by Alvin Halpern, Ph.D Brooklyn College SCHAUM'S OUTLINE SERIES McGraw-Hili New York San Francisco Washington, D.C Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto • Alvin Halpern Ph.D • Professor of Physics at Brooklyn College Dr Halpern has extensive teaching experience in physics and is the chairman of the physics department at Brooklyn College He is a member of the executive committee for the doctoral program in physics at CUNY and has written numerous research articles Project supervision was done by The Total Book Index by Hugh C Maddocks, Ph.D Library of Congress Cataloging-in-Publication Data Halpern, Alvin M Schaum's 3000 solved problems in physics I Physics-Problems, exercises, etc I Title II Title: Schaum's three thousand solved problems in physics QC32.H325 1988 530'.076 87-31075 ISBN 0-07-025636-5 14 15 16 17 18 19 VLP VLP ISBN 0-07-025734-5 (Formerly published under ISBN 0-07-025636-5.) Copyright © 1988 The McGraw-Hill Companies, Inc All rights reserved Printed 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 data base or retrieval system, without the prior written permission of the publisher McGraw-Hill A Division ofTheMcGraw·HiU ~ Companies CONTENTS ix CHAPTER SKELETONS WITH EXAMS Chapter MATHEMATICAL INTRODUCTION 1.1 Planar Vectors, Scientific Notation, and Units / 1.2 Three-Dimensional and Cross Products Chapter EQUILIBRIUM OF CONCURRENT Vectors; Dot 21 FORCES 2.1 Ropes, Knots, and Frictionless Pulleys / 2.2 Friction and Inclined Planes / 2.3 Graphical and Other Problems Chapter KINEMATICS Chapter NEWfON'S 36 IN ONE DIMENSION 3.1 Dimensions and Units; Constant-Acceleration Problems 51 LAWS OF MOTION 4.1 Force, Mass, and Acceleration / 4.2 Friction; Inclined Planes; Vector Notation / 4.3 Two-Object and Other Problems Chapter 76 MOTION IN A PLANE I 5.1 Projectile Motion / 5.2 Relative Motion 94 Chapter MOTION IN A PLANE II 6.1 Circular Motion; Centripetal Force / 6.2 Law of Universal Gravitation; Satellite Motion / 6.3 General Motion in a Plane Chapter 111 WORK AND ENERGY 7.1 Work Done by a Force / 7.2 Work, Kinetic Energy, and Potential Energy / 7.3 Conservation of Mechanical Energy / 7.4 Additional Problems Chapter 136 POWER AND SIMPLE MACHINES 8.1 Power / 8.2 Simple Machines Chapter 146 IMPULSE AND MOMENTUM 9.1 Elementary Problems / 9.2 Elastic Collisions / 9.3 Inelastic Collisions and Ballistic Pendulums / 9.4 Collisions in Two Dimensions / 9.5 Recoil and Reaction / 9.6 Center of Mass (see also Chap 10) Chapter 10 176 STATICS OF RIGID BODIES 10.1 Equilibrium of Rigid Bodies / 10.2 Center of Mass (Center of Gravity) Chapter 11 ROTATIONAL MOTION I: KINEMATICS AND DYNAMICS 207 11.1 Angular Motion and Torque / 11.2 Rotational Kinematics / 11.3 Torque and Rotation / 11.4 Moment of Inertia / 11.5 Translational-Rotational Relationships / 11.6 Problems Involving Cords Around Cylinders, Rolling Objects, etc Chapter 12 ROTATIONAL MOTION II: KINETIC ENERGY, ANGULAR MOMENTUM ANGULAR IMPULSE, 228 12.1 Energy and Power / 12.2 Angular Impulse; the Physical Pendulum / 12.3 Angular Momentum Chapter 13 MATIER IN BULK 247 13.1 Density and Specific Gravity / 13.2 Elastic Properties iii iv D CONTENTS Chapter 14 SIMPLE HARMONIC MOTION 256 14.1 Oscillations of a Mass on a Spring / 14.2 SHM of Pendulums and Other Systems Chapter 15 271 HYDROSTATICS 15.1 Pressure and Density / 15.2 Pascal's and Archimedes' Principles; Surface Tension Chapter 16 285 HYDRODYNAMICS 16.1 Equation of Continuity, Bernoulli's Equation, Torricelli's Theorem / 16.2 Viscosity, Stokes' Law, Poiseuille's