SCHAUM'S OUTLINE OF THEORY AND PROBLEMS OF COLLEGE PHYSICS Ninth Edition FREDERICK J BUECHE, Ph.D Distinguished Professor at Large University of Dayton EUGENE HECHT, Ph.D Professor of Physics Adelphi University SCHAUM'S OUTLINE SERIES McGRAW-HILL New York St Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto abc McGraw-Hill Copyright © 1997, 1989, 1979, 1961, 1942, 1940, 1939, 1936 by The McGraw-Hill Companies, Inc All rights reserved Manufactured in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher 0-07-1367497 The material in this eBook also appears in the print version of this title: 0-07-008941-8 All trademarks are trademarks of their respective owners Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark Where such designations appear in this book, they have been printed with initial caps McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069 TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc (“McGraw-Hill”) and its licensors reserve all rights in and to the work Use of this work is subject to these terms Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited Your right to use the work may be terminated if you fail to comply with these terms THE WORK IS PROVIDED “AS IS” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE McGraw-Hill and its licensors not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom McGraw-Hill has no responsibility for the content of any information accessed through the work Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise DOI: 10.1036/0071367497 Preface The introductory physics course, variously known as ``general physics'' or ``college physics,'' is usually a two-semester in-depth survey of classical topics capped o€ with some selected material from modern physics Indeed the name ``college physics'' has become a euphemism for introductory physics without calculus Schaum's Outline of College Physics was designed to uniquely complement just such a course, whether given in high school or in college The needed mathematical knowledge includes basic algebra, some trigonometry, and a tiny bit of vector analysis It is assumed that the reader already has a modest understanding of algebra Appendix B is a general review of trigonometry that serves nicely Even so, the necessary ideas are developed in place, as needed And the same is true of the rudimentary vector analysis that's requiredÐit too is taught as the situation requires In some ways learning physics is unlike learning most other disciplines Physics has a special vocabulary that constitutes a language of its own, a language immediately transcribed into a symbolic form that is analyzed and extended with mathematical logic and precision Words like energy, momentum, current, ¯ux, interference, capacitance, and so forth, have very speci®c scienti®c meanings These must be learned promptly and accurately because the discipline builds layer upon layer; unless you know exactly what velocity is, you cannot know what acceleration or momentum are, and without them you cannot know what force is, and on and on Each chapter in this book begins with a concise summary of the important ideas, de®nitions, relationships, laws, rules, and equations that are associated with the topic under discussion All of this material constitutes the conceptual framework of the discourse, and its mastery is certainly challenging in and of itself, but there's more to physics than the mere recitation of its principles Every physicist who has ever tried to teach this marvelous subject has heard the universal student lament, ``I understand everything; I just can't the problems.'' Nonetheless most teachers believe that the ``doing'' of problems is the crucial culmination of the entire experience, it's the ultimate proof of understanding and competence The conceptual machinery of de®nitions and rules and laws all come together in the process of problem solving as nowhere else Moreover, insofar as the problems re¯ect the realities of our world, the student learns a skill of immense practical value This is no easy task; carrying out the analysis of even a moderately complex problem requires extraordinary intellectual vigilance and un¯agging attention to detail above and beyond just ``knowing how to it.'' Like playing a musical instrument, the student must learn the basics and then practice, practice, practice A single missed note in a sonata is overlookable; a single error in a calculation, however, can propagate through the entire e€ort producing an answer that's completely wrong Getting it right is what this book is all about Although a selection of new problems has been added, the 9th-edition revision of this venerable text has concentrated on modernizing the work, and improving the pedagogy To that end, the notation has been simpli®ed and made consistent throughout For