Download - Rogers Physics for the Enquiring Mind Text
PHYSICS FOR
THE INQUIRING MINDNature, and
The Methods,
Philosophy of Physical Science
JEREMIAH
HORROCKS'PARK.
MOOR
OBStRYATQRY, PRESTON. -*-
PHYSICSFOR THE INQUIRING
MINDTHE METHODS, NATURE, ANDPHILOSOPHY OF PHYSICAL SCIENCEBY
ERIC M. ROGERS
1960
PRINCETON,
NEW
JERSEY
PRINCETON UNIVERSITY PRESSLONDON: OXFORD UNIVERSITY PRESS
Copyright
1960 by Princeton University Press
London: Oxford University Press
ALL RIGHTS RESERVEDL. C. Card 59-5603Publication of this book has been aided
by
grants
from The Rockefeller Foundation, The Alfred P. Sloan Foundation, and The
Whitney Darrow Publication Reserve Fundof Princeton University Press
Printed in the United States of America
Second Printing 1961Third Printing 1961
Fourth Printing 1962
TO JANET TRAJV ROGERS
PREFACEThis book offers a course in physics to non-physiwho wish to know physics and understand it.
and
for that reason they
form a very important part
cists
of the book's teaching.
Here are the general reading, problems, and laboratory instructionsof
a one-year course given at
Princeton to undergraduates whose chief field of study lies outside technical physics: economists,sciences, and open alike to those who have studied physics before and those who have not. Like that course, this book neitherlifeis
Some problems are dissected into a series of steps, not as spoon-feeding but to take the place of worked examples you should work through those as you
students in humanities and in
many
premedicals.* That course
requires a previous physics course nor repeats in
material or treatment the normal content of high-
school physics
so
it
welcomes
all readers.
This book treats a series of topics intensively: topics chosen to form a coordinated structure of
read the text.** Some problems give necessary preparation for later chapters. Some problems raise general questions whose discussion can do much to advance your understanding. Such general questions ask for opinions as well as reasoning; and they obviously do not have a single, completely right answer. Yet, thinking your way through them and making your own choice of opinion, and discussing other choices, is part of a good education in science.
knowledge. Although mathematics provides the
es-
A NOTE TO INSTRUCTORSThe Originof science of
sential tools of physics, only the simpler parts of
The Courseof us to design
high-school algebra and plane geometry are usedhere.
On the other hand, critical reading, good reasoning and clear thinking are asked for again and again. The problems, which are of primary importance, are not plug-in slots for formulas, but ask for
A dozen years ago, our concern for the good namemoved some
new
courses
for non-scientists:
courses in physical science for
general education in college. In this age of science,
reasoning and critical thinking. In this way, bothtext
and problems ask readers
to learn
by
their
own
educated non-scientists need an understanding knowledge of physics; and they deserve to enjoy that knowledge as part of their intellectual outlookthroughout theirlives.
thinking.
Bankers, lawyers, business
A NOTE TO ALL READERS: THE PROBLEMSThe problemsare an important part of the book's
teaching, because they ask you to discuss and reason
and polish up your own knowledge. There is much discussion and reasoning in physics. To understand how experimental knowledge is fitted with theory and new results extracted, you need to do your own reasoning and thinking. Of course it would be quicker and easier, for both teacher and student, if the text stated all the results and outlined all the reasoning; but it is hard to remember such teaching for long, and harder still to extract a fine understanding of science from it. So, in this book, many of the problems ask you to do your own thinking;* In
men, and administrators of all kinds have to deal with scientists and their work; and educated people everywhere find scientific knowledge offering to influence their interests, outlook, and philosophy. What kind of physics courses could answer such needs? Not the routine training courses in facts and formulas and principles that were designed for future physicists and engineers and that are stilloffered as standard fare.
To many
non-scientists
those courses
fail to
describing
their
physics
requirements,
Deans
of
standing of science and we even hear doubts whether they give professional scientists the best start. Nor does a smorgasbord acquaintance-course of items of information meet the need a course that gives students a temporary sense of satisfaction but cannot convey much lasting understanding. So we designed a "block-and-gap" course that
give an appreciative under-
medical schools now stress thoroughness of understanding more than completeness of coverage. They ask for a course that teaches its material thoroughly and encourages constructive thinking and careful experimenting. So we now welcome many pre-medical students in this course. To cover some extra ground that is important for them, we add classes in acoustics and a series of laboratory sessions with optical instruments, ranging from the eye to the microscope. Those pre-medicals who prefer a more mathematical or "technical" treatment join physicists and engineers in another course.
* Some of the most important problems, which are intended to teach by a series of steps, have been printed in this book as reduced photographs of typewritten sheets. Instructors or Physics Departments can obtain single sample copies of the full-size original sheets from the author, c/o Palmer Physical Laboratory, Princeton University, Princeton, N.J. These specimens may be reproduced by photo-offset, or they may serve as copy for typewriting. Sets of lithographed copies are also available.
)
PREFACEbuilds important blocks of material into a connected
framework.
