by
Alvin Halpern, Ph.D.
Brooklyn College

SCHAUM'S OUTLINE SERIES
McGraw-Hili
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•

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 0 5 4 3 2

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 1 MATHEMATICAL

1

INTRODUCTION


1.1 Planar Vectors, Scientific Notation, and Units / 1.2 Three-Dimensional
and Cross Products

Chapter 2

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 3

KINEMATICS

Chapter 4

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 5

76

MOTION IN A PLANE I
5.1 Projectile Motion / 5.2 Relative Motion

94

Chapter 6 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 7

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 8

136

POWER AND SIMPLE MACHINES
8.1 Power / 8.2 Simple Machines

Chapter 9

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 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 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