Robert March - Instructor's Manual Physics For Poets.pdf

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INSTRUCTOR'S MANUAL

T

ACCOMPANY

SECOND EDITION

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2/22

INSTRUCTOR S MANUAL TO ACCOMPANY

-

Pf1;fta

Po&

SECOND EDITION

B/;PAr IJ.

A1a 1.Ck

Unive

rs

i ty

of sconsin,

Madison Wisconsin

McGraw-Hili Book Company

New York St. Louis San Francisco Au ckland Bogota Dusseldorf

Johannesburg London Madrid Mexico Montreal New Delhi Panama

Par is Sao Paulo Singapore Tokoyo Toronto

Starts from here
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..

TABLE OF CONTENTS

INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

PACING THE COURSE AND TRUNCATED VERSIONS 3

CHAPTER BY CHAPTER CLASSROOM

SUGGESTIONS.. . . . . . . . . . . . .

4

EXAMINATIONS AND

TERM PAPERS 16

Sample

Examination

Questions

17

Semi-Take-Home

Exam

26

Abstracts of Term Papers ' 30

HOMEWORK

ASSIGNMENTS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

ANSWERS TO EXERCISES IN

THE TEXT

34

Instructor's Manual

t

accompany

PHYSICS FOR POETS

Second Edition

Copyright

1978

by

McGraw-Hili Inc All rights reserved

Printed in the United States of America The contents or

parts thereof m ay be reproduced for use with

PHYSICS FOR POETS

Second Edition

by

Robert H March

provided such reproductions bear copyright notice but may not

be reproduced in

any

form for any other purpose without

permisSion of the publisher

0-07-040244-2

1234567890 WHWH

78321098

~ ' . _


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ha.ve some

dif f icul ty

teaching

chapter

19, and might be

well advised

to

omit i t .

Very

few

students

seem to

be "turned on" by

c lass ica l

mechani cs . But

we

have made attempts

a t

Wisconsin

to

move direct ly into

re la t iv i ty

without systematic

devel

opment of the

c lass ica l background,

f i l l ing

t in

as

needed. This experiment was

not too successful , and

i s

not

recommended by

the

author.

The most important

thing

to remember in th is course

is no t t o

give

the student

an

excuse to "cop

out,"

to

decide ea r ly in the course tha t physics

is

beyond

him

and stop trying. To avoid

th is

t helps to s ta r t

slowly,

to

give

assignments

tha t

are

so easy

the

student

can hardly miss, to build

up

his

confidence.

Before

long even the most t imid

student

wil l find himself

handling topics he would have

been a f r a id to

think

about

a few

months

before.

The

sections

tha t follow

give suggestions on the

use

of th is

text

based on my experience a t Wisconsin,

where

the course has been taught s ince 1963. In th is time t

has grown

from

a cozy gathering of 15

students

to a

ful l-dress lecture

o f

380. Throughout th is

period

the

students have remained

the

same an

above-average but

not except ional group of humanities and socia l science

majors from

a

f i rs t-c lass but not ~ l t s t sta te

univer

s i ty .

Other

schools using

the

text

may have bet te r or

weaker students

or a different classroom si tuat ion, and

the suggest ions offered

in

t h i s manual may be

of

l imited

ut i l i ty or val idi ty for many schools.

P CING

THE COURSE

ND TRUNC TED VERSIONS

The ful l

content

of t h i s

book

represents a

re la t ive ly

challenging

one-semester course for

the

format used

a t

Wisconsin (3 lectures, one

discussionper

week). The

number of lectures

devoted

to

each topic

in

t h i s

format

are

indicated in the section

that

follows. Instructors

operating

in a shorter format, or in

schools

on

the

quarter

system, may wish to consider

several po ssible

stratagems for t runcat ing

the

course:

Eliminate

Chapter 19. The

book reaches

a

reasonably

1.

sat is fy ing

conclusion

with non-re la t ivi s t i c

quantum

theory a t Chapter 18. This is especially recom

mended i f the

ins t ructor

is not familiar

with

Feynman

diagrams and

the

quark

model.

2.

Assign

one or

more chapters

for

independent reading.

Chapters 13 and 18

are

quite sui table for th is pur

pose.

I t

is a lso poss ible

to use

Chapter 5

in

t h i s

fashion.

Skip ei ther quantum mechanics or

re la t iv i ty .

The

.

former

route

terminates

with Chapter

12. The

la t te r uses chapters 1 through 7 and 13 through 19.