We taught those blocks carefully to giveshow the building ofusingthatscience as a whole.
added. These additions raise the danger of overcrowding, if users try to cover all the chapters. Onthe other hand, they bring the course of the bookinto line with recent recommendations, such as those of the Carleton Conference.
a sense of genuine understanding; we discussed the connections between one block and another; and
we
tried to
We
were teaching both science and philosophy of
As assurancetopics
that the materialfull
is
lessis
science
without
crowdedof the
forbidding
phrase.
than the traditional
menu, heretrivially
a
list
There was plenty of solid physics (more than half the content of an orthodox one-year course); our treatment was thorough, (within the limitations of mathematical tools); and we aimed for knowledge and a sense of understanding rather than a wealthof information.
omitted or treatedofis
in the
book:
hydrostatics, statics, calorimetry, ray optics, sound,electricity and magnetism. Thus, mainly concerned with dynamics, PLANETARY ASTRONOMY, MOLECULAR THEORY, and PARTS OF ELECTRICITY AND MAGNETISM, AND "ATOMIC physics" interwoven with general discussion. In the Princeton course for which this book is
and parts
the course
The
gaps,
where
topics
were omitted, gave timefor students to learn
for careful teaching
and
reading and thinking things out for themselves; they gave space and time for a developing perspective of science.
by and
used,
we
treat the chapters as
shown
opposite.
(
broken
lines indicate
roughly
and optimistically
The
We
considered the loss of omittedits
the quarter-stages in a year's course.
topics unimportant. If such a course succeeds,
students will be well prepared, in both background
A Word toInits
Critics
fill
and attitude, to read more science on their own, to any gaps they wish. But if it is to succeed, the course must encourage that depth of learning which comes with each student's own reasoning and creative thinking: the course must ask questions rather than hand out results. That is the kind of course for which this book was made.
method of presenting physical science, this makes first moves towards studies of history and philosophy of science. I hope that experts in those fields will pause before condemning ignorance or mistaken judgments in my treatment, and will remember that this is an attempt to teachbookalso
science
itself at first
hand.
Historian, philosopher,
and
scientist:
each
feels
The
Essential Plan of This
Book
that the others are rich in vision but lack
somehis-
To enableits
students and other readers to under-
knowledge of
his field.
To
the historian, the scientist
stand physics as scientists
know
it,
we must show
lacks perspective
and accurate knowledge of
connected framework of knowledge and thought. This book tries to do that by linking one chapter with another so that information here leads to comfuller explanation laterstill;
tory; to the philosopher, the scientist lacks critical
mentary there and a that tools developedand, in
so
one place are used in others; general, so that knowledge grows as anin
organized system.Since relevance to the structure of the course anditsis
teaching
is
more important than coverage, therelike
no single ideal choice of topics for a course
Some basic elements are universal (such as Newton's Laws of Motion), and some are demanded by most teachers or many students ( such as planethis.
and accurate knowledge of philosophy. To the the works of philosopher and historian are a great delight; but he finds that they pre-suppose (rather than lack) a full knowledge of scientific material and a first-hand understanding of the nature of scientific work. To convey the latter to nonscientists seems to me the essential first move in giving them an understanding of science for use in later life and work an understanding comparable with the knowledge of music that a good musicskill
scientist,
course conveys to non-musicians.
tary astronomy for a discussion of Theory; nuclear
physics to keepthereis
up with modern knowledge). Yet
So I believe the non-scientist needs a course that he himself considers a course in science, not a course about science. Although the history and philosophyof science are of the essence in understanding sci-
much room for individual choice, depending
and students, and on equipment available, and on method of teaching. Originally this book contained one man's selection ofoninterests of teachers
ence at a sophisticatedin expertcult
level,
a
first
study of themdiffi-
hands
is
apt to strike the stranger as
topics
a workable course but a prejudiced choice. However, to allow for wider choice by other teachers, some chapters have been expanded and others
commentary rather than science itself. To understand science, each student must be, in his own"scientist for the day."it
mind, aI fear
may be
as difficult for a philosopher or
PREFACEimmerse the beginner in science itself as it is for a scientist to embrace the historian's perspective or do justice to the philosopher's knowledge. Therefore, I have rashly written as a physicist, without shame but in all humility; and I hope that those others will forgive narrowness and errors and will regard this course as a base on which somehistorian toI
IX
want
to thank one colleague for his part in
whole project of course and book. A dozen years ago, when new science courses for nonscientists were being planned, I spent many visits discussing aims, methods, and progress with Prostarting the
students will build the next story in their specialfields.
Thanks
Edwin C. Kemble at Harvard. hammered out the idea of a "block-and-gap" course and planned content and treatment that would favor our aims. We discussed genuine laboratory work, decided on planetary astronomy (following Sir Oliverfessor
We
Lodge)
as our
A physics book, like physics itself, is a cooperativeeffort. It cannot be produced in an ivory tower. This book owes much to many people: to colleagues who have offered experiments, problems, and valuable suggestions; and to many scientists of past and present generations on whose teaching I have drawn and whose problems I have borrowed, often unconsciously. To all who have thus contributed, whether knowingly or not, to this work in physics teaching, I give the most heartfelt thanks. I am grateful to them all, from my own first teachers many years ago
example of theory; decided
to treat
energy-conservation with more discussion and less assertion. looked for inquiring problems and
We
examination questions that asked for thought; and we planned to require long essays or reading papers as a "pay-off" for the course. Many of these ideas arein
now commonplace characteristics of science courses many institutions; but we thought we were making our own discoveries in education; and I shallalways be grateful. Atthis distance in
time
I
do not
remember which
of us
made each
suggestion, but I
to the newest generation of physicists
who have
do know that those early discussions cultivated the ground from which this book and its course havegrown.
taught this course with me, and the thousand students who have read and argued their way throughpreliminary forms of this book. In particular, I am specially grateful to Professor Frederick A. Saunders of Harvard University, who
And
I
amI
grateful to those
who
continued such
discussions as the course
was
given.
