A 50 kg toboggan is coasting

Cutnell & Johnson Physics

Eleventh Edition

DAVID YOUNG SHANE STADLER

Louisiana State University

VICE PRESIDENT AND DIRECTOR, SCIENCE Petra Recter

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iii

About the Authors

DAVID YOUNG received his Ph.D. in experimental condensed matter physics from Florida State University in 1998. He then held a

post-doc position in the Department of Chemistry and the Princeton

Materials Institute at Princeton University before joining the fac-

ulty in the Department of Physics and Astronomy at Louisiana State

University in 2000. His research focuses on the synthesis and char-

acterization of high-quality single crystals of novel electronic and

magnetic materials. The goal of his research group is to understand

the physics of electrons in materials under extreme conditions, i.e.,

at temperatures close to absolute zero, in high magnetic fi elds, and

under high pressure. He is the coauthor of over 200 research publica-

tions that have appeared in peer-reviewed journals, such as Physical Review B, Physical Review Letters, and Nature. Professor Young has taught introductory physics with the Cutnell & Johnson text since he

was a senior undergraduate over 20 years ago. He routinely lectures

to large sections, often in excess of 300 students. To engage such a

large number of students, he uses WileyPLUS, electronic response systems, tutorial-style recitation sessions, and in-class demonstra-

tions. Professor Young has received multiple awards for outstanding

teaching of undergraduates. David enjoys spending his free time with

his family, playing basketball, and working on his house.

I would like to thank my family for their continuous love and support.

—David Young

SH ANE STADLER Shane Stadler earned a Ph.D. in experi- mental condensed matter physics from Tulane University in 1998.

Afterwards, he accepted a National Research Council Postdoctoral

Fellowship with the Naval Research Laboratory in Washington, DC,

where he conducted research on artifi cially structured magnetic ma-

terials. Three years later, he joined the faculty in the Department of

Physics at Southern Illinois University (the home institution of John

Cutnell and Ken Johnson, the original authors of this textbook), be-

fore joining the Department of Physics and Astronomy at Louisiana

State University in 2008. His research group studies novel magnetic

materials for applications in the areas of spintronics and magnetic

cooling.

Over the past fi fteen years, Professor Stadler has taught the full

spectrum of physics courses, from physics for students outside the

sciences, to graduate-level physics courses, such as classical electro-

dynamics. He teaches classes that range from fewer than ten students

to those with enrollments of over 300. His educational interests are

focused on developing teaching tools and methods that apply to both

small and large classes, and which are applicable to emerging teach-

ing strategies, such as “fl ipping the classroom.”

In his spare time, Shane writes science fi ction/thriller novels.

I would like to thank my parents, George and Elissa, for their constant

support and encouragement. —Shane Stadler

C o u rt

es y D

av id

Y o u n g

C o u rt

es y S

h an

e S

ta d le

r

Dear Students and Inst ructors:

Welcome to college ph ysics! To the students:

We know there is a ne gative stigma associate

d with physics, and yo u yourself may har-

bor some trepidation a s you begin this course

. But fear not! We’re h ere to help. Whether y

ou’re worried about yo ur math profi ciency,

understanding the con cepts, or developing yo

ur problem-solving ski lls, the resources avail

able to you are designe d to address all of

these areas and more. Research has shown th

at learning styles vary greatly among student

s. Maybe some of you have a more visual

preference, or auditory preference, or some o

ther preferred learning modality. In any case,

the resources availabl e to you in this course

will satisfy all of these preferences and impro

ve your chance of succ ess. Take a moment to

explore below what th e textbook and

online course have to o ff er. We suspect that, a

s you continue to impr ove throughout the cou

rse, some of that initia l trepidation will be

replaced with exciteme nt.

