The project Physics Course: Text and Handbook Unit 3: The Triumph of Mechanics

PROJECT PHYSICS Text

and Handbook

The Triumph

of

O

Mechanics

I

I

I

I

I

I

c^

PROJECT PH-YSICS

Directors

James Rutherford Gerald Holton F.

Fletcher G. Watson

Published by HOLT,

RINEHART and WINSTON,

Inc.

New

York. Toronto

PROJECT PHYSICS Text

Unit

3 The

and Handbook Triumph of Mechanics

"

Directors of Harvard Project Physics Gerald Holton, Department of Physics, Harvard

The authors and publisher have made every to trace

University

James Rutherford, Chairman

F.

Acknowledgments, Text Section

of the

Department

New

York University Fletcher G. Watson, Harvard Graduate School of Education of Science Education,

the ownership of

make

all

effort

selections found in this

acknowledgment for their use. pubbc domain. Grateful acknowledgment is hereby made to the following authors, publishers, agents, and individbook and

Many

to

full

of the selections are in the

uals for use of their cop^xighted material.

Special Consultant to Project Physics

P. 1 Desagulier, J. T., The Newtonian System of the World, The Best Model of Government an Allegorical Poem. P. 2 Descartes, Rene, The Philosophical Works of Descartes, trans. Haldane, Ehzabeth S. and Ross, G. R. T., Vol. 1, p. 299, copyright 1931 by Cambridge University Press. P. 2 "A Free Inquiry into the received Notion of Nature," The Works of Robert Boyle, Vol. IV, p. 362. P. 3 Newton, Sir Isaac, The Principia, Motte's translation ,

Andrew Ahlgren,

A

University of Minnesota

partial list of staff

and consultants

Project Physics appears in the Text

Handbook, Unit

to

Hansard

and

1.

revised by Florian Cajori, preface to

copyright

xviii,

P. 5 Lucretius,

This Text and Handbook, Unit 3 instructional materials developed

is

one of the many

for the Project

George P. 5

Bell

&

first

edition (1687),

Sons, Book

51.

II, p.

Bacon, Francis, Complete Essays Including the

and Novum Organum, Washington Square Press.

New

by Finch, Henry

Physics Course. These materials include Text, Handbook,

Atlantis

Resource Book, Readers, Programmed Instruction booklets. Film Loops, Transparencies, 16mm films, and laboratory equipment.

facsimile of an original translation by Robert Kerr with

P. 6 Lavoisier, Antoine,

intro.

p.

©1961 by University of California Press. On the Nature of Things, trans. H. Munro,

edit,

L.,

Elements of Chemistry, (1790), a

new

by Professor Douglas McKie, Dover Publications, Inc.

P. 22 Gerhardt, Die Philosophische Schriften von Gottfried Wilhelm Leibniz, 1875-90, Vol. IV, p. 286. Eng. Trans, in Dugas, R., Mechanics in the Seventeenth Century, Central

Book

Co., p. 407.

P. 41

Darwin, Erasmus, Botanic Garden

Vegetation,

Moore,

J.

P. 43 Savery,

p.

Thomas,

in Hart,

I.

B.,

History of Steam Power, copvTight Collier-Macmillan & Co. P. 50 Joule,

James

—The Economy of

49.

Prescott,

The

James Watt

©1961 by

&

the

Crowell

Scientific Papers of James

Prescott Joule, an illustrated facsimile of the 1884 edition,

copyright

©1963

by

Dawson

of Pall Mall.

P. 56 Ibid. P. 58

Helmholtz, H.

L. F.,

Popular Scientific Lectures, ©1962 by

edited by Morris Kline, copyright 1873, 1881,

Dover Publications,

Inc.

La Science et I'Hypothese, E. Flammarion, excerpt trans, by McClaim, John. P. 78 Lord KeKin, "The Size of Atoms,'",\'flfj/re, Vol.

P. 63 Poincare, Henri,

I,

p.

551. P. 86 Frost, Robert,

from "West-Running Brook," The

Poetry of Robert Frost, ed. by Edwiu-d Connery Lathem, p. 259, copyright ©1969 by Holt, Rinehaii and Winston. Inc., copyright

©1956

by Robert Frost. Reprinted by permission

of Holt. Rinehart and Winston, Inc.

