College PhysiCs

College PhysiCs

Putting It All Together

Ron HellingsMontana State University

Jeff AdamsMontana State University

Greg FrancisMontana State University

university science booksmill valley, california

University Science BooksMill Valley, Californiawww.uscibooks.com

Editor: Jane EllisProduction manager: Julianna Scott FeinManuscript editor: Lee YoungIllustrator: Laurel MullerText design: Yvonne Tsang at Wilsted & TaylorCover design: Yvonne Tsang at Wilsted & TaylorCompositor: Laurel MullerPrinter and binder: [to come]

This book is printed on acid-free paper.

Print ISBN 978-1-938787-93-5eBook ISBN 978-1-938787-95-9

Copyright ©2017 by University Science Books

Reproduction or translation of any part of this work beyond that permitted by Sec-tion 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, University Science Books.

Library of Congress Cataloging-in-Publication DataNames: Hellings, Ronald W., author. | Adams, Jeffrey P., author. | Francis, Gregory E.,

author.Title: College physics : putting it all together / Ron Hellings, Jeff Adams, Greg Francis.Description: Mill Valley, California : University Science Books, [2017] | Includes index.Identifiers: LCCN 2017010603| ISBN 9781938787935 (alk. paper) | ISBN 1938787935

(alk. paper) | ISBN 9781938787959 (eBook) | ISBN 1938787951 (eBook)Subjects: LCSH: Physics--Textbooks.Classification: LCC QC21.3 .H45 2017 | DDC 530--dc23LC record available at https://lccn.loc.gov/2017010603

Printed in the United States of America10 9 8 7 6 5 4 3 2 1

To our wives and families for their continual support and to all of our former students who taught us so much.

CONTENTS

Preface vii

1. INTrOduCTION 1

1.1 Measurement 2 1.2 Arithmetic 4 1.3 Working with Units 6 1.4 Mathematics Requirements 7 1.5 Summary 7 1.6 Problems 8

2. ONE-dImENSIONAl KINEmATICS 11

2.1 The Coordinate System 11 2.2 Displacement 12 2.3 Velocity 13 2.4 Straight Line Acceleration:

Speeding Up and Slowing Down 15 2.5 Graphing the Motion 19 2.6 Equations Governing Uniformly

Accelerated Motion 21 2.7 Free Fall 24 2.8 How to Solve Physics Problems 25 2.9 Summary 29 2.10 Problems 30

3. VECTOrS 37

3.1 Superposition 37 3.2 Vectors and Scalars 37 3.3 Vector Addition 38 3.4 Vector Subtraction 40 3.5 Trigonometry Review 41 3.6 Vector Components 44 3.7 Vector Addition (Revisited) 45 3.8 Summary 48 3.9 Problems 30

4. TwO-dImENSIONAl KINEmATICS 55

4.1 Position Vectors and Coordinate Systems 55

4.2 Displacement and Velocity 56 4.3 Acceleration in Two Dimensions 57 4.4 Projectile Motion 61 4.5 Circular Motion and Centripetal

Acceleration 65 4.6 Relative Velocity 68 4.7 Summary 70 4.8 Problems 71

5. NEwTON’S lAwS 79

5.1 Newton’s First Law 79 5.2 Newton’s Second Law 80 5.3 Newton’s Third Law 83 5.4 Forces 85 5.5 Free-Body Diagrams 87 5.6 Statics 90 5.7 Summary 91 5.8 Problems 91

6. FOrCES 97

6.1 Gravitational Force—Weight 00 6.2 Normal Force 00 6.3 Frictional Forces—Kinetic and Static 000 6.4 Problems On an Inclined Plane 000 6.5 Tension 000 6.6 Elastic and Spring Forces 000 6.7 Refrigerator Magnet Force 000 6.8 Apparent Weight 000 6.9 Centripetal Force 000 6.10 Centrifugal and Other Fictitious Forces 000 6.11 Summary 000 6.12 Problems 000

7. ENErgy

7.1 Forms of Energy 7.2 Energy Change and Work 7.3 Power 7.4 Conservative and Non-Conservative

Forces 7.5 Conservation of Energy 7.6 Solving Mechanical Energy Problems 7.7 Summary 7.8 Problems

