to learning physics. For real learning to occur, students must know how to reason and must see
the relationships between the ideas of physics and their direct experiences. Until
the reasoning is sound and the relationships are clear, fundamental learning will
remain illusive.
The central theme of this book is to weave reasoning and relationships into
the way we teach introductory physics. Three important results of this approach

are the following:
1. Establishing the relationship between forces and motion.
2. A systematic approach to problem solving.
3. Reasoning and relationship problems.

PREFACE

xv


From Chapter 2, page 45

|

W H Y D I D I T TA K E N E W T O N T O
D I S CO V E R N E W T O N ’ S L A W S ?
S

Newton’s
second law
tells us that the acceleration of an object is given by a 5
S
S
1 g F 2 /m, where g F is the total force acting on the object. In the simplest situations,
S
there may only be one or two forces acting on an object, and g F is then the sum
of these few forces. In some cases, however, there may be a very large number of
forces acting on an object. Multiple forces can make things appear to be very complicated, which is perhaps why the correct laws of motion—Newton’s laws—were
not discovered sooner.

Forces on a Swimming Bacterium
Figure 2.32 shows a photo of the single-celled bacterium Escherichia coli, usually
referred to as E. coli. An individual E. coli propels itself by moving thin strands of
agella. Most E.
agella as in the photo in Figure 2.32A, but to understand their
coli
agellum as sketched
agellum is fairly rigid, and because it has a spiral shape, one can
think of it as a small propeller. AnSE. coli bacterium moves about by rotating this
propeller, thereby exerting a force SF w on the nearby water. According to Newton’s
third law, the water exerts a force F E of equal magnitude and opposite direction on
the E. coli, as sketched in SFigure 2.32B. One might be tempted to apply Newton’s
second law with the force F E and conclude that the E. coli will move with an acceleration that is proportional to this force. However, this is incorrect because we have
not included the forces from the water on the body of the E. coli. These forces are
also indicated in Figure 2.32B; to properly describe the total force from the water,
we must draw in many force vectors, pushing the E. coli in virtually all directions.
At the molecular level, we can understand these forces as follows. We know that
water is composed of molecules that are in constant motion, and these water molecules bombard the E. coli from all sides. Each time a water molecule collides with
the E. coli, the molecule exerts a force on the bacterium, much like the collision of
the baseball and bat in Figure 2.30. As we saw in that case, the two colliding objects
both experience a recoil force, another example of action–reaction forces. So, in
the present case, the E. coli and the water molecule exert forces on each other. An
individual E. coli is not very large, but a water molecule is much smaller than the
bacterium, and the force from one such collision will have only a small effect on the

2. A systematic approach to problem solving.
Every worked example follows a five-step format.
The fi rst step is to “Recognize the principle” that
is key to the problem. This step helps students
see the “big picture” the problem illustrates. The

other steps in the problem-solving process are
“Sketch the problem,” “Identify the relationships,” “Solve,” and “What does it mean?” The
last step emphasizes the key principles once more
and often describes how
w
the problem relates to
the real world. Explicit
S
v
S
problem-solving strateL
B
gies are also given for
major classes of quantitaClosed path
tive problems, such as
Example 21.3.
conservation of mechanical energy.

© Dr. Dennis Kunkel/Visuals Unlimited

1. Establishing the relationship between forces and
motion. All of Chapter 2 is
devoted to Newton’s laws of
motion and what they tell
us about the way force and
motion are related. This is the
central thread of mechanics.
Armed with an understanding of the proper relationship between kinematics and
forces, students can then
reason about a variety of

problems in mechanics such
as “nonideal” cases in which
the acceleration is not constant, as found for projectiles
with air drag.

