University Physics

880 Pages·1984·20.53 MB·English

by  George Arfken

_ /
UNIVERSITY PHYSICS
George B. Arfken • David F. Griffing
Donald C. Kelly• Joseph Priest
Miami University, Oxford, Ohio
@
ACADEMIC PRESS, INC.
(Harcourt Brace Jovanovich, Publishers)
Orlando San Diego San Francisco New York
London Toronto Montreal Sydney Tokyo
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To: Carolyn
Louise
Jane
Mary Jean
The Cover
The cover design is a modification of a sketch in Sir Isaac
Newton's Principia. The sketch shows the transition from pro
jectile paths on the earth to satellite orbits around the earth.
Aristotle had advocated completely separate laws to describe
motions on the earth and motions in the heavens. When
Newton synthesized these motions under a single set of physi
cal laws he broke a 2000-year-old tradition. With this sketch
Newton made the point that gravitation and his laws of motion
were universal. Beginning with this Newtonian synthesis,
physics has developed as a science concerned with universal
relationships.
Earth photograph courtesy of NASA
Title page art from Isaac Newton's Principia, Volume 2,
page 551, 1966. Reprinted by permission of the University
of California Press.
Copyright © 1984 by Academic Press, Inc.
All rights reserved.
No part of this publication may be reproduced or trans
mitted in any form or by any means, electronic or mechan
ical, including photocopying, recording, or any informa
tion storage and retrieval system, without permission in
writing from the publisher.
Academic Press, Inc.
Orlando, Florida 32887
United Kingdom Edition Published by
Academic Press, Inc. (London) Ltd.
24/28 Oval Road, London NW I ?DX
ISBN: 0-12-059860-4
Library of Congress Catalog Card Number: 83 · 7 I 920
Printed in the United States of America
Photo credits appear on page 894.
PREFACE
After having spent many years-more than I 00, bored with thoughtful, accurate, and thorough expla
collectively- teaching introductory physics to science, nations, and such explanations are required by average
engineering, and mathematics students, we have devel students. The liberal use of examples and illustrations, our
oped strong notions about the type of features a textbook problem solving guide, and the gradual introduction of
should include to meet their needs. The characteristics we calculus help to produce the sensitive atmosphere we are
consider important are: ( 1) an authoritative treatment of striving for.
physics; (2) a special sensitivity to students, particularly We assume no prior knowledge of calculus, but ex
freshmen, who are learning physics and calculus simulta pect that students will study it concurrently with their
neously; (3) an emphasis on the unity of physics; (4) a physics course. Particularly for freshmen, calculus should
sound pedagogical presentation; (5) the development of be integrated into the text carefully and gradually. Accord
problem solving skills; and (6) a broad variety of relevant ingly, calculus-based analyses and problems are introduced
applications, problems, and questions. Some elaboration slowly
of these features should help the reader understand our
intent in developing this book. The Unity of Physics
An Authoritative Treatment of Physics
Newtonian mechanics, one of the foundations of physics,
is normally taught first in an introductory course. To help
A major strength of our book lies in the backgrounds and students recognize the unity of physics, we have illustrated
experiences of its authors. Each author has not only taught Newtonian mechanics with examples from such areas as
introductory physics for many years but has taught physics astrophysics, particle physics, atomic physics, and sports,
courses at all levels. Each has conducted physics research, in addition to using the customary array of inclined plane,
and each has written successful physics textbooks. The rocket, projectile, and billiard ball examples. We have
collective wisdom of the authors, the interchange of ideas constructed a bridge between classical and modern physics
in teaching and writing, and the careful scrutiny given to so students will recognize universal concepts. To reinforce
each others' work have contributed to the goal of creating this bridge, we have used extensive cross-referencing in
what we feel is an authoritative physics textbook. the text.
For several years the manuscript was rigorously class
tested at Miami University by the authors and their colleagues. A Sound Pedagogical Presentation
During its preparation many reviewers, from a broad cross sec
tion of colleges and universities, have constructively criticized
In addition to presenting the most important physical con
the manuscript. The combination of our class-testing experi
cepts in the least intimidating way, we have provided
ence and the reviewer feedback add to our confidence in the
specific pedagogical aids to assist the student in using this
authoritative nature of the book.
textbook.