To start, we have creat ed a new learning med

ium specifi c to this boo k in the form of a comp

rehensive set of LECTURE VIDE OS – one

for every section (259 in all). These animated

lectures (created and n arrated by the authors)

are 2–10 minutes in le ngth, and explain the

basic concepts and lear ning objectives of each

section. They are assig nable within WileyPLU

S and can be paired wi th follow-up ques-

tions that are gradable. In addition to supplem

enting traditional lectu ring, the videos can be

used in a variety of wa ys, including fl ipping

the classroom, a comp lete set of lectures for o

nline courses, and revi ewing for exams. Next

, we have enhanced “T he Physics of …”

examples by increasing the bio-inspired exam

ples by 40%. Although they are of general ins

tructional value, they a re also similar to what

premed students will e ncounter in the Chemical and Ph

ysical Foundations of Biological Systems Passages section of the

MCAT. Finally,

we have introduced new “team problems” in th

e end-of-chapter proble ms that are designed fo

r group problem-solvin g exercises. These

are context-rich proble ms of medium diffi cult

y designed for group c ooperation, but may al

so be tackled by the in dividual student.

One of the great streng ths of this text is the sy

nergistic relationship i t develops between pro

blem solving and conc eptual understand-

ing. For instance, avail able in WileyPLUS are animated

Chalkboard Videos, which cons ist of short (2–3 min) v

ideos demonstrat-

ing step-by-step practi cal solutions to typical

homework problems. Also available are num

erous Guided Online (GO) Tuto rials that

implement a step-by-s tep pedagogical approa

ch, which provides stu dents a low-stakes env

ironment for refi ning t heir problem solving

skills. One of the most important techniques

developed in the text f or solving problems in

volving multiple force s is the free-body

diagram (FBD). Many problems in the force-intensive

chapters, such as chap ters 4 and 18, take adv

antage of the new FBD capabilities

now available online in WileyPLUS, where students can

construct the FBD’s f or a select number of p

roblems and be graded on them.

Finally, ORION, an online adapt ive learning environme

nt, is seamlessly integr ated into WileyPLUS for Cutnell

& Johnson.

The content and functi onality of WileyPLUS, and the a

daptive learning enviro nment of ORION (see below), w

ill provide students wi th

all the resources they n eed to be successful in

the course.

• The Lecture Videos created b y the authors for each

section include questio ns with intelligent feed

back when a student en ters the

wrong answer.

• The multi-step GO Tutorial p roblems created in WileyPLUS a

re designed to provide targeted, intelligent fe

edback.

• The Free-body Diagram vecto r drawing tools provid

e students an easy way to enter answers requi

ring vector drawing, an d also

provide enhanced feed back.

• Chalkboard Video Solutions t ake the students step-b

y-step through the solu tion and the thought pr

ocess of the authors. P roblem-

solving strategies are d iscussed, and common

misconceptions and p otential pitfalls are add

ressed. The students ca n then apply these

techniques to solve sim ilar, but diff erent probl

ems.

All of these features ar e designed to encourag

e students to remain w ithin the WileyPLUS environme

nt, as opposed to pursu ing the

“pay-for solutions” we bsites that short circui

t the learning process. To the students – We s

trongly recommend th at you take this honest

approach to the course . Take full advantage o

f the many features an d learning resources th

at accompany the text and the online con-

tent. Be engaged with the material and push

yourself to work throu gh the exercises. Physi

cs may not be the easie st subject to under-

stand, but with the Wi ley resources at your d

isposal and your hard w ork, you CAN be succ

essful.

We are immensely gra teful to all of you who

have provided feedbac k as we’ve worked on

this new edition, and t o our students who

have taught us how to teach. Thank you for y

our guidance, and keep the feedback coming.

Best wishes for succes s in this course and

wherever your major m ay take you!