A

S
S

Flagellum

B
A E. coli use the
action–reaction principle to propel
themselves. An individual E. coli

Using Lenz’s Law to Find the Direction
of an Induced Current
eld is constant and is
directed into the plane of the drawing. If the bar is sliding to the right, use Lenz’s law
nd the direction of the induced current.
RECOGNIZE T HE PRINCIPLE

eld that opposes the change
ux through the circuit loop.
SK E TCH T HE PROBLEM

Following our “Applying Lenz’s Law” problem-solving strategy (step 2), the sketch
in Figure 21.12 shows a dashed, rectangular path. We are interested in the current

ux through this rectangle.
IDENT IF Y T HE REL AT IONSHIPS

ux
through the rectangular surface is directed into the plane. The area of this chosen surface is wL,
ux through the surface is B BwL. Because the bar is
sliding to the right, B is increasing and is downward.
SOLV E

From Chapter 21, page 698

The induced emf produces an induced current that opposes the downward increase in
eld must be directed upward. Applying right-hand
eld direction is produced by a counterclockwise
induced current.

What does it mean?
ux through a given area may be “upward” or “downward,” and its magnitude may be increasing or decreasing with time. The induced emf always opposes
any changes
ux.

xvi

PREFACE

Fw

FE

P R O B L E M S O LV I N G

Applying Lenz’s Law: Finding the Direction of the Induced emf

RECOGNIZE T HE PRINCIPLE . The induced emf

SOLV E . Treat the perimeter of the surface as a wire

ux through the Lenz’s

runs along the perimeter of a surface crossed by
eld lines.

loop; suppose there is a current in this loop and
determine the direction of the resulting magnetic
eld. Find the current direction for which this
eld opposes the change in
ux. This current direction gives the sign
(i.e., the “direction”) of the induced emf.

ux through the surface is
increasing or decreasing with time.

Always consider what your answer means and
check that it makes sense.

law loop or path.
SK E TCH T HE PROBLEM, showing a closed path that

IDENT IF Y

From Chapter 21, page 698

3. Reasoning and relationship problems. Many realworld applications require
estimates for these quantities. Don’t worry or spend
RECOGNIZE T HE PRINCIPLE . Determine the key
time trying to obtain precise values of every quantity
physics ideas that are central to the problem and
an estimation of certain key
ex in
that connect the quantity you want to calculate with
parameters. For example, the
Fig. 3.23). Accuracy to within a factor of 3 or even
the quantities you know. In the examples found
ne because the goal is to calculate the
in this section, this physics involves motion with
approximate force on a car
quantity of interest to within an order of magnitude
constant acceleration.
bumper during a collision can
(a factor of 10). Don’t hesitate to use the Internet,
SK E TCH T HE PROBLEM. Make a drawing that
be found by making a few
the library, and (especially) your own intuition and
shows all the given information and everything else
experiences.
simplifying assumptions about
that you know about the problem. For problems
SOLV E . Since an exact mathematical solution is
in mechanics, your drawing should include all the

the collision and the way the
not required, cast the problem into one that is easy
forces, velocities, and so forth.
bumper deforms, and estimatto solve mathematically. In the examples in this
IDENT IF Y T HE REL AT IONSHIPS. Identify the
ing the mass of the car. Physisection, we were able to use the results for motion
important physics relationships; for problems
with constant acceleration.
cists fi nd these “back-of-theconcerning motion with constant acceleration, they
Always consider what your answer means and
are the relationships between position, velocity,
envelope” calculations very
check that it makes sense.
and acceleration in Table 3.1. For many reasoning
useful for gaining an intuitive
and relationships problems, values for some of the
As is often the case, practice is a very useful teacher.
understanding of a situation.
essential unknown quantities may not be given. You
must then use common sense to make reasonable
The ability to deal with such
problems requires a good
From Chapter 3, page 78
understanding of the key relationships in the problem and how fundamental
principles can be applied. Most textbooks completely ignore such problems,
but I believe students can, with a careful amount of coaching and practice,
learn to master the skills needed to be successful with these problems. This
kind of creative problem solving is a valuable skill for students in all areas.
P R O B L E M S O LV I N G

Dealing with Reasoning and Relationships Problems

Cars and Bumpers and Walls
Consider a car of mass 1000 kg colliding with a rigid concrete wall at a speed of
2.5 m/s (about 5 mi/h). This impact is a fairly low-speed collision, and the bumpers on
a modern car should be able to handle it without much damage to the car. Estimate
the force exerted by the wall on the car’s bumper.