Among
those
welcomed me to physics teaching in America. provided the original inspiration and showed that a physics text can be humane.
He me
And I am very grateful to many others who have helped with technical skills to produce the book. Some who have helped deserve special mention for devoted skill beyond the measure of general thanks. In naming some of these below, I know thatI
and Gordon Likely and Drs. Robert Dicke, John Fletcher, Wayland Griffith, Claude Kacser, Aaron Lemonick, Robert Naumann, John Wheeler, and many other colleagues, past andsuggestions to Mr.present.
teaching,
owe
special thanks for criticism
Recently,
I
spent long, equally stimulating
visits
at M.I.T. with the Physical Science Studytee,
Commit-
am
equally grateful to
many
others.
found congenial views on physics flourwish that the P.S.S.C. program had started some years earlier, so that this book couldI
where
ishing. I only
Use
of Chapters of This
Book
in
an Actual One-year CourseOMITTED, OR USED FOR
USED FOR THOROUGH STUDYIn class, lecture,
TREATED LIGHTLY
REFERENCE ONLY
&
reading
In lab only
1,7,816, 17, 18, 19, 21, 22, 25,
426(27), 2832,12,
2, 3, 5, 6, 9,
10 (27)
6*, 9, 1120,31,
13,
14,
15,
23,
24 35
29,
30 (parts), 36
(34)(parts)
30
(rest), 33,
34
37,38,39,40,43,44 (parts)
41
42wouldoflike to eliminate
41 (rest), 44 (rest)a few demons by a brief showing as simple examples of Newton's
Surface Tension (Ch. 6) and Fluid Flow (Ch. 9) are examples of an individual teacher's favorites that other teachers can safely exclude. Yet, most of us would like toinclude a measurement of oil-molecule length; and
Bernoulli
paradoxes
Second Law.
some
PREFACEhavefitted
with
it
more
closely.
As
it is,
I
am
espefor
skill
and devotion that can only be rewarded by andelight in creative work.all,
cially grateful to Professor Francis
Friedman
artist's
many a wise word of good physics in time to save an error or add a note in proof. As a special critic, Professor Frederic Keffer ofthe University of Pittsburgh read most of the chapters in manuscript. I am exceedingly grateful to
him for skillful criticism and many suggestions of good changes. I owe special thanks to Professor Henry D. Smyth and Professor Allen G. Shenstone who, as Chairman, encouraged the course; and to Dean J. Douglas Brown and Dean Donald R. Hamilton who did
wish to give special thanks to my Mr. Tracy H. Logan, now of the Department, Hobart College. In the course Physics of years, he has taken charge of many preparations for me. He has drawn some diagrams, processed other diagrams for the Press, supervised draftsmen; he has searched out data, given valuable criticism, kept account of changes, organized records; in general, he has managed the production of material. He has taken a great load of responsibility, with
Above
I
editorial associate,
muchI
to encourage the publication of the book.this
and
book owe great thanks
Schullinger,
to Rudolph N. M.D., of Presbyterian Hospital, for
great
and kindness. and this book owe lifelong thanks to my wife for affection and encouragement. In making the book itself, many have givenskill
And
I
technical
help.
I
am
especially
grateful to:
Mrs.
J.
E. Reef and Mrs.
W.
Parfian have carried
out tasks of technical typewriting with great skill and have safeguarded the making of the book in many ways. Mrs. A. E. Sorenson has made typewritten problems for photographing.
authority and judgment; and I am very grateful. Without his skill and devotion, this book would not be published now. This book owes its present form to the warm encouragement and admirable skill of the Princeton University Press. I wish to thank the Director, Mr. Herbert Bailey, and the two Editors who worked with me, Mr. Benjamin F. Houston and Mr. John Boles: all gave skillful help and welcome encouragement. I would also like to thank the unseen experts of a great Press: the two typesetters who transformed manuscript into linotype; the proofreaders who saved errors with consummate skill; and the
The
proofs have been read
by Mrs.J.
P.
Mrs. M. R. Willison, and Mr.formally
L. Snider,
H. E. Aul, and in-
hand-compositors who assembled pages. And I wish to thank Mr. Jay F. Wilson, now Science Editor of the Princeton University Press,
by many teachers and students. Mrs. T. H. Logan has prepared the index andReducing
who
for his
read proofs.
my
Press proved to be a large task.
drawings to forms suitable for the Many people helped,
took charge in the final stages. I am grateful good advice and his able, enthusiastic help. I wish to thank the Carnegie Corporation of New York for contributing, long ago, to the writing of the
book by providing part
some men,
ofall
them
students, others professional drafts-
under the direction of Mr. Tracy Logan. In the later stages, Mrs. G. L. Carlson took charge of finishing and processing diagrams. Throughout, Mr. Howard Schrader did marvelous photography to produce special effects and changesof scale.
of a sabbatical year of leave. University Press and I join in thanking the The Sloan Foundation and the Rockefeller Foundationfor financial help in connection
with the book as an and the Eugene Higgins Fund for Education in Natural and Physicalexperiment in educational material,Sciences for financial help in production of diagrams, etc. I am grateful to these foundations not only for their financial help but also for this clear sign that
on the diagrams the book has been done by Mrs. C. C.italic lettering
The
all
Pratt,
through with
they consider such aspects of education important.