Sincerely,

David Young and Shan e Stadler, Louisiana St

ate University

email: dyoun14@gma il.com or stadler.ls

u.edu@gmail.com

iv

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v

Brief Contents

1 Introduction and Mathematical Concepts 1

2 Kinematics in One Dimension 27

3 Kinematics in Two Dimensions 55

4 Forces and Newton’s Laws of Motion 80

5 Dynamics of Uniform Circular Motion 121

6 Work and Energy 144

7 Impulse and Momentum 175

8 Rotational Kinematics 200

9 Rotational Dynamics 223

10 Simple Harmonic Motion and Elasticity 257

11 Fluids 289

12 Temperature and Heat 326

13 The Transfer of Heat 360

14 The Ideal Gas Law and Kinetic Theory 380

15 Thermodynamics 401

16 Waves and Sound 433

17 The Principle of Linear Superposition and Interference Phenomena 465

18 Electric Forces and Electric Fields 489

19 Electric Potential Energy and the Electric Potential 523

20 Electric Circuits 551

21 Magnetic Forces and Magnetic Fields 590

22 Electromagnetic Induction 625

23 Alternating Current Circuits 661

24 Electromagnetic Waves 684

25 The Reflection of Light: Mirrors 711

26 The Refraction of Light: Lenses and Optical Instruments 733

27 Interference and the Wave Nature of Light 777

28 Special Relativity 808

29 Particles and Waves 832

30 The Nature of the Atom 853

31 Nuclear Physics and Radioactivity 885

32 Ionizing Radiation, Nuclear Energy, and Elementary Particles 911

Contents

1 Introduction and Mathematical Concepts 1

1.1 The Nature of Physics 1 1.2 Units 2 1.3 The Role of Units in Problem Solving 3 1.4 Trigonometry 6 1.5 Scalars and Vectors 8 1.6 Vector Addition and Subtraction 10 1.7 The Components of a Vector 12 1.8 Addition of Vectors by Means of Components 15 Concept Summary 19 Focus on Concepts 19 Problems 21 Additional Problems 24 Concepts and Calculations Problems 25 Team Problems 26

2 Kinematics in One Dimension 27 2.1 Displacement 27 2.2 Speed and Velocity 28 2.3 Acceleration 31 2.4 Equations of Kinematics for Constant

Acceleration 34 2.5 Applications of the Equations of Kinematics 37 2.6 Freely Falling Bodies 41 2.7 Graphical Analysis of Velocity and

Acceleration 45 Concept Summary 47 Focus on Concepts 48 Problems 49 Additional Problems 53 Concepts and Calculations Problems 54 Team Problems 54

3 Kinematics in Two Dimensions 55 3.1 Displacement, Velocity, and Acceleration 55 3.2 Equations of Kinematics in Two Dimensions 56 3.3 Projectile Motion 60 3.4 Relative Velocity 68 Concept Summary 72 Focus on Concepts 73 Problems 74 Additional Problems 77 Concepts and Calculations Problems 78 Team Problems 79

4 Forces and Newton’s Laws of Motion 80 4.1 The Concepts of Force and Mass 80 4.2 Newton’s First Law of Motion 81 4.3 Newton’s Second Law of Motion 83 4.4 The Vector Nature of Newton’s Second Law of Motion 85 4.5 Newton’s Third Law of Motion 86 4.6 Types of Forces: An Overview 88 4.7 The Gravitational Force 88 4.8 The Normal Force 92 4.9 Static and Kinetic Frictional Forces 95 4.10 The Tension Force 101 4.11 Equilibrium Applications of Newton’s Laws

of Motion 102 4.12 Nonequilibrium Applications of Newton’s Laws

of Motion 106 Concept Summary 111 Focus on Concepts 112 Problems 114 Additional Problems 118 Concepts and Calculations Problems 119 Team Problems 120

5 Dynamics of Uniform Circular Motion 121

5.1 Uniform Circular Motion 121 5.2 Centripetal Acceleration 122 5.3 Centripetal Force 125 5.4 Banked Curves 129 5.5 Satellites in Circular Orbits 130 5.6 Apparent Weightlessness and Artificial Gravity 133 5.7 *Vertical Circular Motion 136 Concept Summary 137 Focus on Concepts 138 Problems 139 Additional Problems 141 Concepts and Calculations Problems 142 Team Problems 143