Sensitivity to Students (I) Each chapter begins with a preview of what is covered
in the chapter. When a chapter is the first in a sequence of
related chapters, the preview introduces the entire group
We believe in being patient with students rather than fol
of chapters.
lowing the sink or swim approach taken in several of the
popular texts. Many capable students enter their first phys (2) A Problem Solving Guide is introduced early to con
ics course with definite insecurities about their ability to vey the importance of problem solving skills. We know
succeed. Our goal is to create a learning environment that that if students cannot solve the problems, they cannot
inspires student confidence. Advanced students do not get understand the physics. Therefore, this step-by-step guide
xi
not only provides the simple mechanics ot problem solving i-mally, we provide prootems mat auow sruaents to test
but also emphasizes the necessity for understanding the their application of these skills.
physics involved.
Problems and Questions
(3) Important principles are generously illustrated with
step-by-step examples and clear, attractive, two-color il
lustrations. Examples provide the basis for developing To increase the value of the problems and questions, they
problem solving skills, and illustrations portray concepts in are: ( 1) made appropriate to the text content; (2) gradu
a way words cannot express. ated to challenge students' increasing abilities; and (3)
varied to incorporate examples that are engaging to stu·
(4) Appropriate end-of-chapter problems are organized
dents. The more than 1700 class-tested problems provide
by section and keyed to specific text discussions to test the
the drill necessary for students to grasp the principles and
student's ability to apply physics principles.
concepts of physics.
(5) Brief summaries at the end of each chapter highlight In addition to the features mentioned above, the book
significant principles, equations, and other topics covered contains sufficient material to serve either a two-, three-,
in the chapter. or four-semester course. We use the Systeme International
d'Unites (SI units) throughout the text, but we occa
Our experience indicates that each of these ped
sionally include pounds, miles, and other British System
agogical features will support the understanding of this
units for comparison.
sometimes difficult subject.
We are indebted to many reviewers for their helpful
criticisms and analyses during the development of this
The Development of
text. The penetrating criticism of Dr. James Smith of the
Problem Solving Skills University of Illinois was especially valuable. We particu
larly appreciate and acknowledge his contribution. A spe
cial thank you is due Kathy Civetta for her fine editorial
A step-by-step problem solving guide is introduced in
work, and to Jane Kelly for her peerless typing.
Chapter 3 and extended in Chapter 6. These two strategi
cally placed chapters provide a basis for developing the
skills necessary to solve word problems in physics. Each George Arfken
step is carefully and systematically described to show stu David F. Griffing
dents how to approach and solve problems. We then illus Donald C. Kelly
trate the use of this guide thorugh step-by-step examples. Joseph Priest
xii
INS'l'RUCl'IONAL
AIDS TO
ACCOMPANY
UNIVERSITY
PHYSTCS
The following ancillaries are available from the publisher explore certain problems in greater depth. Listings are
to augment the text material. given for Apple, IBM, and Radio Shack microcomputers.
Computer Software
Student Study Guide
by T. William Houk, James E. Poth,
An1 imaginative computer software package keyed spe
and John W. Snider, Miami University cifically to sections in the text is available to students to
strengthen their understanding of physics concepts while
providing interest and motivation. Three computer disks,
The study guide provides students with additional drill
with approximately 18 programs per disk, allow students
work and further review of important physics concepts. It
to plug in their own data and watch physics concepts in
includes brief previews of each chapter, section summaries
action. Seeing physics in motion is an excellent way for
highlighting key terms and definitions, detailed solutions
students to gain hands-on experience with relevant physics
of example problems, and additional practice problems for
problems.
students to work.
Instructor's Answer Book
Student Solutions Manual
Answers are provided to instructors for all the problems in
the text.
This manual contains solutions or hints for over 450 of the
problems in Univmity Physics. Solutions are given for prob
Overhead Transparencies
lems that illustrate points not covered in text examples,
and problems that extend ideas developed in the text.