CONTENTSPART ONEMATTER, MOTION, AND FORCE1.
PART THREE
MOLECULES AND ENERGY25.26.
Gravity,
A
Field of Physics
The Great Molecular Theory
of Gases
353
2. Projectiles:
Geometrical Addition:
Vectors3.
36 53
27.
Energy Measuring Heat and Temperature
370 412425
Forces as Vectors
28. Power.29.
A Chapter for Laboratory Work
4. 'It's
Your Experiment":
The
Principle of Conservation of
Laboratory5.6. 7. 8.
Work
61
Energy30. Kinetic
Experimental Basis
432
Law and Order among Stress and StrainSurface Tension: Drops and Molecules
78 87105 135
Theory of Gases:444
Fruitful Expansion
Force and Motion:
F
=M
a
Crashes and Collisions:Fluid Flow
Momentum
INTERLUDE31.
9.
154170
Mathematics and Relativity
468
10. Vibrations
and Waves
PART FOUR
INTERLUDE11.
ELECTRICITY AND MAGNETISM19332. Electric Circuits in 33. Electric
Appendix on Arithmetic
Laboratory
503 533
Charges and Fields
PART
TWO207213
34. 35.
Magnetism: Facts and TheoryChemistry and Electrolysis
568586
ASTRONOMY: A HISTORY OF THEORY12.
Mankind and the Heavensand Early ProgressGreek Astronomy: Great Theories
PART FIVE
13. Facts14.
ATOMIC AND NUCLEAR PHYSICS36. Electrons37.
and Great Observations15. 16. 17. 18.
223241
and Electron Fields
607
Awakening QuestionsNicolaus Copernicus (1473-1543)
Magnetic Catapults: Driving Motors
244251 261
and Investigating Atoms38. Analyzing
615 624of
Tycho Brahe (1546-1601)Johannes Kepler (1571-1630)(1564-1642)
Atomsand the Tools
39. Radioactivity
19. Galileo Galilei
27340.
Nuclear Physics
633648 655
20.
The Seventeenth Centuryand Acceleration
28741.
Atoms: Experiment and TheoryLaboratory Work with Electrons: from Generators to Oscilloscopes
21. Circular Orbits
295
22. Isaac
Newton (1642-1727)andScientific
312 336
42.
Atom
Accelerators
The Big Machines
672 682 714
23. Universal Gravitation
43. Nuclear Physics44.
24. Scientific Theories
Methods
341
More Theory and Experiment: Physics Today760771
General Problems Index
PART ONEMATTER, MOTION, AND FORCE"Give
me
matter and motion, and I will construct the
universe."".
Rene: Descartes (1640)
from the phenomena of motions to investigate the and then from these forces to demonstrate the other phenomena; ... the motions of the " planets, the comets, the moon and the sea.
.
forces of nature,
Isaac Newton (1686)"No one must think that Newton's great creation can be overthrown by [Relativity] or any other theory. His clear and wide ideas will forever retain their significance as the foundation on which our modernconceptions of physics have been built."
Albert Einstein (1948)
PRELIMINARY PROBLEMS LEADING TO CHAPTER
1
A wise explorer reviews his maps before he starts on the expedition. You would be wise to review your present knowledge and prejudices before this chapter offers you new knowledge. The problems below are not intended to discomfort you by asking for answers before you are prepared. They are only intended to clear the ground fordiscussion.
Some ask youwill
questions that
to check minor matters of vocabulary. Others raise major appear again and again through the course.
1. (a) "I shall try
an experiment.
.
.
."
Suppose you have
just
(a)
Write a short explanation ofcial
with your present knowledge and views. Write a note of a few lines to show what you
made such a remark
(b)(c)
would mean by it. Write a similar note Write a similar notecally."
for, "I
have a theory that.
.
.
."
for, "I shall treat this scientifi-
(At this stage, before you begin the course, we do not expect you to know all the answers to questions like this. Here you are asked to describe your present views. Later you may change them.)2.
its meaning, paying spethe part played by the words in italics. (For example, in the version above, where the word "expect" is used, your answer might run thus: "Because the sun has risen in the east so regularly in the past, look for the same thing tomorrow with some shall make my everyday plans on confidence, and have noticed that most such this basis, because natural events continue to repeat themselves uniformly." Note, however, the dangers of this last view for an insect, hatched in the summer, anticipating an endless series of warm mornings, and completely
attention
to
I
I
I
Look up the word "logical"(a) Statein
in
a good dictionary; then(b)
write short answers to the following:
your own words the proper meaning of the
word "logical."(b) State in
your own words the colloquial or slang use(c)
of the word. (c) What word(s) could be used aptly for the meaning in (b), leaving "logical" for its important use in science, philosophy, etc.? (d) Do you consider algebra logical? Give reason(s) for your answer.3.
ignorant of the snowstorm which will end its life.) For each case say whether or not you consider the statement a wise or safe one for a scientist to use. (In other words, do you consider the statement scientific or superstitious, safe or risky, "right" or "wrong"?) Give a brief reason for each answer in (b).
Statements:1I
2.3.