S

F

At start of
collision

A
After collision,
bumper has
compressed a
distance Dx

B

Example 3.6.
When a car collides with a wall,
the wall exerts a force F on the
bumper. This force provides the
acceleration that stops the car.
B During the collision and before
the car comes to rest, the bumper

deforms by an amount x. The car
travels this distance while it comes
to a complete stop.
A

From Chapter 3, page 78

RECOGNIZE T HE PRINCIPLE

rst touches the wall
and ends when the car is stopped. To treat the problem approximately, we assume the
force on the bumper is constant during the collision period, so the acceleration is also
constant. We can then use our expressions from Table 3.1 to analyze the motion. Our
nd the car’s acceleration and then use it to calculate the associated
force exerted by the wall on the car from Newton’s second law.
SK E TCH T HE PROBLEM

Figure 3.24 shows a sketch of the car along with the force exerted by the wall on the
car. There are also two vertical forces—the force of gravity on the car and the normal
force exerted by the road on the car—but we have not shown them because we are
concerned here with the car’s horizontal (x) motion, which we can treat using F
ma for the components of force and acceleration along x.
IDENT IF Y T HE REL AT IONSHIPS

nd the car’s acceleration, we need to estimate either the stopping time or the
distance x traveled during this time. Let’s take the latter approach. We are given the
initial velocity (v 0
nal velocity (v 0). Both of these quantities
are in Equation 3.4:

v 2 5 v 20 1 2a 1 x 2 x0 2

(1)

PREFACE

xvii


Changing the Way Students View Physics

Myosin motor

ATP

Actin filament

P

ADP

ADP

ATP

Some molecular
motors move by “walking” along
long strands of a protein called
actin. These motors are the subject
of much current research. We can

use work–energy principles to
understand their behavior.

From Chapter 6, page 195

The relationships between physics and other areas of science are rapidly becoming
stronger and are transforming the way all fields of science are understood and practiced. Examples of this transformation abound, particularly in the life sciences. Many
students of college physics are engaged in majors relating to the life sciences, and the
manner in which they need and will use physics differs from only a few years ago.
For their benefit, and for the benefit of students in virtually all technical and even
nontechnical disciplines, textbooks must place a greater emphasis on how to apply
the reasoning of physics to real-world examples. Such examples come quite naturally
from the life sciences, but many everyday objects are filled with good applications
of fundamental physics principles as well. For instance, my discussion of molecular
motors in the context of work and
|
W O R K , E N E R G Y, A N D M O L E C U L A R M O T O R S
energy in Chapter
In Section 6.7, we discussed how our ideas about work, energy, and power can be
6 is unique, as
used to understand the behavior of motors and similar devices. The same ideas
are discussions of
apply to all types of motors, including the molecular motors that transport materiphotosynthesis as
als within and between cells. Several different types of molecular motors have been
discovered, one example of which is sketched in Figure 6.34. This motor is based
a thermodynamic
laments composed of actin
process in Chapter
molecules.
16 and electricity

lament in steps, much like a
laments
in the atmosphere
lament, so as
(lightning) in Chaplament relative to another. The operation of
ter 19. Students
your muscles is produced by these molecular motors.
must be made to
Calculating the Force Exerted by a Molecular Motor
see that physics is
The precise biochemical reactions involved in the myosin walking motion are not
relevant to their
completely understood. However, we do know that each step has a length of approxdaily lives and to
imately 5 nm (5 10 –9 m) and that the energy for this motor comes from a chemical
the things they fi nd
interesting.
Although much can be gained by bringing many new and current examples into
the text, traditional physics examples such as inclined planes, pulleys, and resistors in
series or parallel can still be useful pedagogical tools. A good example, however, must
do more than just illustrate a particular principle of physics; students should also
see clearly how the example can be expanded and generalized to other (and, I hope,
interesting) situations. The block-and-tackle example in Chapter 3 is one such case,
illustrating pulleys and tension forces in a traditional way but going on to describe
how this device can amplify forces. This theme of force amplification is revisited in
future chapters in discussions of torque and levers, work, hydraulics, and conservation of energy, and it is also applied to the mechanical function of the human ear.
Returning to key themes throughout the text gives students a deeper understanding of
fundamental physics principles and their relationship to real-world applications.
Encouraging student curiosity. Many important and fundamental ideas about the
world are ignored in most textbooks. By devoting some time to these ideas, this book
helps students see that physics can be extremely exciting and interesting. Such issues