example, force is now symbolized by F and only F; thus centripetal force is FC, weight is FW, tension is FT, normal force is FN, friction is Ff, and so on Work (W ) will never again be confused with weight (FW), and period iii Copyright 1997, 1989, 1979, 1961, 1942, 1940, 1939, 1936 The McGraw-Hill Companies, Inc Click Here for Terms of Use iv SIGNIFICANT FIGURES (T ) will never be mistaken for tension (FT) To better match what's usually written in the classroom, a vector is now indicated by a boldface symbol with a tiny arrow above it The idea of signi®cant ®gures is introduced (see Appendix A) and scrupulously adhered to in every problem Almost all the de®nitions have been revised to make them more precise or to re¯ect a more modern perspective Every drawing has been redrawn so that they are now more accurate, realistic, and readable If you have any comments about this edition, suggestions for the next edition, or favorite problems you'd like to share, send them to E Hecht, Adelphi University, Physics Department, Garden City, NY 11530 Freeport, NY EUGENE HECHT Contents Chapter INTRODUCTION TO VECTORS Chapter UNIFORMLY ACCELERATED MOTION 13 Chapter NEWTON'S LAWS 27 Chapter EQUILIBRIUM UNDER THE ACTION OF CONCURRENT FORCES 47 EQUILIBRIUM OF A RIGID BODY UNDER COPLANAR FORCES 56 Scalar quantity Vector quantity Resultant Graphical addition of vectors (polygon method) Parallelogram method Subtraction of vectors Trigonometric functions Component of a vector Component method for adding vectors Unit vectors Displacement Speed Velocity Acceleration Uniformly accelerated motion along a straight line Direction is important Instantaneous velocity Graphical interpretations Acceleration due to gravity Velocity components Projectile problems Mass Standard kilogram Force Net external force The newton Newton's First Law Newton's Second Law Newton's Third Law Law of universal gravitation Weight Relation between mass and weight Tensile force Friction force Normal force Coecient of kinetic friction Coecient of static friction Dimensional analysis Mathematical operations with units Concurrent forces An object is in equilibrium First condition for equilibrium Problem solution method (concurrent forces) Weight of an object Tensile force Friction force Normal force Chapter Torque (or moment) Two conditions for equilibrium Position of the axis is arbitrary Center of gravity Chapter WORK, ENERGY, AND POWER 69 Chapter SIMPLE MACHINES 80 Work Unit of work Energy Kinetic energy Gravitational potential energy Work-energy theorem Conservation of energy Power Kilowatt-hour A machine Principle of work Mechanical advantage Eciency v Copyright 1997, 1989, 1979, 1961, 1942, 1940, 1939, 1936 The McGraw-Hill Companies, Inc Click Here for Terms of Use vi PREFACE Chapter IMPULSE AND MOMENTUM 87 Chapter ANGULAR MOTION IN A PLANE 99 Chapter 10 RIGID-BODY ROTATION 111 Chapter 11 SIMPLE HARMONIC MOTION AND SPRINGS 126 Chapter 12 DENSITY; ELASTICITY 138 Chapter 13 FLUIDS AT REST 146 Chapter 14 FLUIDS IN MOTION 157 Chapter 15 THERMAL EXPANSION 166 Linear momentum Impulse Impulse causes change in momentum Conservation of linear momentum Collisions and explosions Perfectly elastic collision Coecient of restitution Center of mass Angular displacement Angular speed Angular acceleration Equations for uniformly accelerated motion Relations between angular and tangential quantities Centripetal acceleration Centripetal force Torque (or moment) Moment of inertia Torque and angular acceleration Kinetic energy of rotation Combined rotation and translation Work Power Angular momentum Angular impulse Parallel-axis theorem Analogous linear and angular quantities Period Frequency Graph of a vibratory motion Displacement Restoring force Simple harmonic motion Hookean system Elastic potential energy Energy interchange Speed in SHM Acceleration in SHM Reference circle Period in SHM Acceleration in terms of T Simple pendulum SHM Mass density Speci®c gravity Elasticity Stress Strain Young's modulus Bulk modulus Shear modulus Elastic limit Average pressure Standard atmospheric pressure Hydrostatic pressure Pascal's principle Archimedes' principle Fluid ¯ow or discharge Equation of continuity Shear rate Viscosity Poiseuille's Law Work done by a piston Work done by a pressure Bernoulli's equation Torricelli's theorem Reynolds number Temperature expansion Linear expansion of solids Area expansion Volume vii SIGNIFICANT FIGURES Chapter 16 IDEAL GASES 171 Chapter 17 KINETIC THEORY 179 Chapter 18 HEAT QUANTITIES 185 Chapter 19 TRANSFER OF HEAT ENERGY 193 Chapter 20 FIRST LAW OF THERMODYNAMICS 198 Chapter 21 ENTROPY AND THE SECOND LAW 209 Chapter 22 WAVE MOTION 213 Chapter 23 SOUND 223 Ideal (or perfect) gas One mole of a substance Ideal Gas Law Special cases Absolute zero Standard conditions or standard temperature