Look up the word "data." Thenfollowing:(a) (b)
write short answers to the4.
will rise in the east tomorrow morning. deduce the sun will rise in the east tomorrow morning. conclude from inductive reasoning that the sun will rise in the east tomorrow morning. believe that the sun will rise in the east tomorrow morn-
predict the sun
I
I
I
WhatWhich
is its
origin?5.
ing.I
of the following statements do you consider correct language and which incorrect? (Where incorrect, mention reason.) (i) These data were obtained by my partner,(ii)(iii)
know
6.
I
consider
that the sun will rise in the east tomorrow morning. it highly probable that the sun will rise in the
This data was obtained by my partner, This set of data was obtained by my partner.is
7.
4. (a)(b)(c)
What What What
the plural of the word "apparatus"? the plural of
does "phenomenon" mean?is
phenomenon?
east tomorrow morning. These observations lead to a law which proves that the sun will rise in the east tomorrow morning. 8. Investigations show that the world is a solid spinning body and the Principle of Conservation of Angular Momentum proves that it will continue to spin thus, and therefore proves that sunrise, which is due to this spin, will continueto occur in this6.
5.
(The following questions ask for written answers. Try toshort. Some may require considerable thought. Consult dictionaries if you like. It is hoped that you will enjoy finding answers to these questions. If you have fun puzzling these out, your education will gain; if you do them with a feeling of headache, it will lose. So you are advised to treat these rather lightly, yet fairly
same way each
day.is
make them
Look up the verb "infer." (a) What is the proper meaning? (Thisin science.)
the one to use
(b)
What
is
the colloquial use? Give a better verb to
replace(c)
it.
The word "infer"
seriously.)
"The sun rose in the east this morning, yesterday morning, the morning before that, and for many mornings before that." This is a statement of observations. Scientists and others make statements like the following: "/ expect the sun will rise in the east tomorrow morning." A number of other statements with some differences in wording may be made, and eight of these are shown below. With each of the statements:
is used correctly in one of the statements below and incorrectly, or poorly, in the other. Explain what you think "infer" is intended to mean in each of the passages. Say which passage has the correct use and suggest a substitute for "infer" in the
other one.(i)
"Are you
trying to infer,is
by your remarks, thatyour uncleis
my(ii)
uncle
a fool?"I
"Fromfool."
his behavior,
infer that
a
CHAPTER"Whatword?
1
GRAVITY, A FIELD OF PHYSICSfrom language as we ordinarily understand theinternational?is. ..
distinguishes the language of science
How is
it
that scientific language
is
The
super-national character
of scientific concepts
and
scientific
language
due
to the fact that they
by the best
brains of all countries
and
all
times. In solitude
have been set up and yet in cooperative effort
as regards the final effect, they created the spiritual tools for the technical revolutions which have transformed the life of mankind in the last centuries. Their system of concepts
has served as a guide in the bewildering chaos of perceptions, so that general truths from particular observations."
_A
EmSTEINj
^ %^^welearned to graspof
Introduction
are
moved
out to
make
the text
In this book, and the course that goes with it, we shall study the nature and methods of physicalthat by studying some parts of physics thoroughly and leaving out other parts to gain time for discussion. In the samples we study,science.
a
first
reading. Often the footnotes
more continuous for wander off on a
We shall do
distract attention if placed in Yet this developing of new threads itself shows the complex texture of scientific work; so at a second reading you should include the
side issue
and would
the main
text.
you will learn many scientific facts and principles, some useful for life in general, others important groundwork for discussions in the course. To gain much from the course, you need to learn this "subject matter" thoroughly. In itself it may seem unimportant such factual knowledge is easily forgotten, 1 and we are concerned with a more general understanding which will be of lasting value to you as an
footnotes.
Falling Bodies
Watch aedge of
falling stone
and
reflect
on man's knowl-
falling objects.
What knowledge have we?
How
did
we
obtain
it?
How is
it
codified into lawseasily used?
that are clearly
remembered and
What
educated person
but
weto
shall
use the factual
knowledge
ends. The better your grasp of that factual knowledge, the greater your insight into the science behind it. Andthis
as a
means
more important
use is it? Why do we value scientific knowledge in the form of laws? Try the following experiment before you read further. Take two stones (or books orcoins ) of different sizes. Feel how much heavier the larger one is. Imagine how much faster it will fall if the two are released together. You might well
course
is
concerned with the ways and work ofdiscussing scientific methods or the
science
and
scientists.
To begin by
expect them to fall with speeds proportional to their weights: a two-ounce stone twice as fast as a one-
would be like arguing about a foreign country before you have visited it. So westructure of scienceshall
ounce
plunge at once into a sample of physics
them high and release them you going to believe: what you saw, what you expected, or "what the bookstone.. .
Now holdWhich
together.
.
are
gravity
and
falling bodies
and
later discuss the
says r
general ideas involved.
People must have noticed thousands of years agothat most things fall faster
What to Do aboutYoufirst,
and faster
and that some
Footnotes
are advised to read a chapter straight through omitting the footnotes. Then reread carefully, studying both text and footnotes. Some of the foot-
Yet they did not bother to find out carefully just how things fall. Why should primitive peoplenot.
do
wantall
to find out how or why? If they speculated at about causes or explanations, they were easily led
trivial, but many contain important comments relevant to the work of the course. They are not minor details put there with a twinge of conscience to avoid their being omitted altogether. They
notes are
by superstitiouslife
fear to ideas of
good and
evil spirits.