In th is case, t will be necessary to include a lec

2

ture on the meaning of

E

=

mc ,

which i s

needed in

order

to understand

Chapter

19.

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C H A P T E R - B Y - C H A P T E R

C

L A S

S ROO M S U G G E S T I O N S

CH PTER (3

lectures)

Topics: Introduction to the concepts

o f veloci ty and

ac

celerat ion;

Galileo's descript ion

o f

f l l ing body

motion

as an example o f the

sc ien t i f i c method.

This

i s a very

d i f f icu l t chapter.

I f t i s not t reated

with great care and gone through slowly, you may lose some

o f the

students from

the outset .

What makes

t d i f f icu l t

i s

the

concept of acceleration,

which may

be

the most confusing concept in the course for

students with

a weak

mathematical

background.

I t

i s best

to put

t across

with a lo t of

examples,

emphasizing the

sign

ra ther

than

the magnitude of velocity and accelera

tion. For example, when a car i s

braking,

acceleration

i s

negative, velocity

i s pos i t ive ,

and so on through many

such cases.

I t

also sometimes helps

to

give

examples of second

de

r ivat ives

from

areas outside physics.

For example,

the

stock

market

rose

5

points

today and 15

the day

before;

thus,

the

market

is r i s ing (posit ive velocity) but the

boom i s

taper ing off (negative

acceleration).

I t may also

help

to cover t h i s topic through interpre

t a t ion

of

graphs,

pointing out the

re la t ion between

slope

and velocity, curvature and acceleration. But a t least

one

class

period

wil l

have

to

be

devoted

to

th is

topic

alone.

I t

i s much eas ier to

drive

home the

scient i f ic

point

raised in

the chapter

- -

that

while Galileo was only

t ry

ing to

describe

the motion of a fa l l ing body, even

that

simple process

i s

a

pre t ty abs tract

business. Here a few

extremely simple demonstrations

can

be very helpful . For

example, demonstrate the fa l l of various

objects , such

as

coins, crumpled-up paper, etc . The difference between a

balloon inflated and

the

same balloon deflated, a paper

crumpled and the same paper f la t , e tc . , can

persuade

the

student

that a lo t more variables than

mere

weight are

involved

in

fal l ing-body motion. The

"punch l ine"

i s

that

what Gali leo i s saying is that falling-body motion would

depend on none

of

these variables, were

t

not for the

effec t s of the

a i r .

I t

i s also

in te res t ing to

repeat

Galileo's

inclined

plane experiment. You need a very f la t , r igid , grooved

board

or metal

beam a t least

10

feet

long,

se t a t

such an

angle that a ba l l takes about 10

seconds

to ro l l

the

ful l

length.

A

large coffee pot

or picnic jug

with

a

spigot,

and a

graduated

cylinder , make a reasonable

water

clock.

with a

l i t t l e

pract ice

you can

achieve an accuracy level

of

about a quarter of a second th is way.

CH PTER 2 (2

lectures)

Topics:

Projec t i le

motion;

momentum

conservation (two

bodies,

one-dimensional

motion)

project i le motion

i s analyzed

using three concepts:

the principle of iner t ia and

the mechanical

pr incip le of

superposit ion,

introduced in th is

chapter ,

and

the

de

scr ip t ion of fa l l ing

body

motion

from

the

preceding

chap

t e r .

e

sure those pr incip les get across and emphasize

that

while t i s

possible

to

get

a complete descripti 'on

of

the

combined motion as a parabola, in prac t ica l terms

one

need

not do th is - - t i s suff ic ient

to

t r ea t the

horizontal and

ver t ical

motions separately. I f an appa

ratus

that

produces a col l i s ion between a

project i le

and

a freely

fa l l ing bal l released

a t

the

same ins tant is

available, t h i s makes a

very

convincing

demonstration.

Demonstrations of momentum conservation

with

an a i r

table are also useful

in

th i s

portion of the

course.

CH PTER 3 (2 lectures)

Topic: Newton's laws

No new mathematical

concepts

are introduced

in

th is

section.

Emphasize that

Newton's crucia l

contr ibution

was the real izat ion that change in motion resul ts only

from an in teract ion of two objects , and that

the

dif fer

ence

in how

each

of

them

i s affected

resul ts from

a

dif

ference in

mass

ra ther

than any asymmetry

in

the i n t e r

action.