Lord Kelvin, "The Kinetic Theory of the Dissipation of Energy." Proceedings of the Royal Society of Edinburgh,

P. 92

Copyright All

©

1975, 1970, Project Physics

Rights Reserved

Vol. 8, p. 325.

ISBN 0-03-089638-X

P. 93 Nietzsche, Friedrich.

456789

Nietzsche:

039

Project Physics IV

987654321 is

a registered trademark

Otto,

An Anthology

"Der Wille zur Macht.

of His Works, ed. Manthey-Zorn.

Washington Square

Press,

p.

90.

p. 93 Shelley, Percy Bysshe, Hellas, ed. Wise,

Thomas J.,

&

P. 40 (aeolipile) Science

Turner, pp. 51-52 not inclusive. Pp. 93-94 Poincare, Henri, Kinetic Theory, ed. Stephen Brush, Vol. 2. p. 206, copyright ©1966 by Pergamon Press. Pp. 120-121 Huygens, Christiaan, Treatise on Light,

P. 46 (train)

Reeves

first

published in Paris (1690), trans. Thompson, Silvanus copyright 1912 by Dover Publications, Inc.

P.,

P. 134 Power, Henry,

Experimental Philosophy (1664), reprinted 1966 by Johnson Reprint Corp., p. 192. P. 134 Donne, John, "The First Anniversary," Donne's Poetical Works, ed. Grierson, Herbert J., Oxford University Press (Clarendon Press imprint). Vol. 1, p. 237.

Newcomen

Museum, London.

P.

43

P.

44 (Watt in his laboratory) Figuier, Louis, Les Merveilles

de

la

Society, London.

Science, Furne, Jouvet et Cie, Paris.

Boston

& Maine

Corporation.

P. 49 (top)

Museum, London. Courtesy of General Electric Company; (bottom)

American

Institute of Physics.

P.

48 (steamboat) Science

P. 52 Professor Keith R. Porter, Dept. of Biology,

Harvard

University.

"The Repast of the Lion," by Henri Rousseau,

P. 55

Museum of Art, bequest of Lewisohn, 1951. P. 57 (Goethe) painting by Angelica Kauffmann, 1787, Harvard College Observatory; (Schelling) pastel by Friedrich Tieck, 1801, collection of Dr. Hermann von courtesy of The Metropolitan

Samuel

A.

Schelling. P. 58 Koenigsberger, Leo,

Hermann von

Helmholtz,

Braunschweig Druck und Verlag, von Friedrich Vieweg und Sohn. P. 65 (wrecker)

Picture Credits, Text Section

Inc.;

Cover photograph, p. 134 "Locomotive Wheels" by Farrell Grehan. P. 2 (watch assembly) Swiss Federation of Watch Manufacturers; (Blake drawing) Whitworth Art Gallery, University of Manchester. P. 3 Albert B. Gregory, Jr.

margin) Pictorial Parade, N.Y.C. P. 5 (thunderhead) Peter M. Saunders. Woods Hole Oceanographic Institute, (bonfire) Colgate University.

P. 4, 135 (top

P. 7 (Lavoisier portrait) painted by

Jacques Louis David. Courtesy of The Rockefeller University. Boston Patriots Football Club. P. 14 (hockey players) Pictorial Parade, N.Y.C; (space vehicle) National Aeronautics & Space Administration; (galaxy) Mount Wilson and Palomar Observatories; (colliding balls) National Film Board of Canada. P. 12

Harry Redl, LIFE

Fugazy Travel Bureau,

Inc.

P. 70, 135 (margin, third firom top) Courtesy

P. 86

American

Institute of Physics.

(Maxwell) Courtesy of Trinity College Library, Cambridge; (colliding balls) PSSC Physics, D. C. Heath P. 91

P. 92 (light bulb) Dr. Harold E. Edgerton, M.I.T.

WHbamson — Clearing

Brace

&

World,

reproduced with their permission. second from top) Russ Kinne Photo

Inc.,

P. 28, 135 (margin,

—

Storm," 1944, Ansel Adams.

Thompson, Silvanus

1,

MacmiUan and

Union

P. 35 Albert B. Gregory,

P.,

from red-figured amphora

attributed to the Brygos painter. Courtesy of the

Fine P.