We can imagine how such people living a dangerouswould classify most normal occurrences as "good" and many unusual ones as "bad" today we use "natural" as a term of praise and "unnatural" with a flavor of dislike.
learned, it is easily relearned if needed later. Much of the difficulty of learning a piece of physics lies in under-
1
Once
standing its background. When you understand what physics is driving at, the rules or calculations will seem sensible
and
easy.
This liking for the usual seems wise: a haphazard unregulated world would be an insecure one to live
4in.
PART ONEChildren emerge from the shelteredbruises, hot stoves
MATTER, MOTION, AND FORCEof a
life
baby
essential part in the
development of modern me-
into a
hard unrelenting world where brick walls
chanics in the theory of relativity.
make
a secure well-ordered world,so they are glad to have
make blisters. They want bound by definite rules,its
quirky behavior "ex-
And here is the practical taunt: if you use your ingenuity and only household apparatus to try every relevant experiment you can think of, you(iv)all
plained" by reassuring statements.
The
pattern of
will
still
miss some of the possible discoveries; this
seeking security in order, which
we
find in
growing
children today, probably applied to the slower
growing-up of primitive savages into
civilized
men.
wide and so rich that a neighbor with similar apparatus will find out something you have missed.field of investigation is so
As
civilization developed, the great thinkers codified
the worldreasons.
even the thoughts of
inanimate nature and manthey didthis is
living things
into sets of rules
and and
a difficult question. Perhaps some were acting as priests and teachersfor their simpler brethren.
Why
Perhaps others wereto
driven
by
childish curiosity
again a need
know
definitely,
may have beencuriosity
born of a sense of insecurity. Still others inspired by some deeper senses ofof thinking
and enjoyment
in intellectual delight rather than fear
senses rooted and these
men might be called true philosophers and scientists. You yourself in growing up run through manystages of knowledge,scientific sense.
What
from superstitious nonsense to stage have you reached in the
simple matter of knowledge of falling objects? Check
your present knowledge by actually watching some
Take two different stones (or coins) them fall, starting together. Then start them again together, this time throwing both outward horizontally (Fig. 1-1). Then throw one outwardthingsfall.
and
let
Mankind, of course, did not gather knowledge way. Men did not say, "We will go into the laboratory and do experiments." The experimenting was done in daily life as they learned trades or developed new machines. You have been doing experiments of a sort all your life. When you were a baby, your bathtub and toys were the apparatus of your first physics laboratory. You made good use of them in learning about the real world; but rather poor use in extracting organized scientific knowledge. For instance, did your toys teach you what you have now learned by experimenting on falling objects? Out of man's growing-up came some knowledge and some prejudices. Out of the secret traditions of craftsmen came organized knowledge of nature, taught with authority and preserved in prized books. That was the beginning of reliable science. If you experimented on falling objects you should have extracted some scientific knowledge^ You found thatthis
the small stone and the big one, released together,fall together.etc.,2
of
many
So do lumps of lead, gold, iron, glass, sizes. From such experiments we inferis
a simple general rule: the motion of free fallversally the same, independent of size
uni-
ThisFig,
is
a remarkable, simple fact
and material. which people findit
surprising
in
fact,3
some
will not believe
when
they are told
it,
but yet are reluctant to try a simple
and
at the
same
instant release the other to fall
experiment. 42 Yes; if you did not try the experiment, you now know the result of at least part of it. This is true of a book like this: by reading ahead you can find the answers to questions you are asked to solve. When you work on a crossword puzzle you would feel foolish to solve it by looking at the answers. In reading a detective story, is it much fun to turn to the end at once? Here you lose more still if you skip: you not only spoil the puzzle, but you lose a sense of the reality of science; you damage your own education. It is still not too late. If you have not tried the experiments, try them now. Drop a dime and a quarter together, and watch them fall. You are watching a great piece of simplicity in the structure of nature. 3 Notice your own reaction to this statement: "A heavy boy and a light boy start coasting down a hill together on equal bicycles. In a short run they will reach the bottom together." The statement is based on the same general behavior of nature. See a demonstration. In a long run they gain high speeds and air resistance makes a difference.
vertically.
Watch these motions again and again. See how much information about nature you canIf this
seems a childish extract from such trials. following comments: waste of time, consider the (i) This is experimenting. All science is built withinformation from direct experiments like yours. (ii) To physicists the experiment of dropping light
and heavy stones together is not just a fable of history; it shows an amazing simple fact that is a delight to see again and again. The physicist who does not enjoy watching a dime and a quarter drop together has no heart.(iii)
and
projectiles lies the
In the observed behavior of falling objects germ of a great scientific
notion: the idea of fields of force,
which plays an
CHAPTERstone to fall just as fast as a 10-pound one? Wouldn't it seem more reasonable for the 10-pound one to fall five times as fast? Yet direct trial shows that 1-pound, 2-pound, and 10-pound lumps of metal, stone, etc., all fall with the same motion.
1
GRAVITYhas
5
The pound
result is surprising.
Would you
expect a 2-
made
air resistance
more and more important,
requiring modification of Galileo's simple treatment.Aristotle
and Philosophy
FACT? FANCY ?
great Greek philosopher and scientist Arisappears to have supported the popular idea that heavy things fall faster than light ones. Aristotle was a pupil of Plato and for a time the tutor of Alexander the Great. He founded a great school oftotle
The
philosophy and wrote many books. His writings were the authoritative sources of learning for centuries
-f@-f
or
IDEAL RULE
through the dark ages when there were still no printed books but only handwritten ones copied and
handed down by devouttroubled world.
scholars in a rough
and
-
Then v
Where have weacceleration,
seen (v
+
v
=
2s/t.