6 Work and Energy 144 6.1 Work Done by a Constant Force 144 6.2 The Work–Energy Theorem and Kinetic Energy 147 6.3 Gravitational Potential Energy 153 6.4 Conservative Versus Nonconservative Forces 155 6.5 The Conservation of Mechanical Energy 157 6.6 Nonconservative Forces and the Work–Energy

Theorem 161

Contents vii

6.7 Power 162 6.8 Other Forms of Energy and the Conservation

of Energy 164 6.9 Work Done by a Variable Force 164 Concept Summary 166 Focus on Concepts 167 Problems 168 Additional Problems 172 Concepts and Calculations Problems 173 Team Problems 174

7 Impulse and Momentum 175 7.1 The Impulse–Momentum Theorem 175 7.2 The Principle of Conservation of Linear

Momentum 179 7.3 Collisions in One Dimension 184 7.4 Collisions in Two Dimensions 189 7.5 Center of Mass 189 Concept Summary 192 Focus on Concepts 193 Problems 194 Additional Problems 197 Concepts and Calculations Problems 198 Team Problems 199

8 Rotational Kinematics 200 8.1 Rotational Motion and Angular Displacement 200 8.2 Angular Velocity and Angular Acceleration 203 8.3 The Equations of Rotational Kinematics 205 8.4 Angular Variables and Tangential Variables 208 8.5 Centripetal Acceleration and Tangential

Acceleration 210 8.6 Rolling Motion 213 8.7 *The Vector Nature of Angular Variables 214 Concept Summary 215 Focus on Concepts 216 Problems 216 Additional Problems 220 Concepts and Calculations Problems 221 Team Problems 222

9 Rotational Dynamics 223 9.1 The Action of Forces and Torques on Rigid

Objects 223 9.2 Rigid Objects in Equilibrium 226 9.3 Center of Gravity 231 9.4 Newton’s Second Law for Rotational Motion About a

Fixed Axis 236 9.5 Rotational Work and Energy 241 9.6 Angular Momentum 244

Concept Summary 246 Focus on Concepts 247 Problems 248 Additional Problems 254 Concepts and Calculations Problems 255 Team Problems 256

10 Simple Harmonic Motion and Elasticity 257

10.1 The Ideal Spring and Simple Harmonic Motion 257 10.2 Simple Harmonic Motion and the Reference Circle 261 10.3 Energy and Simple Harmonic Motion 267 10.4 The Pendulum 270 10.5 Damped Harmonic Motion 273 10.6 Driven Harmonic Motion and Resonance 274 10.7 Elastic Deformation 275 10.8 Stress, Strain, and Hooke’s Law 279 Concept Summary 280 Focus on Concepts 281 Problems 282 Additional Problems 287 Concepts and Calculations Problems 288 Team Problems 288

11 Fluids 289 11.1 Mass Density 289 11.2 Pressure 291 11.3 Pressure and Depth in a Static Fluid 293 11.4 Pressure Gauges 297 11.5 Pascal’s Principle 298 11.6 Archimedes’ Principle 300 11.7 Fluids in Motion 305 11.8 The Equation of Continuity 307 11.9 Bernoulli’s Equation 309 11.10 Applications of Bernoulli’s Equation 311 11.11 *Viscous Flow 314 Concept Summary 317 Focus on Concepts 318 Problems 319 Additional Problems 323 Concepts and Calculations Problems 324 Team Problems 325

12 Temperature and Heat 326 12.1 Common Temperature Scales 326 12.2 The Kelvin Temperature Scale 328 12.3 Thermometers 329 12.4 Linear Thermal Expansion 330 12.5 Volume Thermal Expansion 337 12.6 Heat and Internal Energy 339