Museum

John Michael Rodocanachi Fund. 119 National Film Board of Canada. Arts, Boston.

Pp. 120, 122-123, 125 (ripple tank photos) Courtesy, Film

Studio Educational Development Center. P. 121 Courtesy, College of Engineering, University of

California, Berkeley. P. 125 (radiotelescope) National

Radio Astronomy

Observatory, Green Bank, W.Va. P. 128 U.S.' Nav7. P. 130

Schaefer and Seawell

chamber)

Bell

Telephone Laboratories;

(concert haU) Hedrich-BIessing

Jr.

P. 36 Dr. Harold E. Edgerton, M.I.T.

P. 143 U.S. Na\^.

LIFE MAGAZINE, © Time Inc. P. 39 (camel & waterwheel) C. W, Kirkland, LIFE Time Inc.; (reversible overshot MAGAZINE, waterwheel) Agricola, Georgius, De Re Metallica, 1556, Houghton Library, Harvard University; (windmill) M. G. Time Inc. Walker, LIFE MAGAZINE,

by the

P. 37 Dimitri Kessel,

©

©

vol.

Co., Ltd.,

Pacific Railroad.

P. 133 (anechoic

Researchers.

(bonfire)

Life of William Thomson, London. P. 94 P. E. Genereux, E. Lynn. P. 96 Greek National Tourist Office, N.Y.C. P. 100, 111, 135 (bottom margin) Magnum Photos Inc., N.Y.C. Werner Bischof P. 93

P. 117 "Singer with Lyre"

Amsterdam. P. 21 (Descartes) the Franz Hals portrait in the National Art Museum, Copenhagen. P. 22 (Leibniz) Burndy Library, Norwalk, Conn. P. 27 "The Little Prince" ft-om THE LITTLE PRINCE by Antoine de Saint Exupery, copyright 1943 by Harcourt,

;

Colgate University; (landscape) "Mount

P. 105

Letters,

&

Co., 1965.

P. 18 (galaxy)

and

AMF-Voit.

P. 71 (balloon) U.S. Air Force.

P. 17

The Boeing Company. Mount Wilson and Palomar Observatories; (colliding cars) Henry Groskwsky, LIFE MAGAZINE, © Time Inc. P. 20 (Huygens) Royal Netherlands Academy of Sciences

MAGAZINE, © Time & Eckhardt, Inc. and

(ocean liner) courtesy of Kenyon

All

photographs not credited above were made staff of Harvard Project Physics.

of

Science is an adventure of the ivhole human race to learn to live in and perhaps to love the universe in which they are. To be a part of it is to understand, to understand oneself, to begin to feel that there is a capacity within man far beyond what he felt he had, of an infinite extension of

human

possibilities ....

propose that science be taught at whatever level, from the loivest to the highest, in the humanistic way. It should be taught with a certain historical understanding, ivith a certain philosophical understanding, xvith a social understanding and a human understanding in the sense of the biography, the nature of the people who made this construction, the triumphs, the trials, the I

tribulations. I.

Nobel Laureate

Preface

The Project Physics Course

Background research of

is

based on the ideas and that worked in

a national curriculum development project

three phases.

First,

the

instructor, a

authors— a high school physics

university physicist, and a professor of science education to lay out the

main goals and topics

of a

new

— collaborated

introductory physics

course. They worked together from 1962 to 1964 with financial support from the Carnegie Corporation of New York, and the first version of

was tried out in two schools with encouraging These preliminary results led to the second phase when a series of major grants were obtained from the

the text

results.

of the Project

U.S. Office of

Education and the National Science Foundation, starting in 1964. Invaluable additional financial support was also provided by the Ford Foundation, the Alfred P. Sloan Foundation, the Carnegie Corporation, and Harvard University.

A

large

number

of collaborators

were brought together from all parts of the nation, and the group worked together for over four years under the title Harvard Project Physics. At the Project's center, located at Harvard University,

Cambridge, Massachusetts, the

staff

and consultants included college

and high school physics instructors, astronomers, chemists, historians and philosophers of science, science educators, psychologists, evaluation specialists, engineers, film makers, artists and graphic designers. The instructors serving as field consultants and the students in the trial classes were also of vital importance to the success of Harvard Project Physics. As each successive experimental version of was developed, it was tried out in schools throughout the

the course

United States and Canada. The instructors and students reported their criticisms and suggestions to the

and these reports became the basis the course materials. In the Preface major aims vi

of the course.

for the

staff in

in

those schools

Cambridge,

subsequent revisions of you will find a list of the

to the Text

in

I.