Hints are supplied for some of the more challenging prob Acetate transparencies of important text illustrations are
lems and in instances where the hint can shorten the solu available to adopters as a support to text discussions. In
tion. Following selected solutions is a collection of com structors can point out the pertinent features of text illus
puter programs written in BASIC that allows students to trations and discuss these concepts in the classroom.
c h t e r
EN
INIRODIJCIION
I. The Development of Science
2 Science and Measurement
1. 3 Length
1.4 Time
l. 5 Mass
1.6 Dimensions and Units
1.7 Physics, Mathematics, and You
Summary
Suggested Reading
Problems
1.1
The Development of
Science
From earliest history people have been curious about the
world around them, and have sought correlations and pat
terns of behavior in nature. The early Egyptians, for in
stance, noticed that the Nile River flooded each year when
the bright star Sirius rose at dawn, and wondered whether
these events were connected.
Curiosity about the motion of the planets eventually
led to the Copernican revolution.* In fact, people's curi
osity and their attempts to find an order to the universe led
directly to the development of physics as a science. Today
the patterns and the order of our physical world are ex
pressed by physical laws and conservation principles.
These laws and principles are concise expressions that en
able scientists and engineers to describe many aspects of
physical behavior and to predict future physical behavior.
The goal of physics is often described as a search for the
physical laws that govern the universe.
Physics is a diverse and evolving collection of special
branches of knowledge unified by common physical laws.
Table 1. 1 lists a number of these branches. The division of
these branches into the areas of classical physics and mod
ern physics is arbitrary but convenient. Roughly speaking,
classical physics consists of the branches that were well
developed by 1900. Modern physics has emerged since
that time. The distinction between classical and modern
*The Polish astronomer Nicolaus Copernicus (1473-1543) developed the
theory that the sun was the center of our solar system. This theory
implied a radically new view of the universe and of the place of humans
in it.
1. 1 The Development of Science 3
lable 1.1
Areas of physics
Classical Modern
Mechanics Special relativity
Gravitation
General relativity
Thermodynamics (heat) Gravitation
Cosmology
Electromagnetism
(electricity, magnetism) Quantum mechanics Interdisciplinary Areas
Atomic physics Astrophysics
Optics (light)
Molecular physics Biophysics
Acoustics (sound) Nuclear physics Chemical physics
Solid-state physics Engineering physics
Hydrodynamics
Particle physics Geophysics
(fluid flow)
Superconductivity Medical physics
Superflui di ty Physical oceanography
Physics of music
Plasma physics
Magnetohydrodynamics
Space and planetary physics
physics does become blurred, however, when a new de measure these physical quant1t1es In physics, the
vice, such as a laser, rejuvenates an old field, such as definition and measurement of a quantity are interrelated.
optics. This text emphasizes the aspects of classical physics Physics is built on operational definitions-definitions
that lead into modern physics, and includes an intro that are expressed in terms of measurements. For example,
duction to two areas of the latter: special relativity and average speed is defined as the (measured) distance trav
quantum theory. eled divided by the (measured) time that has elasped.
Table 1. l does not list some subjects (such as elec There are two basic types of physical quantities
trical engineering and computer technology) that were fundamental quantities and derived quantities. Funda
developed as part of physics but are now considered to be mental quantities are those quantities that cannot be
part of engineering. This movement of these topics from defined in terms of other quantities. To define a particular
physics into engineering illustrates the close relationship fundamental quantity, two steps are necessary. First, its
between physics and engineering, as well as the changing measurement must be fully specified. Then, a standard of
nature of physics. Some old areas of physics have been comparison must be established. Derived quantities, on
revolutionized, new areas have opened up, and the existing the other hand, are defined in terms of fundamental quan
areas continue to expand. tities by means of a defining relationship that is normally
Physics can be defined as the study of matter and an equation.
energy. As you work through this text, however, you will In the 19th century European scientists saw the need
find that physics is also a way of thinking. You will want for a coherent system of fundamental physical quantities
to master both the content of physics and this method of and their corresponding standards of measurement. This
thinking. The problems at the end of the chapters are concern led to the signing of the Treaty of the Meter in
designed to help you do this. They are not abstract math 1875 and the establishment of the International Bureau of
ematical riddles, but instead explore the behavior of real Weights and Measures. This bureau was created to "estab
physical systems. lish new metric standards, conserve the international pro
totypes, and carry out the comparisons necessary to insure
the uniformity of measures throughout the world. 11
1.2 The present metric system, called the Systeme Inter
national d' Unites, or SI for short, recognizes seven funda
mental physical quantities. We will consider three of these
Science and
fundamental quantities-length, time, and mass
immediately Three of the remaining four quantities will
Measurement be introduced as they are needed: Temperature, measured
in kelvins, first appears in Chapter 21; number of particles
(such as atoms or molecules), measured in moles, in Chap
The laws that unify physics refer to particular physical ter 25; and electric current, measured in amperes, in Chap
quantities-for example, forces and positions. Before we ter 30. The seventh fundamental SI quantity, luminous
can understand the laws of physics, we must define and intensity, measured in candelas, is not used in this text.
