Physics for Engineers and Scientists (Third Edition) (Vol. 1) by Hans C. Ohanian PDF

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W. W. Norton & Company, Inc. • www.NortonEbooks.com

PHYSICS FOR ENGINEERS AND SCIENTISTS THIRD EDITION Volume One

Hans C. Ohanian, John T. Markert

Physics for Engineers and Scientists Third Edition

Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY OSCILLATIONS, WAVES, AND FLUIDS TEMPERATURE, HEAT, AND THERMODYNAMICS

B

W • W • NORTON & COMPANY 

NEW YORK • LONDON

Physics for Engineers and Scientists T hird Edition Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY OSCILLATIONS, WAVES, AND FLUIDS TEMPERATURE, HEAT, AND THERMODYNAMICS

HANS C. OHANIAN, UNIVERSITY OF VERMONT

JOHN T. MARKERT, UNIVERSITY OF TEXAS AT AUSTIN

B

W • W • NORTON & COMPANY 

NEW YORK • LONDON

To Susan Ohanian, writer, who gently tried to teach me some of her craft.—H.C.O. To Frank D. Markert, a printer by trade; to Christiana Park, for her thirst for new knowledge; and to Erin, Ryan, Sean, and Gwen, for their wonder and clarity.—J.T.M.

Copyright © 2007 by W.W. Norton & Company, Inc. All rights reserved Printed in the United States of America Third Edition Composition: Techbooks Manufacturing: RR Donnelley & Sons Company Editor: Leo A. W. Wiegman Media Editor: April E. Lange Director of Manufacturing—College: Roy Tedoff Senior Project Editor: Christopher Granville Photo Researcher: Kelly Mitchell Editorial Assistant: Lisa Rand, Sarah L. Mann Copy Editor: Richard K. Mickey Book designer: Sandy Watanabe Layout artist: Paul Lacy Illustration Studio: JB Woolsey Arts, Inc. Cover Illustration: John Belcher, inter alia. Cover Design: Joan Greenfield

ISBN 978-0-393-11101-9 (ebook)

W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110 www.wwnorton.com W. W. Norton & Company Ltd., Castle House, 75/76 Wells Street, London W1T 3QT 1234567890 W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union.The Nortons soon expanded their program beyond the Institute, publishing books by celebrated academics from America and abroad. By mid-century, the two major pillars of Norton’s publishing program—trade books and college texts— were firmly established. In the 1950s, the Norton family transferred control of the company to its employees, and today—with a staff of four hundred and a comparable number of trade, college, and professional titles published each year—W. W. Norton & Company stands as the largest and oldest publishing house owned wholly by its employees.

Brief Contents Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; Chapters 37–41 appear in Volume 3. 20. HEAT 628 PREFACE xiii OWNER’S MANUAL xxv PRELUDE: THE WORLD OF PHYSICS xxxv

21. THERMODYNAMICS 661

PART

IV

ELECTRICITY

MAGNETISM 22.

AND

ELECTRIC FORCE AND

ELECTRIC CHARGE 23. THE ELECTRIC FIELD 24. GAUSS’ LAW

PART I MOTION, FORCE, AND ENERGY 1

25. ELECTROSTATIC POTENTIAL AND ENERGY

1. SPACE, TIME, AND MASS 2

26. CAPACITORS AND DIELECTRICS

2. MOTION ALONG A STRAIGHT LINE 28

27. CURRENTS AND OHM’S LAW

3. VECTORS 69

28. DIRECT CURRENT CIRCUITS

4. MOTION IN TWO AND THREE DIMENSIONS 94 5.

29. MAGNETIC FORCE AND FIELD

NEWTON’S LAWS OF MOTION 130

30. CHARGES AND CURRENTS IN MAGNETIC FIELDS

6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173 7.

31. ELECTROMAGNETIC INDUCTION

WORK AND ENERGY 204

32. ALTERNATING CURRENT CIRCUITS

8. CONSERVATION OF ENERGY 235 9. GRAVITATION 271 10. SYSTEMS OF PARTICLES 305 11. COLLISIONS 338 12. ROTATION OF A RIGID BODY 365 13. DYNAMICS OF A RIGID BODY 394

PART V WAVES AND OPTICS 33. ELECTROMAGNETIC WAVES 34. REFLECTION, REFRACTION, AND OPTICS 35. INTERFERENCE AND DIFFRACTION

14. STATICS AND ELASTICITY 429

PART II OSCILLATIONS, WAVES, AND FLUIDS 466 15. OSCILLATIONS 468 16. WAVES 507 17. SOUND 536 18. FLUID MECHANICS 565

PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600

PART VI RELATIVITY, QUANTA, AND PARTICLES 36. THE THEORY OF SPECIAL RELATIVITY 37. QUANTA OF LIGHT 38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS 39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS 40. NUCLEI 41. ELEMENTARY PARTICLES AND COSMOLOGY