RABI

Physics

We

wish

were possible

it

person who participated

Unhappily

it

is

to

in detail

list

some

in

not feasible, since most staff

variety of materials

the contributions of each

part of Harvard Project Physics.

and had multiple

members worked on

a

responsibilities. Furthermore,

every text chapter, experiment, piece of apparatus, film or other item in

the experimental program benefitted from the contributions of a

many

great

partial

many

fact,

people. Beginning on page A21 of the Text Appendix

of contributors to

list

a

in

other contributors too numerous to mention. These include

school administrators

members

is

Harvard Project Physics. There were,

in

participating schools, directors and staff

of training institutes for teachers, instructors

who

tried the

course after the evaluation year, and most of all the thousands of students who not only agreed to take the experimental version of the course, but

who were

also willing to appraise

it

critically

and contribute

their

opinions and suggestions.

The Project Physics Course Today. Using the

last of the

experimental

versions of the course developed by Harvard Project Physics in 1964-68 as a starting point, and taking into account the evaluation results from the tryouts, the three original collaborators set out to

develop the version suitable for large-scale publication.

We

take

acknowledging the assistance of Dr. Andrew the University of Minnesota. Dr. Ahlgren was invaluable

particular pleasure in

Ahlgren of

because

of his skill as a physics instructor, his editorial talent, his

and energy, and above

versatility

his

all,

commitment

to the

goals of

Harvard Project Physics.

We

would also especially

administrative

much of

skills,

to our work.

New

thank Ms. Joan Laws whose

The

publisher, Holt, Rinehart

and Winston,

Inc.

York, provided the coordination, editorial support, and general

backing necessary version of

all

company

to the large

components

texts, laboratory

to

like to

dependability, and thoughtfulness contributed so

undertaking of preparing the

final

of the Project Physics Course, including

apparatus, films, etc. Damon-Educational Division, a

in Westwood, Massachusetts, worked closely with us improve the engineering design of the laboratory apparatus and to

see that In

Course

located

it

was properly integrated

into the

program.

the years ahead, the learning materials of the Project Physics will

be revised as often as

is

necessary to remove remaining

ambiguities, clarify instructions, and to continue to

more

interesting

and relevant

students and instructors

who use

We

make

the materials

therefore urge

all

send to us (in care 383 Madison Avenue, New York, this

course

to

of

and Winston, Inc., York 10017) any criticism or suggestions they may have.

Holt, Rinehart

New

to students.

F.

James Rutherford

Gerald Holton Fletcher G.

Watson

VII

Answers

to End-of-Section

Chapter 9

02

No. Don't confuse

mass

with

volume or mass

with weight.

Answer C No. Change speed

Q6

in

momentum:

Least

mass and Greatest

fairly

jet

Q12

plane

in flight

(very large

4 cm/sec. Faster ball delivers

momentum

to

more

girl.

about 4 cm/sec. More massive

(b)

ball delivers

more

girl.

about 1 cm/sec. With same gain in momentum more massive girl gains less speed. (d) about 4 cm/sec. Momentum change of ball is (c)

greater

if

its

mass

ball is

much

Same, Same,

and

final

positions are identical.

if

initial

if

frictional forces are negligible.

frictional forces

Q13 Q14 Q15 Q16 Q17 Q18 Q19

Q20 Q21

of the girl.)

can be applied to situations where only masses and speeds can be determined. Q9 Conservation of mass: No substances are added

Q8

to be. (For further

between

skis

It

Answer Answer

(c)

False. It was the other way around. Chemical, heat, kinetic or mechanical

Answer Answer

(d)

a unit of power, or rate of doing work,

is

It

(b)

Answer Answer

(d) (b)

A small amount was transformed energy of the slowly descending weights and the water container would also have been Q22

Nearly

all.

into kinetic

to

warmed. Answer (a) Answer (e) The statement means

that the

Q10

the lion obtains from eating

comes

Conservation of momentum: No net force from outside the system acts upon any body considered

be part of the system. None of these is an isolated system. In cases (a) and (b) the earth exerts a net force on the system. In case (c) the sun exerts a net force on the system. Q11 Answer (c) (Perfectly elastic collisions can only occur between atoms or subatomic particles.) Q12 Answer (d) (This assumes mass is always positive.)