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CH PTER 6 (2 lectures)

Topics: Electr ic i ty and magnetism; the

concept

o f

f ie lds;

philosophical

consequences

o f deterministic laws in

physics

There is nothing ter r ib ly

d i f f icu l t

in th is chapter.

y now

most

students

should

be suff ic ient ly

conditioned

to the physicist ' s point of view to a t least be to le rant

of the argument

that i f

the

f ie ld

has

to

take up momentum

and energy to

save

the conservation laws for these

quan

t i t i e s and Newton's laws, then the f ie ld must in

some

sense be rea l .

Some of the bet te r

students

may f ind the rather sketchy

introduction to

e lec t r i c i ty a b i t

too

open-ended

to

be

sat is fy ing .

t

might not hurt to give

such

students

sup

plementary

reading

in a

conventional

physics

text .

The

usual amber rod, ca t ' s fur, and pi th-bal l demon

s t ra t ions of elect rostat ics can be effect ive

here.

CH PTER 7 1 lecture)

Topics: Wave pulses; wave superposition;

periodic

waves;

standing waves; two sl i t interference

This chapter

stands

alone as an

introduction to waves.

I t

makes

no reference to per iodic

motion, nor

does

it

mention

the

trigonometric functions, an omission which a

few

superior

students may find dissat is fy ing .

The emphasis of the chapter i s on wave laws themselves,

independent

of the underlying

dynamics of

the wave-propa

gat ing

medium

Thus, such

t radi t iona l

topics as the

dis t inc t ion

between

longitudinal

and

t ransverse

waves

are

also omitted.

The major goal of

the chapter

i s

for the student to

understand standing waves and two-s l i t interference.

At Wisconsin

we

have found the

text mater ial

i s rea

sonably self-explanatory.

The bes t

use of lecture

t ime

i s

for demonstrations.

For two-s l i t interference, a

pair

of loudspeakers

about s ix feet apar t

driven by

the same monotone audio

8

source

gives

a s t r iking

ef fect .

A low-wattage laser pro

duces

spectacular

two-s l i t

fringe

pat terns . A r ipple

tank can

a lso

be effec t ive ,

but to

make

the ef fect

rea l ly

convincing

takes a good r ipple

tank and

a reasonable

amount

of

pract ice.

A

slinky

spring

toy mounted between

two f ixed

posts

is

a

good

way

to demonstrate standing waves.

But

fa r and

away

the most popular and effect ive demonstration we have

used a t Wisconsin i s the observation

of

a mechanically

driven vibra t ing

rope in

various

modes

with

a

strobe

l ight . This both enables

the

students

to

rea l ly see

standing wave patterns and

convinces them that

standing

waves

are

beaut i fu l ,

which

i s a great motivational aid .

CH PTER

8

(2

lectures)

Topic: The

Michelson-Morley

experiment

This

i s

the

f i r s t of

four

chapters

on

r e l a t iv i ty

and,

as

was

the case

with

the f i r s t of

the

chapters on c las

s ica l mechanics, contains most of the

math

needed to

un

derstand the subject . Continually emphasize to the stu

dent that i f he has

a

feeling for

how

y varies

with

vic

he

wil l need no further

mathematical sk i l l s

to follow the

remaining

three

chapters on r e l a t iv i ty . At

the

r i sk

of

boring

the bet ter students,

devoting

one

class

session

to

a slow,

careful

review of

the derivation, with careful

and repeated explanations of

the motivation

for every

step, seems

to

help reassure the

students tha t r e l a t iv i ty

will

not prove

mathematically

beyond them.

CH PTER

9

(3

lectures)

Topics:

Non-quantitative

arguments

for time

dilation;

the

FitzGerald

contraction;

re lat iv i ty o f simultaneity;

and uniqueness o f the speed o f

l ight

t

i s in

th is

chapter

that the

bat t le to teach r e l a t iv

i ty

i s won

or lost , and it cal ls for a l l of

the teacher ' s

sk i l l .

The

method used in the text i s the analysis of

gedanken experiments, and

the

bes t use of classroom time

i s

to repeat these

examples, answer questions about

them,

and add further

examples. I

have found that every

s tu

dent seems

to

have

a

di ffe rent point a t which

it suddenly

h i t s him what r e l a t iv i ty

i s

a l l about; each

example

makes

a few new

converts .