APPENDICES A-1

v

Table of Contents

2.7* Integration

of the Equations of Motion 54

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 57

Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; and Chapters 37–41 appear in 3. VECTORS 69 Volume 3. 3.1 The PREFACE xiii OWNER’S MANUAL xxv

Displacement Vector and Other Vectors 70 3.2 Vector  Addition and Subtraction 72 4. MOTION IN TWO AND THREE DIMENSIONS 94

PRELUDE: THE WORLD OF PHYSICS xxxv 4.1 Components

of Velocity and Acceleration 95 4.2 The  Velocity and Acceleration Vectors 98 4.3 Motion  with Constant Acceleration 102 4 .4 The Motion of Projectiles 104 4.5 Uniform Circular Motion 112 4.6 The

Position Vector; Components of a Vector 76 3.4 Vector Multiplication 81

Relativity of Motion and the Addition of Velocities 115

3.3 The

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 87

PART I MOTION, FORCE, AND ENERGY 1 1. SPACE, TIME, AND MASS 2 1.1 Coordinates

and Reference Frames 3 Unit of Length 5 1.3 The Unit of Time 9 1.4 The Unit of Mass 11 1.5 Derived Units 13 1.6 Significant Figures; Consistency of Units and Conversion of Units 14 1.2 The

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 20

2. MOTION ALONG A STRAIGHT LINE 28 2.1 Average

Speed 29 Velocity for Motion along a Straight Line 32 2.3 Instantaneous Velocity 35 2.4 Acceleration 39 2.5 Motion with Constant Acceleration 42 2 6 The Acceleration of Free Fall 49 2.2 Average

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 118

5. NEWTON’S LAWS OF MOTION 130 5.1 Newton’s

First Law 131 Second Law 133 5.3 The Combination of Forces 138 5.4 Weight; Contact Force and Normal Force 141 5 .5 Newton’s  Third Law 144 5.6 Motion with a Constant Force 151 5.2 Newton’s

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 159

6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173 6.1 Friction

174 Force of a Spring; Hooke’s Law 182 6.3 Force for Uniform Circular Motion 184 6 .4* The Four Fundamental Forces 191 6.2 Restoring

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 192

vii viii CONTENTS

7. WORK AND ENERGY 204 7.1 Work

205 7.2 Work for a Variable Force 211 7.3 Kinetic Energy 214 7.4 Gravitational Potential Energy 218 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 224

8. CONSERVATION OF ENERGY 235 8.1 Potential

Energy of a Conservative Force 236 8.2 The Curve of Potential Energy 244 8.3 Other Forms of Energy 248 8.4* Mass and Energy 251 8.5 Power 253 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 259

9. GRAVITATION 271 9.1 Newton’s

Law of Universal Gravitation 272 9 .2 The Measurement of G2  77 9.3 Circular Orbits 278 9.4 Elliptical 9.5 Energy

Orbits; Kepler’s Laws 282 in Orbital Motion 288

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 293

10. SYSTEMS OF PARTICLES 305

306 10.2 Center of Mass 313 10.3 The Motion of the Center of Mass 323 1 0.4 Energy of a System of Particles 327

12.1 Motion

of a Rigid Body 366

12.2 Rotation

about a Fixed Axis 367 with Constant Angular Acceleration 374 12.4* Motion with Time-Dependent Angular Acceleration 376 12.5 Kinetic Energy of Rotation; Moment of Inertia 378

12.3 Motion

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 384

13. DYNAMICS OF A RIGID BODY 394 13.1 Work,

Energy, and Power in Rotational Motion; Torque 395 13.2 The Equation of Rotational Motion 399 13.3 Angular Momentum and its Conservation 406 1 3.4* Torque and Angular Momentum as Vectors 410 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 417

14. STATICS AND ELASTICITY 429 14.1 Statics

of Rigid Bodies 430 of Static Equilibrium 433 14.3 Levers and Pulleys 441 14.4 Elasticity of Materials 445 14.2 Examples

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 450

10.1 Momentum

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 328

PART II OSCILLATIONS, WAVES, AND FLUIDS 466 15. OSCILLATIONS 468 15.1 Simple

11. COLLISIONS 338 11.1 Impulsive

Forces 339 Collisions in One Dimension 344 11.3 Inelastic Collisions in One Dimension 348 1 1.4* Collisions  in Two and Three Dimensions 351 11.2 Elastic

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 354

Harmonic Motion 469 Simple Harmonic Oscillator 476 15.3 Kinetic Energy and Potential Energy 480 1 5.4 The Simple Pendulum 484 15.5* Damped Oscillations and Forced Oscillations 488 15.2 The