Q13 Q14

Answer (c) (a) It becomes stored as the object rises. (b) It becomes "dissipated among the small parts" which form the earth and the object.

Answer (b) Answer (b) Answer (c) Answer (c) The increase in potential energy equals the work done on the spring. Q5 Answer (e) You must do work on the objects to push them closer together. Q6 Answer (e) Kinetic energy increases as gravita-

Q2 Q3 Q4

same

(if

energy decreases. Their sum remains

air resistance is negligible).

Potential energy

where the speed is

is

greatest at extreme position

of the string

is

zero. Kinetic energy

greatest at midpoint where the string

Q8

is

unstretched.

The less massive treble string will gain more speed although both gain the same amount of kinetic VIII

energy which

ultimately from

eats animals, which eat plants which

He

total

energy of the

system

AW system

—

031

1.

2.

the net work (the work done on the

is

the work done by the system) the net heat exchange (heat

is

the system

Q1

Q7

sunlight.

grow by absorbed sunlight. Q26 Answer (c) Q27 Answer (a) Q28 Answer (c) Q29 Answer (c) Q30 AE is the change in the

AH

Chapter 10

the

if

(c)

Q23 Q24 Q25

or allowed to escape.

tional potential

Less

and snow are taken

equal to 746 watts.

direction reverses.

(These answers assume the mass of the less than the

seems 10.15.)

into account.

mass and high speed)

Q7 (a) about momentum to

it

SG

Q10 None. Centripetal force is directed inward along the radius which is always perpendicular to the direction of motion for a circular orbit. Q11

a pitched baseball (small

small speed)

momentum: a

level that

discussion see

and perform

and (d) (Their momenta before collision magnitude and opposite in direction.)

(a), (c)

Multiply the weight of the boulder (estimated from density and volume) by the distance above

Q9

ground to velocity

additions by vector techniques. are equal

energy given by

guitarist).

False

Q5

to elastic potential

energy (equal

Q1

Q3 Q4

Questions

—

added

to

heat lost by the system)

heating (or cooling) it doing work on it (or allowing

it

to

do work)

Chapter 11

01

Answer

02 03 04 05

True

06 07 08 09

Answer Answer Answer Answer

(c)

False

Answer

(b)

gases the molecules are far enough apart that the rather complicated intermolecular forces can safely be neglected. In

(b) (b) (d) (c)

(continued on

p.

Al)

Project Physics

O

Text

The Triumph

of

Mechanics

1

r

I

ri

...^

r

9 5 6 2 7 1

1

Things to Do and Use L37 L38 L39 L40

Experiments 3-1

3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-1

3-12 3-13

One Dimension Collisions in One Dimension Collisions in Two Dimensions Collisons in Two Dimensions Collisions

in

I

II

I

L41

II

Conservation of Energy Conservation of Energy Measuring the Speed of a Bullet Energy Analysis of a Pendulum Swing Least Energy

L42 L43

I

II

The

Calorimetry Ice Calorimetry Monte Carlo Experiment on Molecular

Behavior of Gases 3

Measuring Wavelength

4

Sound Ultrasound

5

Activities

Mass Conserved? Exchange of Momentum Devices Student Horsepower Steam-powered Boat Problems of Scientific and Technological Growth Predicting the Range of an Arrow Drinking Duck

6

Is

7 8 9

James

10

1

IVaves by Richard Stevenson and R. B. Moore What is a Wave? by Albert Einstein and Leopold Infeld l\/lusical Instruments and Scales by Harvey E. White Founding a Family of Fiddles by Carteen M. Hutchins The Seven Images of Science by Gerald Holton Scientific Cranks by Martin Gardner Physics and the Vertical Jump by Elmer L. Offenbacher

13

Sound

14

Wave Machines

Letter

1

Fii!