and pressure (S.T.P.) Dalton's Law of partial pressures Gas-law problems Kinetic theory Avogadro's number Mass of a molecule Average translational kinetic energy Root mean square speed Absolute temperature Pressure Mean free path Thermal energy Heat Speci®c heat Heat gained (or lost) Heat of fusion Heat of vaporization Heat of sublimation Calorimetry problems Absolute humidity Relative humidity Dew point Energy can be transferred Radiation Conduction Thermal resistance Convection Heat Internal energy Work done by a system First Law of Thermodynamics Isobaric process Isovolumic process Isothermal process Adiabatic process Speci®c heats of gases Speci®c heat ratio Work related to area Eciency of a heat engine Second Law of Thermodynamics Most probable state Entropy Entropy is a measure of disorder Propagating wave Wave terminology In-phase vibrations Speed of a transverse wave Standing waves Conditions for resonance Longitudinal (compressional) waves Sound waves Equations for sound speed Speed of sound in air Loudness Intensity (or loudness) level Beats Doppler e€ect Interference e€ects Intensity viii CONTENTS Chapter 24 COULOMB'S LAW AND ELECTRIC FIELDS 232 Chapter 25 POTENTIAL; CAPACITANCE 243 Chapter 26 CURRENT, RESISTANCE, AND OHM'S LAW 256 Chapter 27 ELECTRICAL POWER 265 Chapter 28 EQUIVALENT RESISTANCE; SIMPLE CIRCUITS 270 Chapter 29 KIRCHHOFF'S LAWS 283 Chapter 30 FORCES IN MAGNETIC FIELDS 289 Chapter 31 SOURCES OF MAGNETIC FIELDS 299 Chapter 32 INDUCED EMF; MAGNETIC FLUX 305 Coulomb's Law Charge quantized Conservation of charge Test-charge concept Electric ®eld Strength of the electric ®eld Electric ®eld due to a point charge Superposition principle Potential di€erence Absolute potential Electrical potential energy V related to E Electron volt energy unit Capacitor Parallel-plate capacitor Capacitors in parallel and series Energy stored in a capacitor Current Battery Resistance Ohm's Law Measurement of resistance by ammeter and voltmeter Terminal potential di€erence Resistivity Resistance varies with temperature Potential changes Electrical work Electrical power Power loss in a resistor generated in a resistor Convenient conversions Resistors in series Thermal energy Resistors in parallel Kirchho€'s node (or junction) rule equations obtained Kirchho€'s loop (or circuit) rule Set of Magnetic ®eld Magnetic ®eld lines Magnet Magnetic poles Charge moving through a magnetic ®eld Direction of the force Magnitude of the force Magnetic ®eld at a point Force on a current in a magnetic ®eld Torque on a ¯at coil Magnetic ®elds are produced Direction of the magnetic ®eld Ferromagnetic materials Magnetic moment Magnetic ®eld of a current element Magnetic e€ects of matter Magnetic ®eld lines Magnetic ¯ux Faraday's Law for induced emf Lenz's Law Motional emf Induced emf ix SIGNIFICANT FIGURES Chapter 33 ELECTRIC GENERATORS AND MOTORS 315 Chapter 34 INDUCTANCE; R-C AND R-L TIME CONSTANTS 321 Chapter 35 ALTERNATING CURRENT 329 Chapter 36 REFLECTION OF LIGHT 338 Chapter 37 REFRACTION OF LIGHT 346 Chapter 38 THIN LENSES 353 Chapter 39 OPTICAL INSTRUMENTS 359 Chapter 40 INTERFERENCE AND DIFFRACTION OF LIGHT 366 Chapter 41 RELATIVITY 374 Electric generators Electric motors Self-inductance Mutual inductance Energy stored in an inductor constant R-L time constant Exponential functions R-C time Emf generated by a rotating coil Meters Thermal energy generated or power lost Forms of Ohm's Law Phase Impedance Phasors Resonance Power loss Transformer Nature of light Law of re¯ection Plane mirrors Mirror equation Size of the image Speed of light Index of refraction total internal re¯ection Prism Refraction Type of lenses Object and image relation Lenses in contact Combination of thin lenses Telescope Spherical mirrors Snell's Law Critical angle for Lensmaker's equation The eye Magnifying glass Lens power Microscope Coherent waves Relative phase Interference e€ects Di€raction Single-slit di€raction Limit of resolution Di€raction grating equation Di€raction of X-rays Optical path length Reference frame Special theory of relativity Relativistic linear momentum Limiting speed Relativistic energy Time dilation Simultaneity Length contraction Velocity addition formula .. .SCHAUM'' S OUTLINE OF THEORY AND PROBLEMS OF COLLEGE PHYSICS Ninth Edition FREDERICK J BUECHE, Ph.D Distinguished Professor at Large University of Dayton EUGENE HECHT, Ph.D Professor of Physics. .. the name ` `college physics'' '' has become a euphemism for introductory physics without calculus Schaum'' s Outline of College Physics was designed to uniquely complement just such a course, whether... course, variously known as ``general physics'' '' or ` `college physics, '''' is usually a two-semester in-depth survey of classical topics capped o€ with some selected material from modern physics Indeed