include the following. (1) Why is the inertial mass equal to the gravitational mass?
(This question is mentioned in Chapter 3, revisited in the discussion of gravitation,
and mentioned again in Chapter 27 on relativity.) (2) What is “action-at-a-distance,”
and how does it really work? (The concept of a fi eld is mentioned in several places,
including but not limited to the sections on gravitation and Coulomb’s law.) (3) How
do we know the structure of Earth’s core? (4) What does color vision tell us about the
nature of light? These issues and others like them are essentially unmentioned in current texts, yet they get to the heart of physics and can stimulate student curiosity.
Starting where students are and going farther than you imagined possible. Many
students come to their college physics course with a common set of pre-Newtonian
misconceptions about physics. I believe the best way to help students overcome these

xviii

PREFACE


misconceptions is to address them directly and help students see where and how
their pre-Newtonian ideas fail. For this reason, College Physics: Reasoning and
Relationships devotes Chapter 2 to the fundamental relationships between force
and motion as Newton’s laws of motion are introduced. The key ideas are then
reinforced in Chapter 3 with careful discussions of several applications of Newton’s laws in one dimension. This approach allows us to get to the more interesting
material faster, and, in my experience, the students are more prepared for it then.
Building on prior knowledge. A good way to learn is to build from what is
already known and understood. (Learning scientists call this “scaffolding.”) This
book therefore revisits and builds on selected examples with a layered development, deepening and extending the analysis as new physical principles are
introduced. In typical cases, a topic is revisited two or three times, both within
a chapter and across several chapters. One example is the theme of amplifying
forces, which begins in Chapter 3. This theme reappears in a number of additional
topics, including the mechanics of the ear and the concepts of work and energy.
Layered or scaffolded development of concepts, examples, and problem topics

helps students see relationships between various physical principles.

From Chapter 3, page 74

Using Pulleys to Redirect a Force
cient way to transmit force from one place to another,
but they have an important limitation: they can only “pull,” and this force must be
directed along the direction in which the cable lies. In many situations, we need to
change the direction of a force, which can be accomplished by using an extremely
useful mechanical device called a pulley. A simple pulley is shown in Figure 3.21A;
it is just a wheel free to spin on an axle through its center, and it is arranged so that
a rope or cable runs along its edge without slipping. For simplicity, we assume both
the rope and the pulley are massless. Typically, a person pulls on one end of the rope
so as to lift an object connected to the other end. The pulley simply changes the
direction of the force associated with the tension in the rope as illustrated in Figure
3.21B, which shows the rope “straightened out” (i.e., with the pulley removed). In
either case—with or without the pulley in place—the person exerts a force F on
one end of the rope, and this force is equal to the tension. The tension is the same
everywhere along this massless rope, so the other end of the rope exerts a force
of magnitude T on the object. A comparison of the two arrangements in Figure
3.21—one with the pulley and one without—suggests the tension in the rope is the
same in the two cases, and in both cases the rope transmits a force of magnitude
T F from the person to the object.

S

F

S

T

S

T
S

F

A

B

A A simple pulley.
If the person exerts a force F on a
massless string, there is a tension T
in the string, and this tension force
can be used to lift an object.
B The string “straightened out.”
The pulley simply redirects the
force.