12.7 Heat and Temperature Change: Specific Heat Capacity 340

12.8 Heat and Phase Change: Latent Heat 343 12.9 *Equilibrium Between Phases of Matter 347 12.10 *Humidity 350 Concept Summary 352 Focus on Concepts 352 Problems 353 Additional Problems 358 Concepts and Calculations Problems 358 Team Problems 359

13 The Transfer of Heat 360 13.1 Convection 360 13.2 Conduction 363 13.3 Radiation 370 13.4 Applications 373 Concept Summary 375 Focus on Concepts 375 Problems 376 Additional Problems 378 Concepts and Calculations Problems 379 Team Problems 379

14 The Ideal Gas Law and Kinetic Theory 380

14.1 Molecular Mass, the Mole, and Avogadro’s Number 380 14.2 The Ideal Gas Law 383 14.3 Kinetic Theory of Gases 388 14.4 *Diff usion 392 Concept Summary 395 Focus on Concepts 396 Problems 397 Additional Problems 399 Concepts and Calculations Problems 400 Team Problems 400

15 Thermodynamics 401 15.1 Thermodynamic Systems and Their Surroundings 401 15.2 The Zeroth Law of Thermodynamics 402 15.3 The First Law of Thermodynamics 402 15.4 Thermal Processes 404 15.5 Thermal Processes Using an Ideal Gas 408 15.6 Specific Heat Capacities 411 15.7 The Second Law of Thermodynamics 412 15.8 Heat Engines 413 15.9 Carnot’s Principle and the Carnot Engine 414 15.10 Refrigerators, Air Conditioners, and Heat Pumps 417 15.11 Entropy 420 15.12 The Third Law of Thermodynamics 425

Concept Summary 425 Focus on Concepts 426 Problems 427 Additional Problems 431 Concepts and Calculations Problems 432 Team Problems 432

16 Waves and Sound 433 16.1 The Nature of Waves 433 16.2 Periodic Waves 435 16.3 The Speed of a Wave on a String 436 16.4 *The Mathematical Description of a Wave 439 16.5 The Nature of Sound 439 16.6 The Speed of Sound 442 16.7 Sound Intensity 446 16.8 Decibels 448 16.9 The Doppler Eff ect 450 16.10 Applications of Sound in Medicine 454 16.11 *The Sensitivity of the Human Ear 455 Concept Summary 456 Focus on Concepts 457 Problems 458 Additional Problems 463 Concepts and Calculations Problems 464 Team Problems 464

17 The Principle of Linear Superposition and Interference Phenomena 465

17.1 The Principle of Linear Superposition 465 17.2 Constructive and Destructive Interference of

Sound Waves 466 17.3 Diff raction 470 17.4 Beats 473 17.5 Transverse Standing Waves 474 17.6 Longitudinal Standing Waves 478 17.7 *Complex Sound Waves 481 Concept Summary 482 Focus on Concepts 483 Problems 484 Additional Problems 487 Concepts and Calculations Problems 488 Team Problems 488

18 Electric Forces and Electric Fields 489 18.1 The Origin of Electricity 489 18.2 Charged Objects and the Electric Force 490 18.3 Conductors and Insulators 493 18.4 Charging by Contact and by Induction 493 18.5 Coulomb’s Law 495 18.6 The Electric Field 500

viii Contents

Contents ix

18.7 Electric Field Lines 505 18.8 The Electric Field Inside a Conductor: Shielding 508 18.9 Gauss’ Law 510 18.10 *Copiers and Computer Printers 513 Concept Summary 516 Focus on Concepts 516 Problems 517 Additional Problems 521 Concepts and Calculations Problems 521 Team Problems 522

19 Electric Potential Energy and the Electric Potential 523

19.1 Potential Energy 523 19.2 The Electric Potential Diff erence 524 19.3 The Electric Potential Diff erence Created by Point

Charges 530 19.4 Equipotential Surfaces and Their Relation to the

Electric Field 534 19.5 Capacitors and Dielectrics 537 19.6 *Biomedical Applications of Electric Potential