)? In the definition of
Laterof v,
we
shall
want a
relation expressing v in termst explicitly.
weat.
wrote
a=(v vwant v 2
)/t.2,
a, s,
but not involving the time
Therefore, (v
v =
Now we
u
CHAPTERwhich we can get by multiplying (v v ) and (v v ). We do this, using (v v ) =2s/t and (v v ) =at.
1
GRAVITYz sec
29
+
+
.'.
v2
(o + Oo) (v-v = (2s/t) (at) v = 2 as, which leads to the form) 2
Site.
46
sec
we*
want. Now, having found the method by analysis, we erase the details of our search and start afresh,thus:
4
8
S
in
5 Sec
=j
net travelFig. 1-17. S is
NET
distance
To
derive v 2
= v + 2 as2fl
by an elegant method,Thusfinish.
start
with the definition of acceleration,
s
always gives the net distance from
start to
=
(o
-vfor
)/t,
and with the formula
distance travelled in
terms of average speed, s )t, and just multiply these two equations together, obtaining a s % (v 2 v 2 ) which reduces to
= %(v+v
tools, not vital pieces are absolutely true for motion with constant acceleration, and they are not reliable for
These useful relations are
of science.
They
=
v
2
= v + 2 as2
other motions. Only experiment can they apply in the real world.
tell
us where
Here, then, are four relations between
v,
v
,
a, s,
PROBLEMS FOR APPENDIX A
andv
t.
= v + at
s
= A(v + v )t v = v + 2as12
s
= v + y*att
2
A-l.
NON CALCULUS PROOF
2
Galileo, lacking the help of calculus and preferring geometry to algebra, dealt with uniformly accelerated motion as follows: Imagine a graph with time plotted along and velocity
They provide a quick way of calculating the value of any one of these quantities, given the values of three others.Algebra Yields Net Distancevalues must be given appropriate For example, if the initial velocity is 6 ft/sec eastward and the acceleration 2 ft/ sec/sec eastward, we can say o +6 and a +2. However, if is 6 ft/sec eastward but the accelera-
of a moving body plotted upwards. If the body has constant acceleration, its velocity must increase steadily as time goes on. The graph must be a straight line. It will not necessarily pass through the origin, but will start at the initial velocity, vo when time is zero, and run up to some value v at time t.
The numericaland
+
signs.
=
=
tion is in the opposite direction, 2 ft/sec/sec westward, then one of them must have a minus value. If we say u 2, using -f 6 we must say a
V-
=
=
-f
signs
for
eastward
velocities,
travel-distances,
and
accelerations
andones.
signs for
westward
Thenthe
the net distance travelled in time *, not arithmetic sum of westward and eastwardsis
This is because in calculating each part of the trip the algebra will give sign to eastward travels and sign to westward ones and in addingtravels.
+
and parts to find s the algebra will give the net difference. With v +6 and a 2 the motion is decelerated: slower and slower for-
up these
+
=
=
ward for 3 sees, then at rest, then faster and faster backward. In 5 seconds it will show a path like Fig. 1-17, with 9 ft forward travel, then 4 ft backward, giving a net travel 5 ft. Algebra gives:s
(U)Fig.1-18. Galileo's
Proof
= v + %at = (+6)(5) + %(-2)(5) = 30 - 25 = 5t2
2
ft.
Now consider what happens in some very short interval of time At, when the velocity is, say, vi. (Of course v is increasing, but we can take vi as the average during short At.) Then the body moves a distance [(vi) (At)] in that time. But on the graph [(vO (At)] is the {height width] of the small pillar
30resting
PART ONE
MATTER, MOTION, AND FORCEA-3.
of that
on At and running up to the graph-line. It is the area pillar, shaded in sketch (i). Therefore, the total distance covered is given by the total i.e., the shaded area in sketch (ii). area of all such pillars
GRAPHS OF MOTION1-19 shows an arrangement of three time-graphs forI
Fig.
(a)
Vo
the heights of this patch at its edges are is time t, what expression gives the area? (Outline your geometrical argumentIf in
sketch
(ii)
and v as marked, and the base
briefly.)
(b)
* (which folIf the heights at the edges are v and v lows from the definition of acceleration), what expression gives the area? (Outline your argument briefly.)
+
the motion of an object along a straight track. Graph shows distance plotted against time; graph II velocity against time; graph III acceleration against time. They are drawn with matching time-scales. The graphs sketched relate to an object moving with constant acceleration, starting at s 0. In (shown by B) at t (shown by A) and velocity v graphs for more complicated motions, all three lines may be
=
=
=
curved.(a)
(c)
Write the results of (a) and (b) as expressions for s the distance covered by the body in time t.
the general case of any motion, one or more of the graphs can be derived from another of the three by tangent slopes. Which one(s)? Explain why.In
(d)
Now suppose the acceleration is not constant but starts with a smaller value, rising to a greater one, so that the velocity still changes from v to v in time t, but not steadily, (i) Sketch the new graph picture, (ii) Will the expressions from (a) and (b) apply now? (iii) What weakness in the earlier algebraic discussion in Appendix
(b)
the general case, one or more of the graphs can be derived from another of the three by measuring areas under the curve. Which one(s)? Explain why.In
(c)
A
has now been removed?
motorcycle policeman starts from rest, accelerates 5 ft/sec 2 for 6 sees; runs at constant velocity for 1 sees; then skids to a stop in 4 sees, with constant deceleration. Sketch a trio of graphs I, II, 111, for his motion.I
A
*dv dt
A-2.