Work, Energy,
and Amplifying Forces
Amplifying
Forces
In Chapter 3, we encountered a device called the block and tackle and showed how

A pulley can do much more than simply redirect a force. Figure 3.22 shows a pulley
es forces by

gured as a block and tackle, a device used to lift heavy objects. To analyze this
a factor of two. We saw in Chapter 3 that if a person applies a force F to the rope,
case,
we
have
to
think
carefully
about
the
force
between
the
string
andportions
the surface
the tension in the rope is T
F. Because the pulley is suspended by two
ofof the
pulley.
have force
already
mentioned
that
the
does
nota slip
the rope,
theWe
upward

on the
pulley is 2T
and
therope
pulley
exerts
totalalong
force this
surface.
There
a which
frictional
force between
rope
and
surface
of the
pulley
2T on the
objectisto
it is connected,
that the
is, the
crate
in the
Figure
6.8. Let’s
now
wherever the two are in contact, which iscation
all along

thethe
bottom
half of
affects
work done
by the
the pulley
per- in
Figure
3.22. Since
the rope
does
relative
the pulley,
the rope
exertswill
a force
son. Suppose
the person
lifts
his not
end slip
of the
rope to
through
a distance
L. That
raise the pulley by half that amount, that is, a distance of L/2. You can see why by
noticing that when the pulley moves upward through a distance L/2, the sections of
the rope on both sides become shorter by this amount, so the end of the rope held

by the person must move a distance L.
When the pulley moves upward by a distance L/2, the crate is displaced by the
same amount. The work done by the pulley on the crate is equal to the total force of
the pulley on the crate (2T) multiplied by the displacement of the crate, which is L/2:
Won crate 5 2T1 L/2 2 5 TL
At the same time, the person does work on the end of the rope since he exerts a
force F T and the displacement of the end of the rope is L. The work done by the
person on the rope is equal to the force that he exerts on the rope (T) multiplied by
the displacement of the rope, which is L, so
Won rope 5 FL 5 TL

From Chapter 6, page 173

Thus, the work done on the rope is precisely equal to the work done on the crate.

T
T

Tension

2T
Crate

The person applies
a force T to the rope. The block
es this force, and
the total force applied to the crate
by the rope is 2T. However, when
he moves the end of the rope a distance L, the crate moves a distance
of only L/2.

PREFACE

xix


Going the extra step: reasoning and relationship problems. Many interesting real-world physics problems cannot be solved exactly with the mathematics
appropriate for a college physics course, but they can often be handled in an
approximate way using the simple methods (based on algebra and trigonometry)
developed in such a course. Professional physicists are familiar with these backof-the-envelope calculations. For instance, we may want to know the approximate
force on a skydiver’s knees when she hits the ground. The precise value of the
force depends on the details of the landing, but we are often interested in only an
approximate (usually order-of-magnitude) answer. We call such problems reasoning and relationship problems because solving them requires us to identify the
key physics relationships and quantities needed for the problem and that we also
estimate values of some important quantities (such as the mass of the skydiver and
how she flexes her knees) based on experience and common sense.
Reasoning and relationship problems provide physical insight and a chance to
practice critical thinking (reasoning), and they can help students see more clearly
the fundamental principles associated with a problem. A truly unique feature of
this book is the inclusion of these problems in both the worked examples and
the end-of-chapter problems. The ability to deal with this class of problems is an
extremely useful skill for all students, in all fields.
Problem solving: a key component to understanding. Although reasoning and
relationship problems are used to help students develop a broad understanding of
physics, this book also contains a strong component of traditional quantitative
problem solving. Quantitative problems are a component of virtually all college
physics courses, and students can benefit by developing a systematic approach to
such problems. College Physics: Reasoning and Relationships therefore places
extra emphasis on step-by-step approaches students can use in a wide range of
situations. This approach can be seen in the worked examples, which use a fivestep solution process: (1) recognize the physics principles central to the problem,

(2) draw a sketch showing the problem and all the given information, (3) identify the relationships between the known and unknown quantities, (4) solve for
the desired quantity, and (5) ask what the answer means and if it makes sense.
Explicit problem-solving strategies are also given for major classes of quantitative
problems, such as applying the conservation of mechanical energy.