Law, Turbulence, Reynolds Number Chapter 17 TEMPERATURE AND THERMAL EXPANSION 297 17.1 Temperature Scales; Linear Expansion / 17.2 Area and Volume Expansion Chapter 18 HEAT AND CALORIMETRY 307 18.1 Heat and Energy; Mechanical Equivalent of Heat / 18.2 Calqrimetry, Specific Heats, Heats of Fusion and Vaporization Chapter 19 19.1 Conduction Chapter 20 316 HEAT TRANSFER / 19.2 Convection / 19.3 Radiation 326 GAS LAWS AND KINETIC THEORY 20.1 The Mole Concept; the Ideal Gas Law / 20.2 Kinetic Theory / 20.3 Atmospheric Properties; Specific Heats of Solids Chapter 21 THE FIRST LAW OF THERMODYNAMICS 345 21.1 Basic Thermodynamic Concepts / 21.2 The First Law of Thermodynamics, Internal Energy, p - V Diagrams, Cyclical Systems Chapter 22 THE SECOND LAW OF THERMODYNAMICS 357 22.1 Heat Engines; Kelvin - Planck and Clausius Statements of the Second Law / 22.2 Entropy Chapter 23 366 WAVE MOTION 23.1 Characteristic Properties Chapter 24 / 23.2 Standing Waves and Resonance 379 SOUND 24.1 Sound Velocity; Beats; Doppler Shift / 24.2 Power, Intensity, Reverberation Time, Shock Waves Chapter 25 COULOMB'S LAW AND ELECTRIC FIELDS 387 25.1 Coulomb's Law of Electrostatic Force / 25.2 The Electric Field; Continuous Charge Distributions; Motion of Charged Particles in an Electric Field / 25.3 Electric Flux and Gauss's Law Chapter 26 ELECTRIC POTENTIAL AND CAP ACIT ANCE 407 26.1 Potential Due to Point Charges or Charge Distributions / 26.2 The Potential Function and the Associated Electric Field / 26.3 Energetics; Problems with Moving Charges / 26.4 Capacitance and Field Energy / 26.5 Capacitors in Combination Chapter 27 SIMPLE ELECTRIC CIRCUITS 432 27.1 Ohm's Law, Current, Resistance / 27.2 Resistors in Combination / 27.3 EMF and Electrochemical Systems / 27.4 Electric Measurement / 27.5 Electric Power / 27.6 More Complex Circuits, Kirchhoff's Circuit Rules, Circuits with Capacitance Chapter 28 THE MAGNETIC FIELD 28.1 Force on a Moving Charge / 28.2 Force on an Electric Current / 28.3 Torque and Magnetic Dipole Moment / 28.4 Sources of the Magnetic Field; Law of Biot and Savart / 28.5 More Complex Geometries; Ampere's Law 467 CONTENTS Chapter 29 MAGNETIC PROPERTIES 510 OF MATTER 29.1 The Hand M Fields; Susceptibility; Relative Permeability Strength Chapter 30 D v / 29.2 Magnets; Pole INDUCED EMF: GENERA TORS AND MOTORS 526 30.1 Change in Magnetic Flux, Faraday's Law, Lenz's Law / 30.2 Motional EMF; Induced Currents and Forces / 30.3 Time-Varying Magnetic and Induced Electric Fields / 30.4 Electric Generators and Motors Chapter 31 INDUCTANCE 31.1 Self-Inductance Chapter 32 552 / 31.2 Mutual Inductance: The Ideal Transformer ELECTRIC CIRCUITS 566 32.1 R-C, R-L, L-C and R-L-C Circuits; Time Response Steady State / 32.3 Time Behavior of AC Circuits Chapter 33 ELECTROMAGNETIC / 32.2 AC Circuits in the 590 WAVES 33.1 Displacement Current, Maxwell's Equations, the Speed of Light / 33.2 Mathematical Description of Waves in One and Three Dimensions / 33.3 The Component Fields of an Electromagnetic Wave; Induced EMF / 33.4 Energy and Momentum Fluxes Chapter 34 LIGHT AND OPTICAL PHENOMENA 34.1 Reflection and Refraction and Illumination Chapter 35 / 607 34.2 Dispersion and Color / 34.3 Photometry MIRRORS, LENSES, AND OPTICAL INSTRUMENTS 634 35.1 Mirrors / 35.2 Thin Lenses / 35.3 Lensmaker's Equation; Composite Lens Systems / 35.4 Optical Instruments: Projectors, Cameras, the Eye / 35.5 Optical Instruments: Microscopes and Telescopes Chapter 36 INTERFERENCE, DIFFRACTION, 36.1 Interference of Light Polarization of Light Chapter 