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.

u

143

3

a o> i

1i

+"+"

~ 4*

-p

bO

ID

*H

e

c

to

>d

h ftH Oio

o a41

(D

g

1

1 .933

43

O

HbO

O

?V

H-

>

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