3000 solved problems in physcis

782 Pages·1988·32.919 MB·English

by  Alvin Halpern

by
Alvin Halpern, Ph.D.
Brooklyn College
SCHAUM'S OUTLINE SERIES
McGraw-Hili
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Caracas Lisbon London Madrid Mexico City Milan
Montreal New Delhi San Juan Singapore
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• Alvin Halpern. Ph.D.•Professor of Physics at Brooklyn College
Dr. Halpernhasextensiveteachingexperience inphysicsandisthechairmanof
the physics department at Brooklyn College. He is a member of the executive
committeeforthedoctoralprograminphysicsatCUNYandhaswrittennumerous
research articles.
Project supervision wasdone byThe Total Book.
Index byHugh C. Maddocks, Ph.D.
Library ofCongress Cataloging-in-Publication Data
Halpern, Alvin M.
Schaum's 3000 solvedproblems inphysics.
I. Physics-Problems, exercises, etc. I. Title.
II. Title: Schaum's threethousand solvedproblems
inphysics.
QC32.H325 1988 530'.076 87-31075
ISBN0-07-025636-5
14 15 16 17 18 19 VLP VLP 0 5 4 3 2
ISBN 0-07-025734-5 (Formerly published under ISBN 0-07-025636-5.)
Copyright © 1988The 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 ~
ADivision ofTheMcGraw·HiU Companies
CONTENTS
CHAPTER SKELETONS WITH EXAMS ix
Chapter 1 MATHEMATICAL INTRODUCTION 1
1.1 Planar Vectors, Scientific Notation, and Units / 1.2 Three-Dimensional Vectors; Dot
and Cross Products
Chapter 2 EQUILIBRIUM OF CONCURRENT FORCES 21
2.1 Ropes, Knots, and Frictionless Pulleys / 2.2 Friction and Inclined Planes /
2.3 Graphical and Other Problems
Chapter 3 KINEMATICS IN ONE DIMENSION 36
3.1 Dimensions and Units; Constant-Acceleration Problems
Chapter 4 NEWfON'S LAWS OF MOTION 51
4.1 Force, Mass, and Acceleration / 4.2 Friction; Inclined Planes; Vector
Notation / 4.3 Two-Object and Other Problems
Chapter 5 MOTION IN A PLANE I 76
5.1 Projectile Motion / 5.2 Relative Motion
Chapter 6 MOTION IN A PLANE II 94
6.1 Circular Motion; Centripetal Force / 6.2 Law of Universal Gravitation; Satellite
Motion / 6.3 General Motion in aPlane
Chapter 7 WORK AND ENERGY 111
7.1 Work Done by aForce / 7.2 Work, Kinetic Energy,. and Potential
.Energy / 7.3 Conservation of Mechanical Energy / 7.4 Additional Problems
Chapter 8 POWER AND SIMPLE MACHINES 136
8.1 Power / 8.2 Simple Machines
Chapter 9 IMPULSE AND MOMENTUM 146
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 STATICS OF RIGID BODIES 176
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 IMPULSE,
ANGULAR MOMENTUM 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 aMass on aSpring / 14.2 SHM of Pendulums and Other Systems
Chapter 15 HYDROSTATICS 271
15.1 Pressure and Density / 15.2 Pascal's and Archimedes' Principles; Surface Tension
Chapter 16 HYDRODYNAMICS 285
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 ofHeat / 18.2 Calqrimetry, Specific
Heats, Heats of Fusion and Vaporization
Chapter 19 HEAT TRANSFER 316
19.1 Conduction / 19.2 Convection / 19.3 Radiation
Chapter 20 GAS LAWS AND KINETIC THEORY 326
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 ofThermodynamics, Internal
Energy, p-VDiagrams, 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 WAVE MOTION 366
23.1 Characteristic Properties / 23.2 Standing Waves and Resonance
Chapter 24 SOUND 379
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 CAPACITANCE 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 467
28.1 Force on aMoving Charge / 28.2 Force on an Electric Current / 28.3 Torque and
Magnetic Dipole Moment / 28.4 Sources of the Magnetic Field; Law ofBiot and
Savart / 28.5 More Complex Geometries; Ampere's Law
CONTENTS D v
Chapter 29 MAGNETIC PROPERTIES OF MATTER 510
29.1The Hand M Fields; Susceptibility; Relative Permeability / 29.2Magnets; Pole
Strength
Chapter 30 INDUCED EMF: GENERA TORS AND MOTORS 526
30.1Change in Magnetic Flux, Faraday's Law, Lenz's Law / 30.2Motional
EMF; Induced Currents and Forces / 30.3Time-Varying Magnetic and Induced
Electric Fields / 30.4Electric Generators and Motors
Chapter 31 INDUCTANCE 552
31.1Self-Inductance / 31.2Mutual Inductance: The Ideal Transformer
Chapter 32 ELECTRIC CIRCUITS 566
32.1R-C, R-L, L-C and R-L-C Circuits; Time Response / 32.2AC Circuits in the
Steady State / 32.3Time Behavior ofAC Circuits
Chapter 33 ELECTROMAGNETIC WAVES 590
33.1Displacement Current, Maxwell's Equations, the Speed of Light / 33.2
Mathematical Description of Waves in One and Three Dimensions / 33.3The
Component Fields ofan Electromagnetic Wave; Induced EMF / 33.4Energy and
Momentum Fluxes
Chapter 34 LIGHT AND OPTICAL PHENOMENA 607
34.1Reflection and Refraction / 34.2Dispersion and Color / 34.3Photometry
and Illumination
Chapter 35 MIRRORS, LENSES, AND OPTICAL INSTRUMENTS 634
35.1Mirrors / 35.2Thin Lenses / 35.3Lensmaker's Equation; Composite
Lens Systems / 35.4Optical Instruments: Projectors, Cameras, the Eye / 35.5
Optical Instruments: Microscopes and Telescopes
Chapter 36 INTERFERENCE, DIFFRACTION, AND POLARIZATION 668
36.1Interference of Light / 36.2Diffraction and the Diffraction Grating / 36.3
Polarization of Light
Chapter 37 SPECIAL RELATIVITY 688
37.1Lorentz Transformation, Length Contraction, Time Dilation, and Velocity
Transformation / 37.2Mass-Energy Relation; Relativistic Dynamics
Chapter 38 PARTICLES OF LIGHT AND WAVES OF MATTER 708
38.1Photons and the Photoelectric Effect / 38.2Compton Scattering; X-rays; Pair
Production and Annihilation / 38.3de Broglie Waves and the Uncertainty
Principle
Chapter 39 MODERN PHYSICS: ATOMS, NUCLEI, SOLID-STATE ELECTRONICS 720
39.1Atoms and Molecules / 39.2Nuclei and Radioactivity / 39.3Solid-State
Electronics
INDEX 737
TO THE STUDENT
This book is intended for use by students of general physics, either in calculus- or noncalculus-
based 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 do 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 bylooking at sample problems and their solutions. Ifyou hav.edifficulty
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 togain understanding ofhowto approach various classesofproblems, rather than memorizing
particular solutions. Understanding isbetter 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 willprovide you with plenty ofpractice
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 self-
evident; 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 seean example.)
• To gain a quick overview of the basic ideas in a chapter, review the SCAN problems and
study their printed solutions.
• HOMEWORK problems arefor practicing your problem-solving skills;cover thesolution 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 60minutes,
unless otherwise indicated.
• Stillfurther problems constitute the two groups ofFinal Exams. Stay inyour category(ies), and
good luck.
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