P R O B L E M S O LV I N G

The electric force on
a charged particle can be found using Coulomb’s law
together with the principle of superposition.
SK E TCH T HE PROBLEM. Construct a drawing
(including a coordinate system) and show the
location and charge for each object in the problem.
Your drawing should also
show the directions of
S S
all the electric forces—F 1, F 2, and so forth—on the
particle(s) of interest.

SOLV E . The total force on a particle is the sum

(the superposition) of all the individual forces from
steps 2 and 3. Add these forces as vectors to get the
total force. When adding these vectors, it is usually
S
simplest
to work in terms of the components of F 1,
S
F 2, . . . along the coordinate axes.
Always consider what your answer means and

check that it makes sense.

P R O B L E M S O LV I N G

IDENT IF Y T HE REL AT IONSHIPS. Use Coulomb’s

Plan of Attack for Problems in Statics

nd the magnitudes of the
S S
RECOGNIZE THE PRINCIPLE. For an object to be in
forces F 1, F 2, . . . acting on the particle(s) of interest.
static equilibrium, the sum of all the forces on the
object must be zero. This principle leads to Equation
4.2, which can be applied to calculate any unknown
forces in the problem.
SKETCH THE PROBLEM. It is usually a good idea

to show the given information in a picture, which
should include a coordinate system. Figures 4.1
through 4.3 and the following examples provide
guidance and advice on choosing coordinate axes.
IDENTIFY THE RELATIONSHIPS.

From Chapter 4, page 95

xx

PREFACE

From Chapter 17, page 535

Calculating Forces with Coulomb’s Law

• Find all the forces acting on the object that is (or
should be) in equilibrium and construct a free-body
diagram showing all the forces on the object.

• Express all the forces on the object in terms of their
components along x and y.
• Apply the conditions3 a Fx and a Fy 0.
SOLVE. Solve the equations resulting from step 3 for
the unknown quantities. The number of equations
must equal the number of unknown quantities.

Always consider what your answer means and check
that it makes sense.


ORGANIZATION AND CONTENT
Translational motion. The organization of topics in this book follows largely
traditional lines with one exception. Forces and Newton’s laws of motion are
introduced in Chapter 2 along with basic defi ning relationships from kinematics.
In almost all other texts, kinematic equations are covered fi rst in the absence of
Newton’s laws, which obscures the cause of motion. This text presents the central
thread of all mechanics from the beginning, allowing students to see and appreciate the motivations for many kinematic relationships. Students can then address
and overcome common misconceptions early in the course. They are also able to
deal sooner with interesting and realistic problems that do not involve a constant
acceleration. When forces and Newton’s laws are introduced early, we can discuss
issues such as air drag and terminal velocity at an earlier stage, which avoids giving students the impression that physics problems are limited to the mathematics

of ideal cases. Chapters 2 and 3 are limited to one-dimensional problems for simplicity before moving on to two dimensions in Chapters 4 and 5. Major conservation principles (of energy and momentum) are introduced in Chapters 6 and 7
before moving on to rotational motion.
Rotational motion. In the same way that force is connected to acceleration in
Chapters 2 and 3 while introducing the variables of translational motion, torque
is connected to angular acceleration while the variables of rotational motion are
introduced in Chapter 8. Parallel development of topics in translational and rotational motion is direct and deliberate. The central thread in Chapters 8 and 9 is
once again Newton’s laws of motion, this time in rotational form.
Fluids. Chapter 10 discusses fluids, including the principles of Pascal, Archimedes, and Bernoulli.
Waves. Chapters 11 through 13 cover harmonic motion, waves, and sound.
Waves—moving disturbances that transport energy without transporting matter—provide a link to later topics in electromagnetism, light, and quantum
physics.
Thermal physics. Chapters 14 through 16 on thermal physics have conservation
of energy as their central thread. Thermodynamics is about the transfer of energy
between systems of particles and tells how changes in the energy of a system can
affect the system’s properties.
Electricity and magnetism. Chapters 17 through 23 keep conservation of energy
as an important thread, with additional development of concepts introduced
earlier such as that of a field (action-at-a-distance). The topic of magnetism brings
in the new concept of a velocity-dependent force. The importance of Maxwell’s
theory of electromagnetism is emphasized without undue mathematical details.
Light and optics. In Chapters 24 through 26, students can compare and contrast
properties of light that depend on its wave nature with properties that require a
particle (or ray) approach. Students can apply the principles of optics to model
how the human eye works, including the mechanism of color vision.
Twentieth-century physics. Students are introduced to the modern concepts of
relativity, quantum, atomic and nuclear physics in Chapters 27 through 31. Quantum physics reveals that matter, like light and other electromagnetic radiation, has
both particle and wave properties.