4 Chapter 1 General Introduction
Question · 1· he precision ot visual comparisons is limited to about
one part in ten million ( 107). As science and technology
1. One philosophic school held that if a quantity developed, this precision became inadequate. In addition,
could not be defined by an operational, or there was the danger that the platinum-iridium bar might
measurement-specifying, definition, then that quan be damaged or destroyed. Consequently, the meter was
tity had no real meaning and no physical reality. redefined in 1960 by international agreement as the length
Defend or criticize this view. (Physicists today want equal to 1, 650, 763. 73 wavelengths (in vacuum) of a partic
operational definitions for physical quantities, but ular color of light (a shade of orange) emitted by krypton-
they generally reject this extreme position.) 86 atoms. (This peculiar number was chosen in order to
match the old standard meter as closely as possible.) Once
again, the standard meter is tied to a property of the
1. 3 natural world and is thus presumably indestructible. The
krypton light source is reproducible and permits con
venient and precise measurements. In effect, every labora
Length
tory can now have its own primary standard of length.
Remember, though, that all standards are, in principle,
temporary, because they are chosen by consensus. The
Length is the first fundamental physical quantity that we
krypton standard quite possibly will be replaced by an even
will consider. An ordinary length such as the length,
more precise laser standard within a few years.
width, or height of a table can be measured by comparing
In Table I. 2 we list the range of lengths that we are
it to a secondary standard such as a t-foot (ft) ruler, a
concerned with in physics, from the size of nuclear par
yardstick, or a meter stick. Indeed, we may consider such ticles (about 10-15 m) to the distances from the Earth to
a comparison to be an operational definition of length. But far away quasars (perhaps 1025-1026 m). When one length
what do we use as the primary standard of length? In other
in this list is approximately ten times longer than the next
words what is the meter stick measured against? In earlier
length, we say that the first length is an order of mag
times ~he king's foot was often the primary standard, but its
nitude larger than the second. The second length is an
length changed each time a new king appeared on the
order of magnitude smaller than the first. Orders of mag
scene. Scientists need standards that do not change.
nitude, in other words, are associated with powers of I 0.
Eighteenth-century French scientists sought a natural,
For convenience in handling such a wide range of
universal standard, free of political differences. They pro
values, the set of prefixes listed in Table t. 3 is used in
posed the meter (m), a unit of length that they defined as
conjunction with SI units. The prefixes for positive powers
equal to one ten-millionth of the distance from one of the
of I 0 are from Greek; those for negative powers are from
earth's poles to the equator. Because this standard was tied
Latin (except for the recently adopted prefixes femto- and
to nature, it seemed indestructible. But although it was
atto- which come from old Norse). All of the lengths
available to all scientists, the use of this standard was
kilo~eters (km), millimeters (mm), and so on-are related
difficult. For example, what multiple of one ten-millionth
to the standard meter by powers of I 0. SI is thus a decimal
of the pole-equator distance is your height? This difficulty
system, which makes it easy to use. Note carefully that all
was resolved by constructing a bar of an alloy consisting of
90% platinum and 10% iridium, and defining the standard
meter as the distance between two lines engraved on the
bar when the bar was at the temperature of melting ice. Table t. 2
Accurate comparisons between the meter bar and objects
Range of lengths
of unknown length could then be made by using elaborate
(orders of magnitude)
and very precise optical techniques. Under the auspices of
the International Bureau of Weights and Measures, sec
Length Meters
ondary standards of length were made and distributed to
(powers of 10)
other nations of the world (see Figure I. I).