L18 LI 9

L20 L21

L22 L23 L24 L25 L26 L27 L28 L29 L30 L31

One-Dimensional Collisions One-Dimensional Collisions Inelastic One-Dimensional Collisions Two-Dimensional Collisions Two-Dimensional Collisions Inelastic Two-Dimensional Collisions

18

II

1

Tr;: I

II

Recoil Colliding Freight

Dynamics A Method

T19 T20 T21

Cars

a Billiard Ball of Measuring Enegy

— Nails

Wood

Energy Energy Conservation of Energy Pole Vault Conversation of Energy Aircraft Gravitational Potential

Kinetic

— —

Reversibility of

Time

One-Dimensional Collisions Equal Mass Two-Dimensional Collisions Unequal Mass Two-Dimensional Collisions

of

Take-off

L36

1

I

Driven into

L32 L33 L34 L35

1

I

II

Scattering of a Cluster of Objects Explosion of a Cluster of Objects Finding the Speed of a Rifle Bullet Finding the Speed of a Rifle Bullet

Clerk !\Aaxwell

by James R. Newman Frontiers of Physics Today: Acoustics by Leo L. Beranek Randomness and the Twentieth Century by Alfred M. Bork

1

Perpetual Motion Machines? Standing Waves on a Drum and Violin Moire Patterns Music and Speech Activities

Resource

1 The Superposition Principle 2 Periodic Waves

by Kenneth W. Ford The Law of Disorder by George Gamow The Law by Robert M. Coates The Arrow of Time by Jacob Bronowski

Gauge

of

Instruction Booklets Kinetic-Molecular Theory of Gases

Thermodynamics

Mechanical Equivalent of Heat A Diver in a Bottle Rockets How to Weigh a Car with a Tire Pressure

Speed

Vibrations of a Metal Plate

by Arthur C. Clarke The Steam Engine Comes of Age by R. J. Forbes and E. J. Dijksterhuis The Great Conservation Principles by Richard P. Feynman The Barometer Story by Alexander Calandra The Great Molecular Theory of Gases by Eric M. Rogers Entropy and the Second Law of

2

of the

Hose

Drum

Silence, Please

1

Wave Properties Waves in a Ripple Tank

Mechanical

Vibrations of a

Waves Waves

Temperature and Thermometers

Measurement

Vibrations of a Wire Vibrations of a Rubber

Programmed

Collisions

3-14 3-15 3-16 3-17 3-18 3-19

Superposition Standing Waves on a String Standing Waves in a Gas

T22 T23 T24 T25 T26 T27 T28 T29

Two-Dimensional Collisions Slow Collisions The Watt Engine Inelastic

Superposition

Square Wave Analysis Standing

Waves

Two-Slit Interference Interference Pattern Analysis

5

Contents

TEXT, UNIT 3

Prologue

1

Chapter 9

Conservation of Mass and

Conservation of mass Collisions

5

9

momentum

Conservation of

Momentum and

1

Newton's laws of motion

Elastic collisions

Leibniz and the conservation law

Work and

1

18 19

Isolated systems

Chapter 10

Momentum

21

Energy 29

kinetic energy

31 Conservation of mechanical energy Forces that do no work 37 Heat energy and the steam engine Potential energy

34 39

James Watt and the Industrial Revolution 43 The experiments of Joule 49 Energy in biological systems 51 Arriving at a general law 56 A precise and general statement of energy conservation Faith in the conservation of energy

The

Chaoter 11

Kinetic

60

62

Theory of Gases

An overview of the chapter 69 A model for the gaseous state 71 The speeds of molecules 74 The sizes of molecules 76 Predicting the behavior of gases from the kinetic theory

The second law of thermodynamics and the Maxwell's demon and the statistical view of Time's arrow and the recurrence paradox

Chapter 12

Wave

propagation

Periodic

02 05

1 1

106

waves

When waves A

meet: the superposition principle

two-source interference pattern

and

fronts

Reflection

diffraction

1

20

22 1 26

Sound waves

1

28

134

Acknowledgments Picture Credits

Answers

iv

Iv

to End-of-Section Questions

A25

Brief Answers to Study Guide Questions

Index

09

1

Refraction

Epilogue

1

110

115

Standing waves

Wave

91

101

Properties of waves

A44

85

the second law of thermodynamics

Waves

Introduction

79

dissipation of energy

A36

88

^.

av

m^ ^

^ y^-^

->^

> >

h \^

>v

'5/

^^

-^

**^»

V

^>^-

.^ y

^*^'

^^

>v

^