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1ft

The f i r s t s t ep

i s to convince

t he s tudent

t h a t i

two

observers r e l a t i v e l y in motion

a re

to

ag ree on t he

speed

o f

one

and the

same

l i g h t s ig n a l ,

th ey

must obviously

di sagree about

some o f the

th ings

t h a t go i n to measuring

t h a t speed. For the t ime being, one must suspend d i s

b e l i e f , as

in

the

thea t re ;

one must not inqui re how

it

i s

poss ib le for two obse rve rs to

di sagree on

such e lemen

t a ry

mat te r s , but merely whether it i s poss ib le to l i v e

with t hese disagreements .

To provide reassurance

to the

s tudents , con t inua l ly

remind

them

t h a t r e l a t i v i s t i c

disagreements

apply only to

remote event s , event s d i sp laced from one anothe r along

t he

l i n e of r e l a t i v e motion.

Furthermore ,

two

obse rve rs

a t t he same poin t w i l l

always ag ree on

what they a re see

ing

a t tha t in s tan t ;

it is when

th ey

t r y to i n t e rp re t

t he

p a s t phenomena re spons ib le

for what they now observe t h a t

disagreement

a r i s e s . Fina l ly , each i s p e r f ec t l y

cap ab le

of r econs t ruc t ing t he o th e r ' s poin t o f view, so the re i s

no

communication

gap. Lest

t h i s make

it

seem as

i

r e l a t i v i s t i c e f f ec t s

a re

merely i l l u s o ry , t he

l a s t

ex

ample of fe red

in

t he chapte r i s t h a t o f t he

garage

p a r a

dox.

The most

use fu l

gedanken experiment to add to those in

t he t ex t i s

E i n s t e i n ' s own or ig inal one,

t h a t

o f a

t r a in

t h a t

i s

s t ruck

a t both ends by

l igh tn ing

f la shes , s imu l

taneously in

t he re fe rence frame

o f

t he t r a in .

A

moving

and a

s t a t i o n a r y obse rve r ,

bo th o f whom

a re a t

the cen te r

o f t he

t r a in

when the f la shes a r r i v e ,

ag ree

t h a t the

f lashes

appear

to

be

simul taneous.

The obse rve r on t he

ground

concludes

t h a t

s ince the

l igh tn ing

b o l t

a t

the

f ron t of

t he t r a in

was c loser ,

it

must have come

l a t e r .

The ana lys is can be

extended.

Suppose

t h a t c locks

synchronized

in t he t r a i n ' s r e s t frame

a re

placed a t

e i t h e r

end

o f the

t r a in

and

a re

s topped by

t he

l igh tn ing

bol t s . Again, t he obse rve rs

agree

t h a t t he two clocks

s topped a t t he same s e t t i n g . Afte r a l l ,

they

a re no

l onger running

and

can be

brough t to t he

same

p o in t and

compared

d i r ec t l y . The obse rve r

on t he t r a in f ee ls

t h a t

t h i s i s

because

wel l - sy n ch ro n ized c lo ck s were

h i t

by

t r u l y s imultaneous l igh tn ing b o l t s . The obse rve r

on

the

ground f e e l s t h a t unsynchronized clocks were stopped by

non-s imultaneous

l igh tn ing bol t s .

10

I f t he

l igh tn ing bol t s

leave marks on

the ra i l road

t i e s , the s t a t i o n a r y observer f e e l s they a re far ther

apa r t

th an t he l ength

o f the

t r a in . Again ,

the observer

on t he t r a in agrees , bu t he sees

it

as

a

consequence

o f

the f ac t t h a t t he ra i l s had shrunk, whereas t he obse rve r

on t he ground sees

it

as

a

consequence

o f

t he

f ac t

t h a t

the l igh tn ing bol t s

were

non-simul taneous, which more

than

compensates

for the shr inkage o f the

t r a in .

To emphasize the cont ra s t with the

expected

non

r e l a t i v i s t i c behavior , p o in t out

t h a t

t he

thunder

c laps

produced

by

t hese f la shes do no t

arr ive

s imultaneously a t

t he

cente r

o f the t r a in , and t he re i s

no

disagreement be

tween t he moving

and

the s t a t i o n a r y obse rve r on t h i s

poin t .

CHAPTER 10

(3 l ec tures )

Topics : Quant i ta t i ve bas i s for r e l a t i v i s t i c e f f e c t s ;

space- t ime;

the twin paradox

The

f i r s t p a r t

o f

t h i s chapte r s imply demonstra tes

t h a t t he f ac tor Y derived in Chapter gives the cor rec t

q u a n t i t a t i v e r e su l t for the t ime d i l a t i o n and FitzGerald

cont rac t ion . Thus,

i

the proper

groundwork

has been

l a i d ,

t he

mathematics in

t h i s chapte r

w i l l presen t

no

d i f f i c u l t i e s .