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 494

16. WAVES 507 12 ROTATION OF A RIGID BODY 365

16.1 Transverse and Longitudinal Wave Motion 508 16.2 Periodic Waves 509

REVIEW PROBLEMS / ANSWERS TO CHECKUPS 650

CONTENTS ix

21. THERMODYNAMICS 661 16.3 The

Superposition of Waves 516 Waves 520

16.4 Standing

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 524

17. SOUND 536

Waves in Air 538 of Sound 540 17.3 The Speed of Sound; Standing Waves 543 1 7.4 The  Doppler Effect 574 17.5* Diffraction 553

21.1 The

First Law of Thermodynamics 663 21.2 Heat Engines; The Carnot Engine 665 21.3 The Second Law of Thermodynamics 675 2 1.4 Entropy  677 SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 681

17.1 Sound

17.2 Intensity

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 555

18. FLUID MECHANICS 565 18.1 Density

and Flow Velocity 567 Steady Flow; Streamlines 569 1 8.3 Pressure  573 18.4 Pressure in a Static Fluid 575 18.5 Archimedes’ Principle 580 18.6 Fluid Dynamics; Bernoulli’s Equation 582 18.2 Incompressible

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 587

PART IV ELECTRICITY AND MAGNETISM 22. ELECTRIC FORCE AND ELECTRIC CHARGE 22.1 The

Electrostatic Force Law 22.3 The Superposition of Electrical Forces 22.4 Charge Quantization and Charge Conservation 22.5 Conductors and Insulators; Charging by Friction or by Induction 22.2 Coulomb’s

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

23. THE ELECTRIC FIELD 23.1 The

Electric Field of Point Charges Electric Field of Continuous Charge Distributions 23.3 Lines of Electric Field 23.4 Motion in a Uniform Electric Field 23.5 Electric Dipole in an Electric Field 23.2 The

PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600 19. THE IDEAL GAS 602

Ideal-Gas Law 603 Temperature Scale 609 19.3 Kinetic Pressure 613 19.4 The Internal Energy of an Ideal Gas 616

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

19.1 The 19.2 The

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 619

20. HEAT 628 20.1 Heat

as a Form of Energy Transfer 629 Expansion of Solids and Liquids 633 2 0.3 Thermal  Conduction 638 20.4 Changes of State 642 20.2 Thermal

20.5 The

Specific Heat of a Gas 644 Expansion of a Gas 647

20.6* Adiabatic

24. GAUSS’ LAW 24.1 Electric

Flux Law 24.3 Applications of Gauss’ Law 24.4 Superposition of Electric Fields 24.5 Conductors and Electric Fields 24.2 Gauss’

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

25. ELECTROSTATIC POTENTIAL AND ENERGY 25.1 The

Electrostatic Potential 25.2 Calculation of the Potential from the Field

CONTENTS

25.3 Potential

in Conductors of the Field from the Potential 25.5 Energy of Systems of Charges

25.4 Calculation

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

30.2 Force on a Wire 30.3 Torque on a Loop 30.4 Magnetism

in Materials 30.5* The Hall Effect SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

31. ELECTROMAGNETIC INDUCTION 26. CAPACITORS AND DIELECTRICS

in Combination

26.3 Dielectrics 26.4 Energy

EMF Law 31.3 Some Examples; Lenz’ Law 31.4 Inductance 31.5 Magnetic Energy  ircuit 31.6* The RL C 31.2 Faraday’s

26.1 Capacitance 26.2 Capacitors

31.1 Motional

in Capacitors

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

27. CURRENTS AND OHM’S LAW 27.1 Electric

Current 27.2 Resistance and Ohm’s Law 27.3 The Resistivity of Materials 27.4 Resistances in Combination SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

28. DIRECT CURRENTS CIRCUITS

Force 28.2 Sources of Electromotive Force 28.3 Single-Loop Circuits 28.4 Multi-Loop Circuits 28.5 Energy in Circuits; Joule Heat 28.6* Electrical Measurements  ircuit 28.7* The RC C 28.8* The Hazards of Electric Currents

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

32. ALTERNATING CURRENT CIRCUITS* 32.1 Resistor

Circuit 32.2 Capacitor Circuit 32.3 Inductor Circuit  nd RLC 32.4* Freely Oscillating LC a Circuits 3 2.5* Series Circuits with Alternating EMF 3 2.6 Transformers  SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

28.1 Electromotive

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

29. MAGNETIC FORCE AND FIELD 29.1 The

Magnetic Force 29.2 The Magnetic Field 29.3 Ampére’s Law 29.4 Solenoids and Magnets 29.5 The Biot-Savart Law SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