8. mOmENTum

8.1 Impulse and Momentum 8.2 Collisions 8.3 The Three Flavors of Collisions 8.4 Collisions in Two Dimensions 8.5 Elastic Collisions in One Dimension 8.6 Summary 8.7 Problems

9. rOTATIONAl mEChANICS

9.1 The Radian 9.2 Rotational Kinematics 9.3 Torque 9.4 Center of Mass 9.5 Extended Free-Body Diagrams 9.6 Rotational Inertia 9.7 Angular Momentum and Kinetic Energy 9.8 Summary 9.9 Problems

10. PrESSurE ANd FluIdS

10.1 Pressure 10.2 Pressure in Fluids 10.3 Pascal’s Principle 10.4 Archimedes’ Principle 10.5 And What If It Floats? 10.6 Summary 10.7 Problems

11. SImPlE hArmONIC mOTION

11.1 Period and Frequency 11.2 Simple Harmonic Motion 11.3 The Hanging Block on a Spring 11.4 The Period Formula 11.5 Energy in Simple Harmonic Motion 11.6 Other Harmonic Oscillators 11.7 Summary 11.8 Problems

12. PulSES ANd wAVES

12.1 Definitions 12.2 Wave Speed 12.3 Superposition of Pulses 12.4 Reflection of Pulses at a Boundary 12.5 Reflection of Pulses at a Boundary Between

Two Media 12.6 Properties of Continuous Waves 12.7 Sound 12.8 Beats 12.9 The Doppler Effect 12.10 Summary 12.11 Problems

13. STANdINg wAVES

13.1 Standing Wave on a String 13.2 Reflection of Sound in an Air Column 13.3 Longitudinal Standing Waves:

Open–Open Tube 13.4 Longitudinal Standing Waves:

Open–Closed Tube 13.5 Summary 13.6 Problems

14. ThErmAl PhySICS

14.1 Temperature 14.2 Thermal Expansion 14.3 Specific Heat 14.4 Latent Heats 14.5 Summary 14.6 Problems

15. ThErmOdyNAmICS

15.1 Kinetic Theory of Gases 15.2 Thermodynamics 15.3 Specific Heats of a Gas 15.4 Summary 15.5 Problems

16. ElECTrIC FOrCES ANd FIEldS

16.1 Charge 16.2 Coulomb’s Law 16.3 Induction and Polarization 16.4 Electric Fields 16.5 Superposition 16.6 Electric Field Lines 16.7 Uniformly Charged Sheets 16.8 Charged Conducting Plates 16.9 Electric Flux and Gauss’s Law 16.10 Summary 16.11 Problems

17. VOlTAgE

17.1 The Gravitational Potential 17.2 Electric Potential Energy and Voltage 17.3 Uniformly Charged Parallel Plates 17.4 Equipotential Surfaces 17.5 Capacitance 17.6 Polarization and Dielectrics 17.7 Energy in a Capacitor 17.8 Summary 17.9 Problems

18. CIrCuITS

18.1 Current and Wires 18.2 Batteries 18.3 Resistors and Light Bulbs 18.4 Energy and Power in Circuit Elements 18.5 Circuits 18.6 Experiments with Batteries and Light

Bulbs 18.7 Equivalent Resistance 18.8 Kirchoff’s Laws 18.9 RC Circuits 18.10 Summary 18.11 Problems

19. mAgNETIC FOrCES ANd FIEldS

19.1 Magnetic Poles 19.2 Magnetic Fields 19.3 Magnetic Force on a Charged Particle 19.4 Magnetic Force on a Current-carrying

Wire 19.5 Magnetic Field Due to a Wire 19.6 Loops and Solenoids 19.7 Calculating the Magnetic Field 19.8 Ampere’s Law 19.9 Magnetic Polarization and Refrigerator

Magnets 19.10 Summary 19.11 Problems

20. INduCTION

20.1 Faraday’s Law 20.2 Lenz’s Law 20.3 Inductors 20.4 Induced Magnetic Fields 20.5 Maxwell’s Equations 20.6 Summary 20.7 Problems

