College Physics. Putting It All Together. Jeff Adams. Greg Francis. Ron Hellings. Montana State University. Montana State University

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1 College Physics

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3 College Physics Putting It All Together Ron Hellings Montana State University Jeff Adams Montana State University Greg Francis Montana State University university science books mill valley, california

4 University Science Books Mill Valley, California Editor: Jane Ellis Production manager: Julianna Scott Fein Manuscript editor: Lee Young Illustrator: Laurel Muller Text design: Yvonne Tsang at Wilsted & Taylor Cover design: Yvonne Tsang at Wilsted & Taylor Compositor: Laurel Muller Printer and binder: [to come] This book is printed on acid-free paper. Print ISBN ebook ISBN Copyright 2017 by University Science Books Reproduction or translation of any part of this work beyond that permitted by Section 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 Data Names: 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 ISBN (alk. paper) ISBN (alk. paper) ISBN (ebook) ISBN (ebook) Subjects: LCSH: Physics--Textbooks. Classification: LCC QC21.3.H DDC 530--dc23 LC record available at Printed in the United States of America

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

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7 CONTENTS Preface vii 1. Introduction Measurement Arithmetic Working with Units Mathematics Requirements Summary Problems 8 2. One-Dimensional Kinematics The Coordinate System Displacement Velocity Straight Line Acceleration: Speeding Up and Slowing Down Graphing the Motion Equations Governing Uniformly Accelerated Motion Free Fall How to Solve Physics Problems Summary Problems Two-Dimensional Kinematics Position Vectors and Coordinate Systems Displacement and Velocity Acceleration in Two Dimensions Projectile Motion Circular Motion and Centripetal Acceleration Relative Velocity Summary Problems Newton s Laws Newton s First Law Newton s Second Law Newton s Third Law Forces Free-Body Diagrams Statics Summary Problems Vectors Superposition Vectors and Scalars Vector Addition Vector Subtraction Trigonometry Review Vector Components Vector Addition (Revisited) Summary Problems Forces Gravitational Force Weight Normal Force Frictional Forces Kinetic and Static Problems On an Inclined Plane Tension Elastic and Spring Forces Refrigerator Magnet Force Apparent Weight Centripetal Force Centrifugal and Other Fictitious Forces Summary Problems 000

8 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 Summary 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

9 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 Summary Problems 17. Voltag e 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 Summary 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 Summary 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

10 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 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 Problems Index 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

11 PREFACE 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 motivated 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 professor 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 presentation. 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 encounter. 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. xi

12 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 understand everyday things as diverse as the tides in the Bay of Fundy or the iridescence of dragonfly 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.

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