PART V WAVES AND OPTICS 33. ELECTROMAGNETIC WAVES 33.1 Induction

of Magnetic Fields; Maxwell’s Equations 33.2* The Electromagnetic Wave Pulse 33.3 Plane

Waves; Polarization Generation of Electromagnetic Waves 33.5 Energy  of a Wave 33.6* The Wave Equation 33.4 The

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

34. REFLECTION, REFRACTION, AND OPTICS 34.1 Huygens’

Construction

34.2 Reflection 34.3 Refraction 34.4 Spherical

30. CHARGES AND CURRENTS IN MAGNETIC FIELDS 30.1 Circular

Field

Motion in a Uniform Magnetic

Mirrors Lenses 34.6* Optical Instruments 34.5 Thin

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

35. INTERFERENCE AND DIFFRACTION

39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS

35.1 Thin

Films 35.2* The Michelson Interferometer 35.3 Interference from Two Slits 35.4 Interference from Multiple Slits 35.5 Diffraction by a Single Slit 35.6 Diffraction by a Circular Aperture; Rayleigh’s Criterion

39.1 Principal,

Orbital, and Magnetic Quantum Numbers; Spin 39.2 The Exclusion Principle and the Structure of Atoms 39.3* Energy Levels in Molecules 39.4 Energy

Bands in Solids Devices

39.5 Semiconductor

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

40. NUCLEI

PART VI RELATIVITY, QUANTA, AND PARTICLES

40.1 Isotopes 40.2 The

Strong Force and the Nuclear Binding Energy 40.3 Radioactivity

36. THE THEORY OF SPECIAL RELATIVITY 36.1 The

40.4 The

36.2 Einstein’s

40.5 Fission

Speed of Light; the Ether Principle of Relativity 36.3 Time Dilation 36.4 Length Contraction 36.5 The Lorentz Transformations and the Combination of Velocities 36.6 Relativistic Momentum and Energy 3 6.7* Mass  and Energy

Law of Radioactive Decay

40.6* Nuclear

Bombs and Nuclear Reactors

40.7 Fusion SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

41. ELEMENTARY PARTICLES AND COSMOLOGY

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

41.1 The

Tools of High-Energy Physics Multitude of Particles 41.3 Interactions and Conservation Laws 41.4 Fields and Quanta 41.5 Quarks 41.6 Cosmology 41.2 The

37. QUANTA OF LIGHT 37.1 Blackbody

Radiation Quanta 37.3 Photons and the Photoelectric Effect 3 7.4 The Compton Effect 37.5 X Rays 37.2 Energy

37.6 Wave

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

xii CONTENTS APPENDICES

vs. Particle

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

CONTENTS xi APPENDIX 1: GREEK ALPHABET A-1

38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS 38.1 Spectral

Lines 38.2 Spectral Series of Hydrogen 38.3 The Nuclear Atom 38.4 Bohr’s Theory 38.5 Quantum Mechanics; The Schrödinger Equation SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

APPENDIX 2: MATHEMATICS REVIEW A-1 A2.1 Symbols

A-1 and Roots A-1 A2.3 Arithmetic in Scientific Notation A-2 A2.4 Algebra A-3 A2.5 Equations with Two Unknowns A-5 A2.2 Powers

A2.6 The

Quadratic Formula A-5 and the Exponential Function A-5

A2.7 Logarithms

APPENDIX 3: GEOMETRY AND TRIGONOMETRY REVIEW A-7

A3.1 Perimeters,

Areas, and Volumes A-7

A3.2 Angles

A-7 A3.3 The Trigonometric Functions A-8 A3.4 The Trigonometric Identities A-9 A3.5 The Laws of Cosines and Sines

A6.3 Prefixes

A-23

APPENDIX 7: BEST VALUES OF FUNDAMENTAL CONSTANTS A-23

APPENDIX 8: CONVERSION FACTORS A-26

A-10 APPENDIX 4: CALCULUS REVIEW A-10 A4.1 Derivatives

A-10 A4.2 Important Rules for Differentiation A-11 A  4.3 Integrals  A-12 A4.4 Important Rules for Integration A-15 A  4.5 The  Taylor Series A-18 A4.6 Some Approximations A-18 APPENDIX 5: PROPAGATING UNCERTAINTIES A-19

APPENDIX 9: THE PERIODIC TABLE AND CHEMICAL ELEMENTS A-31

APPENDIX 10: FORMULA SHEETS A-33

Chapters 1–21 A-33 Chapters 22–41 A-34 APPENDIX 11: ANSWERS TO ODD-NUMBERED PROBLEMS AND REVIEW PROBLEMS A-35

PHOTO CREDITS A-51 APPENDIX 6: THE INTERNATIONAL ...