PREFACE

xxi


FEATURES OF THIS BOOK
Worked Examples
Worked examples are problems that are solved quantitatively within a chapter’s
main text. They are designed to teach sound problem-solving skills, and each
involves a principle or result that has just been introduced. The worked examples
also have other attributes:
• Extra emphasis is placed on step-by-step approaches that students can use
in a wide range of situations. All worked examples use a five-step solution
process: (1) recognize the physics principles central to the problem, (2) draw
a sketch showing the problem and all the given information, (3) identify the
relationships between the known and unknown quantities, (4) solve for the
desired quantity, and (5) ask what the answer means and if it makes sense.
Answers are boxed for clarity, and all examples emphasize the key fi nal step
of asking what the answer means, whether it makes sense, or what can be
learned from it.
• Some worked examples are designated with the symbol
as reasoning and
relationship problems, designed for back-of-the-envelope solutions. A reasoning and relationship problem requires an approximate mathematical solution, a rough estimate of one or two key unknown quantities, or both. These
examples and corresponding homework problems begin in Chapter 3, where
Section 3.6 introduces and explains the notions of estimating and reasoning.
Reasoning and relationship problems and examples are distributed throughout later chapters.
• Worked examples of special interest to life science students are designated
with the symbol .

Problem-Solving Strategies
The five-step problem-solving method is adapted to suit broad classes of problems
students will encounter, such as when applying Newton’s second law, using the

principles of conservation of momentum and energy, or finding the current in two
branches of a DC circuit. For these classes of problems, a problem-solving strategy
is highlighted within the chapter for special study emphasis.

From Chapter 6, page 187

At various points in the chapter are conceptual questions, called “Concept
Checks.” These questions are designed to make the student reflect on a fundamental issue. They may involve interpreting the content of a graph or drawing
a new graph to predict a relationship between quantities. Many Concept Check
questions are in multiple-choice format to facilitate their use in audience response
systems. Answers to Concept Checks are given at the end of the book. Full explanations of each answer are given in the Instructor’s Solutions Manual.

S

F

A
S

F

S

F

B

Concept Check 6.5.

xxii

PREFACE

Concept Checks

| Spring Forces and Newton’s Third Law
Figure 6.26 shows two identical springs. In both cases, a person exerts a force of
magnitude F on the right end of the spring. The left end of the spring in Figure
6.26A is attached to a wall, while the left end of the spring in Figure 6.26B is
held by another person, who exerts a force of magnitude F to the left. Which
statement is true?
(1) The spring in Figure 6.26A is stretched half as much as the spring in
Figure 6.26B.
(2) The spring in Figure 6.26A is stretched twice as much as the spring in
Figure 6.26B.
(3) The two springs are stretched the same amount.


Insights
EFFICIENCY OF A DIESEL ENGINE
A diesel engine is similar to a gasoline
internal combustion engine (Example
16.8). One difference is that a gasoline
engine ignites the fuel mixture with a
spark from a spark plug, whereas a
diesel engine ignites the fuel mixture
purely “by compression” (without a
spark). The compression of the fuel
mixture is therefore much greater in a
diesel engine, which leads to a higher

temperature in the hot reservoir.
According to Equation 16.21 and
Example 16.8, this higher temperature gives a higher theoretical limit
ciency of a diesel engine.