Distance to distant quasars 1026
Distance to nearest star 1016
(Proxima Centauri)
Radius of solar system 1013
Earth-sun distance 1011
Mean radius of earth 107
Height of person 100
Air-polluting aerosol particle 10-6
Diameter of influenza virus 10-7
Radius of a hydrogen atom 10-10
Figure I. I
Radius of a hydrogen nucleus 10-15
This postage stamp was issued by France in 1954 to remind
(proton)
the world that France developed the metric system.
1. 3 Length 5
Table t. 3 6. Explain how the length of an arc of a circle can be
measured. (The length of the arc becomes part of the
SI prefixes
definition of an angle in Chapter 12.)
Power of 10 Prefix Symbol 7. When the platinum-iridium meter bar was the stan
dard meter, why was it essential to specify the tem
1018 exa E
perature at which measurements were made?
1015 peta p
8. Many length measurements are indirect. How would
10'2 tera T you measure the radius of the earth? the distance to
the moon?
109 giga G
9. List and explain the advantages of an atomic length
106 mega M
standard over the platinum-iridium meter bar stan
103 kilo k dard.
10-2 centi c
10-3 mi Iii m 1.4
10-6 micro µ
10-9 nano n Time
10-12 pico p
10- 15 fem to f Time is another fundamental quantity, and therefore can
not be defined in terms of other quantities. However, we
10- 18
atto a can measure time, and thus obtain an operational definition
of time, by using a clock.
Examples: 10' 6 watts l megawatt ( 1 MW)
Any repetitive, periodic phenomenon can serve as a
103 meters 1 kilometer ( 1 km) clock. The Italian astronomer Galileo Galilei used his pulse as
a clock to measure the time that it took for a swinging chande
10 - 3 gram 1 milligram ( l mg)
lier to return to its original position. The earth, by rotating on
10-9 second = 1 nanosecond ( 1 ns) its axis, constitutes a clock. Originally the second was defined
as 1/86, 400 the length of one complete revolution of the
earth* (averaged over a year). The earth, however, is not a suf
ficiently accurate clock for today's measurements for two rea
sons. First, because of the effects of lunar and solar tides, the
rotation of the earth is gradually slowing down. Second, the
but one of the exponents are multiples of 3. The only
earth's rate of rotation is slightly irregular, varying with the sea
exception, the cenitimeter (cm), is occasionally used when
sons and from year to year.
it is inconvenient to use millimeters or meters.
By international agreement, the second was redefined
By law, our U.S. units of length (English system) are
in 1969 as the duration of 9, 192, 631, 770 periods of the
defined in terms of the standard meter. Thus
microwave radiation from a cesium-133 atom. A time inter
=
1 yard 0.9,144 m (exactly) val in seconds is measured as the number of cesium-133
periods in that interval divided by 9, 192, 631, 770. Thus
and
the unit of time, like the unit of length, is now based on
l inch = 2. 54 cm (exactly) the behavior of atoms. This new standard of time has made
12
it possible to measure time intervals to one part in 10 .
From time to time in this text we will use English units,
The cesium clock is reproducible and readily available to
since you are probably more familiar with these units, in
scientists and engineers the world over. The second is the
order to give you 'I better feeling for the physical situation.
unit of time in both the English and SI systems. Table 1.4
In most such examples, however, the English units will be
shows the range of times in orders of magnitude as ex
converted to SI units and the calculation carried out in SI
pressed in seconds (powers of 10). Of course the time
units.
standard is arbitrary, just as is the standard of length.
Ultraprecise hydrogen clocks may eventually replace the
Questions cesium clock as the international standard of time.
Figure 1. 2 shows the variation in the rate of rotation
2. We are already using SI units in sports. How does
of the earth as measured by a cesium clock. But how do we
the length of the 1500-m run compare with the mile?
know that the irregularity is in the earth's rotation and not
3. Why is it desirable to have a standard tied to some in the cesium clock? The way that physicists answer this
natural phenomenon?
4. What is your height in centimeters? in meters?
5. Why wasn't the meter defined as 1,000,000.00, in
*The division of a minute (min) into 60 seconds (s), an hour (hr) into 60
stead of the cumbersome number 1, 650, 763. 73
min, and a day into 24 hr (60 X 60 X 24 = 86,400) began in ancient
wavelengths of krypton-86 light? Babylon.
6 Chapter l General Introduction