CALCULUS PROOFis is
In the limit, velocity, v, anu u(.tciciuuuii ds/dt, and acceleration, a,
rate-of-change of distance, rate-of-change of velocityif
dor
/ds\
Velocity
cPs
dT
\&)is is
or
5?
Show that
a
is
constant, each
of the following(i)
true:
dv/dt
= a integrates to v = v + ata constant, the value of v at timet2
Tun*
(ii)
(where v v Vo
=
0)
(iii)
+ at integrates to s = v t + iaf {Hint: remember v = ds/dt.) dv/dt = a integrates to V = Vo + 2as {Hint: try multiplying both sides by v.)
Fig. 1-20.
Problem
A-3, part
d
Acceienxtion.
DistanceFig. 1-21.
Ti/m/t
Problem
A-3, part e
Distance.
Vefocitij
Fig. 1-22.
Problem
A-3, part f
Tune(d)Fig.it
1-20 shows graph
II
for the motion of a car.I
Copy
and add sketches of graphs
and
III.
(e)
Fig. 1-21it
AcceCeratum.
M(f)
shows graph III for the motion of a truck. Copy and add sketches of graphs and II.I
TurnFig. 1-19.
for the motion of the bob of a -22 shows graph pendulum along its almost-straight path. Copy it and add sketches of graphs II and III. (.Difficult: DeservesFig.1I
long
Problem
A-3, parts
a, b,
and c
careful guessing.)
CHAPTERAPPENDIX BMeasurement of "g"have glibly announced the value of "g" as 9.8 meters/sec 2 (or 32 ft/sec 2 ), but this came fromlaboratory measurements.
1
GRAVITYValues of "g" in variouslocalities
31
g
"g" has been measured very precisely at a
few
We
standard laboratories. Comparative measurements have then provided accurate values of "g" at manyplacesall
You
will use
it
for simple
over the world.
calculations concerning falling bodies, and for important calculations of forces when you treat "g"as gravitational field-strength, "g"is
New YorkValue in meters/sec/sec 9.80267 Value in feet/sec/sec 32.16
Equator Pole9.78032.09 9.832
such a useful
quantity that you should see its value measured before you use it. You could make a very rough estimate with a stone and a stopwatch and a meterstick.
32.26in experi-
For ordinaryment-design,
calculations, in
problems or
you should use the rough values g
g1 wintakes "just over" 3 seconds to reach the ground. If the window is 1 50 ft from the ground, (a) Make an estimate of "g."
= 9.8 meters/sec/sec,
= 32 ft/sec/ sec.
PROBLEM B-l. ROUGH MEASUREMENT OF "g" An experimenter drops a big stone from a 4th-storyfindsit
dow and
Arithmetical Problems on Free Fall: Dissected
Problems
(b)
Taking 150 meters/sec 2
ft to.
be about 46 meters, estimate "g"
in
When you know the value of "g," you can make simple calculations about dropping stones, arrowsshot at monkeys, etc. Such calculations are occa-
measurement can be made with an electric clock, as illustrated in Fig. 1-23, and you should see some such demonstration. For very accurate measurements you must wait for the promised scheme which avoids friction and takes a groupbetter
A
used by physicists in designing apparatus some experiment, but they are not important physics. Elementary textbooks andsionally
or in dealing with
examinations
make much
of
them "because they
of
falls.
make
accelerated motion clearer." Students trained to solve them mechanically may gain little but a
PROBLEM
B-2.
MORE ACCURATE MEASUREMENTOF"g"
damaging prejudice that "physics consists of putting numbers in the formulas." We wish to avoid that
allowed to fall from ceiling to floor. At the held against two metal pins so that it makes an electrical connection which prevents the electric clock from starting. The ball is released abruptly, and the clock starts.ball is
A
metal
ceiling
it is
Fig. 1-23.
Measuring "g"
reaches the floor, the ball pushes two light metal plates making another electrical connection which stops the clock. In an actual experiment, the height of the fall was 7.00 meters from ceiling pegs to floor contacts, and the clock recorded a time of 1 .20 sees. (a) Estimate the value of "g," using these data. (b) Say what assumptions you made in (a) concerning the type of motion; the apparatus; the conduct of the experiment. (Give details; avoid prim generalities such as "apparatus accurate" or "avoided personal error.")it
As
together,
and we would not give two reasons: (1) You may meet similar calculations, that are important, in atomic physics; (2) They will show you something important about the place of mathematics in physics. For these two reasons you should work through Problems B-3, 4, 5, and 6. Even so, if earlier studies have made you a convinced formula-monger you had better omit these problems unless you are prepared to start with an open mind. Problems B-3 to B-6 have been dissected. You should answer them step by step, on question sheets reproduced from the small ones printed here. This scheme which you will meet several times in the course is intended to give you preliminary help and teaching towards later problems to be done on your own. Note that this insulting simplicity is meant to help you with the mathematics but not to save you from thinking out the physics for yourself. As you work such problems you should stop to notice that you are learning a method of solving them, but you should then concentrate onfoolish picture of science,
you such problems
in this course except for
the physical results that emerge.
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