Each chapter contains several special marginal comments called “Insights” that
add greater depth to a key idea or reinforce an important message. For instance,
Insight 3.3 emphasizes the distinction between weight and mass, and Insight 16.1
explains why diesel engines are inherently more efficient than conventional gasoline internal combustion engines.

Diagrams with Additional Explanatory Labeling
Every college physics textbook contains line art with labeling. This book adds
another layer of labeling that explains the phenomenon being illustrated, much
as an instructor would explain a process or relationship in class. This additional
labeling is set off in a different style.
From Chapter 3, page 80

From Chapter 16, page 512

Slope a
g
(motion is like free fall)

Different ways to
produce an induced emf.

t

Time t

Time t

Dt

S

B

a 0 (air drag is
important here)
Different ways
to change FB
and produce an
induced emf

(1) Change B
v

vterm

terminal velocity

The skydiver’s
motion is initially like free fall;
compare with Figure 3.15 A .
Eventually, however, air drag
becomes as large as the force of
gravity and the skydiver reaches
her terminal velocity v term.

(2) Change area

Small B

(3) Rotate loop

From Chapter 21, page 696

Large B

(4) Move the loop

Chapter Summaries
To make the text more usable as a study tool, chapter summaries are presented in
a modified “study card” format. Concepts are classified into two major groups:
Key Concepts and Principles
Applications
Each concept is described in its own panel, often with an explanatory diagram.
This format helps students organize information for review and further study.
Relation between the electric field and the electric potential
Suppose the potential changes by an amount V over a distance x. The comeld along this direction is then
DV
Dx
eld thus has units of volts per meter (V/m).
E52

Dx

DV

Q
(18.30) (page 581)
C
This relation holds for any type of capacitor. For a parallel-plate capacitor, the
capacitance is
DV 5

e0 A
1 parallel-plate capacitor 2
d

V2

(18.18) (page 573)

Capacitors
Two parallel metal plates form a capacitor. The capacitance C of this structure
determines how easily charge can be stored on the plates. The charge on a capacitor is related to the magnitude of the potential difference between the plates by

C5

DV
Dx

E
V1

(18.31) (page 581)

V2

V1

Parallel plate
capacitor

Area

A

Q
d

Q

C

e0A
d

From Chapter 18, page 594

PREFACE

xxiii


End-of-Chapter Questions
Approximately 20 questions at the end of each chapter ask students to reflect on
and strengthen their understanding of conceptual issues. These questions are suitable for use in recitation sessions or other group work. Answers to questions designated SSM are provided in the Student Companion & Problem-Solving Guide,

and all questions are answered in the Instructor’s Solutions Manual.
13. Two workers are carrying a long, heavy steel beam (Fig. Q8.13).
Which one is exerting a larger force on the object? How can you
tell?

Figure Q8.13

From Chapter 8, page 273

End-of-Chapter Problems
Homework problems are designed to match the examples that are worked
throughout the chapter. Most of these problems are grouped according to the
matching chapter section. A fi nal list of “Additional Problems” contains problems that bring together ideas from across the chapter or from multiple chapters.
Unmarked problems are straightforward, and intermediate and challenging problems are indicated. Problems of special interest to life science students , reasoning and relationship problems , and problems whose solutions appear in the
Student Companion & Problem-Solving Guide SSM are so indicated. Answers to
odd-numbered problems appear at the end of the book.
6.

A bar magnet is thrust into a current loop as sketched in
Figure P21.6. Before the magnet reaches the center of the loop,
what is the direction of the induced current as seen by the
observer on the right, clockwise or counterclockwise?

S

N

From Chapter 21, page 718
Observer

Figure P21.6 Problems 6, 7, and 8.

ANCILLARIES
Using Technology to Enhance Learning
Enhanced WebAssign is the perfect solution to your homework management
needs. Designed by physicists for physicists, this system is a reliable and userfriendly teaching companion. Enhanced WebAssign is available for College Physics: Reasoning and Relationships, giving you the freedom to assign
• Selected end-of-chapter problems, algorithmically driven where appropriate
and containing an example of the student solution.

xxiv

PREFACE