37 / AND POLARIZATION 36.2 Diffraction and the Diffraction Grating 668 / 36.3 SPECIAL RELATIVITY 688 37.1 Lorentz Transformation, Length Contraction, Time Dilation, and Velocity Transformation / 37.2 Mass-Energy Relation; Relativistic Dynamics Chapter 38 708 PARTICLES OF LIGHT AND WAVES OF MATTER 38.1 Photons and the Photoelectric Effect / 38.2 Compton Scattering; X-rays; Pair Production and Annihilation / 38.3 de Broglie Waves and the Uncertainty Principle Chapter 39 MODERN PHYSICS: ATOMS, NUCLEI, SOLID-STATE ELECTRONICS 39.1 Atoms and Molecules Electronics INDEX / 39.2 Nuclei and Radioactivity / 720 39.3 Solid-State 737 TO THE STUDENT This book is intended for use by students of general physics, either in calculus- or noncalculusbased courses Problems requiring real calculus (not merely calculus notation) are marked with a small superscript c The only way to master general physics is to gain ability and sophistication in problem-solving This book is meant to make you a master of the art - and should so if used properly As a rule, a problem can be solved once you have learned the ideas behind it; sometimes these very ideas are brought into sharper focus by looking at sample problems and their solutions If you hav.e difficulty with a topic, you can select a few problems in that area, examine the solutions carefully, and then try to solve related problems before looking at the printed solutions There are numerous ways of posing a problem and, frequently, numerous ways of solving one You should try to gain understanding of how to approach various classes of problems, rather than memorizing particular solutions Understanding is better than memory for success in physics The problems in this book cover every important topic in a typical two- or three-semester general physics sequence Ranging from the simple to the complex, they will provide you with plenty of practice and food for thought The Chapter Skeletons with Exams, beginning on the next page, was devised to help students with limited time gain maximum benefit from this book It is hoped that the use of this feature is selfevident; still, the following remarks may help: • The Chapter Skeletons divide the problems in this book into three categories: SCAN, HOMEWORK and EXAMS (Turn to page ix to see an example.) • To gain a quick overview of the basic ideas in a chapter, review the SCAN problems and study their printed solutions • HOMEWORK problems are for practicing your problem-solving skills; cover the solution with an index card as you read, and try to solve, the problem Do both sets if your course is calculus based • No problem from SCANor HOMEWORKis duplicated in EXAMS,and no two Exams overlap Calculus-based students are urged also to take the Hard Exam Exams run about 60 minutes, unless otherwise indicated • Still further problems constitute the two groups of Final Exams Stay in your category(ies), and good luck vii ix ... Cataloging -in- Publication Data Halpern, Alvin M Schaum's 3000 solved problems in physics I Physics -Problems, exercises, etc I Title II Title: Schaum's three thousand solved problems in physics QC32.H325 1988 530'.076... solving one You should try to gain understanding of how to approach various classes of problems, rather than memorizing particular solutions Understanding is better than memory for success in physics. .. select a few problems in that area, examine the solutions carefully, and then try to solve related problems before looking at the printed solutions There are numerous ways of posing a problem