21. lIghT ANd ElECTrOmAgNETIC wAVES

21.1 Electromagnetic Waves 21.2 The Electromagnetic Spectrum 21.3 Huygens’s Principle 21.4 Reflection and Refraction 21.5 Energy in Electromagnetic Waves 21.6 Summary 21.7 Problems

22. gEOmETrICAl OPTICS

22.1 Spherical Waves and Curvature 22.2 Thin Lenses 22.3 Ray Tracing and Image Size 22.4 Spherical Mirrors 22.5 Combining Optical Elements 22.6 Optical Instruments 22.7 Summary 22.8 Problems

23. wAVE OPTICS

23.1 Double-Slit Interference 23.2 Gratings 23.3 Diffraction 23.4 Resolution 23.5 Thin Films 23.6 Polarization 23.7 Summary 23.8 Problems

24. SPECIAl rElATIVITy

24.1 The Two Principles of Relativity 24.2 The Three Effects 24.3 Applications and Paradoxes 24.4 Relative Velocity (Again) 24.5 Relativistic Mechanics 24.6 Summary 24.7 Problems

25. ATOmIC PhySICS ANd QuANTum mEChANICS

25.1 Photons 25.2 Atomic Physics 25.3 Quantum Mechanics 25.4 Spin and The Exclusion Principle 25.5 Summary 25.6 Problems

26. NuClEAr ANd PArTIClE PhySICS

26.1 Nuclear Forces 26.2 Nuclear Reactions 26.3 Elementary Particles 26.4 Fundamental Forces 26.5 Epilogue 26.6 Summary 26.7 Problems

Appendices Answers to Odd-Numbered ProblemsIndex

xi

What should a student expect to find in a physics textbook? What should be included that the reader will find useful and worth his or her effort? And what things that are commonly included in physics textbooks might effectively be left out? These are the questions that moti-vated us as we produced this book. We would like to preface our book by stating what the reader may expect to find and not to find in these pages.

First, most students in general college physics classes will depend on lectures by the pro-fessor for the introduction of new material, for explanations of the principles that describe how the universe behaves. But new material will often not be grasped at the first presenta-tion. An important goal of a textbook should be to provide a second look at the principles the student has learned in class. We want to be as clear as we can; we want to get quickly to the point of the principles being taught, without getting off on tangents; but we also want to provide enough background information that the situations where the principles apply are clearly understood.

Second, with an eye to learning where the principles apply, we provide many worked examples in which we use the principles to solve sample problems. But we do not feel that our examples need to explain how to solve all physics problems that the student may ever encoun-ter. On the contrary, the goal of the worked examples is simply to help the reader understand the principles by showing typical ways in which they apply. In particular, students should not expect to be able to read a problem from the back of the chapter and then browse through the worked examples to find one that tells them exactly how to solve their problem. That would mean that we were teaching procedures, not principles.

Third, the path the student should follow through the textbook should be clear. Many textbooks attach boxes and sidebars and web links, places where the reader will find all kinds of supplemental material—biographies of famous physicists, block diagrams showing how to solve certain kinds of problems, summaries of reasoning strategies, concept checks, etc. This often leaves the reader not knowing whether to stop and follow a parallel path or jump forward to stay with the text. We provide a single string to follow. Even when we break the narrative to display a worked example, the example is meant to be read in sequence. It will usually be introduced in the main text and then discussed in the text afterwards.

Fourth, the text should be readable. We find that a more informal style is easier to follow and more interesting. We talk with the reader about the physics. If we find something funny about our subject, we will share it with the reader. If we know of something that is difficult to understand, we will try to summarize and restate it in clear, short sentences.

PrEFACE

xii Preface

Fifth, the entire text should be short and to the point. Most textbooks spend pages and pages explaining interesting ways in which the principles of the chapter can be used to under-stand everyday things as diverse as the tides in the Bay of Fundy or the iridescence of drag-onfly wings. And we understand why books do this. We, ourselves, are fascinated by these applications and would dearly love to tell you all about them. But it all takes time to read and, truth be told, it does not help the student learn the physics any better or any more quickly. You will find a few such applications in our pages, but only a few.

In summary, let us just say that we have tried to always keep in mind that this book is for you, not for us.

College PhysiCs