A

more r igorous der iva t ion of the c lo c k - s e t t i n g prob

lem can

be

done as fo l lows: cons ide r the

measurement o f

t he speed o f a l i g h t s igna l moving the l eng th o f a

t r a in ,

using clocks a t both ends o f the t r a in . Afte r t ak ing

in to

account

the

shr inkage

of the

t r a in

and

the c lock

slowdown,

a

s t a t i o n a r y

obse rve r still

f inds

a discrepancy,

as

a

r e su l t

o f the

Be prepared

to

go over

the

twin

paradox ca re fu l ly ;

most

s tudent s

are p a r t i cu l a r l y in t r igued

by t h i s example.

CHAPTER

11 (2 l ec tures )

Topics : Re l a t i v i s t i c mass i nc re ase and the surv iva l

o f

Newton s laws; mass-energy equivalence;

exper imen ta l

conf irmat ion o f

spec ia l

r e l a t i v i t y

This chapte r i s not p a r t i cu l a r l y

d i f f i c u l t .

I t s main

objec t ive i s to

t ak e

some o f t he mystery away

from

E mc

11


10/22

by

showing how universal ly

the

formula

applies .

e

sure to emphasize that making mass a function

of

velocity is the only conceptual modification in Newton's

mechanics required

by re la t iv i ty , aside from,

of

course,

using the

appropriate

space-time coordinates and t rans-

formations.

The

only

puzzling point

for

average

students is

why

res t

mass should exist a t al l why should an object

have

energy

simply by

vir tue

of

i t s existence?

Examples

useful here are those where what

appears

as r es t mass

when a

system

i s viewed as a whole

from

outside becomes

par t ly dynamical

when the

system i s analyzed in to

i t s

component

par t s .

The

best

example i s

binding

energy

of

a

nucleus.

CHAPTER 12

4

lectures)

Topics:

More detail on twin paradox; genera1 re lat iv i ty

black holes;

cosmology

This chapter makes severe demands

on

the students '

power of

abs tract

reasoning. I t helps

to

reassure them

that

not even

experts

in

the

f i e ld can t ruly visualize

curved space-time. I t

i s

also important

to

st ress that

th is is

an

alternative to the newtonian approach to

motion;

where

newtonianism

cal ls

for

force

laws,

general

re la t iv i ty

cal ls

for

theories in which fields

produce

curvature of

space-time. Fortunately, you

can exploi t

the students ' inherent

cur ios i ty

about black holes and

the

big bang.

CHAPTER

13

1

lecture)

Topics: Ancient atomic

theories and the

phases

o f

matter;

chemical

evidence

for atomism;

kinet ic

theory

o f gases;

atomic

s ize electrochemistry; the

discovery

o f

the

atom

This

chapter

provides a very sketchy

introduction

to

the emergence of the atomic theory

in c lass ica l

physics

and

chemistry.

As such,

t

presents no

diff icul t ies to

the average

student , nor i s

t

important that the mater ial

in t be well mastered. I t s major purpose

i s

to

provide

a

proper

histor ical s tar t ing point for

the

quantum

theory.

12

_ _

_

In a longer course, you may use t h i s chapter as a peg

on which

to

hang a more thorough and general survey

of

physical

science

from supplementary

materials .

CHAPTER 14 (2

lectures)

Topics: Plum-pudding and planetary atomic models; spectra

and spectral

laws;

the

Rutherford-Geiger-Marsden

experiments

Here

the

student

i s

introduced

to

what modern experi

mental physics is a l l about, as

the

experimental technique

and interpretat ion are

fu l ly

modern.

Some

students are puzzled by

the l / ( s in

)4

law, which

seems

unnecessarily

complicated

for

such

a

simple

si tua-

t ion

to

someone

without

much mathematical experience.

There

i s l i t t l e value

in

deriving i t , and that

i s

why the

derivation i s omitted

here.

But a la-minute rundown of

the

factors that

go in to

the der ivation

might

remove the

mystery, while persuading

the student that

quite simple

s i tuat ions

can

quickly

get mathematically messy, a valu

able lesson to learn.

Keep in mind

that

to many students,

the

process of

plot t ing

measurements on a graph and seeing which

of

two

curves f i t s best i s a new experience that may require

some explanation.

CHAPTER

15

(3

lectures)

Topics: Planck's theory;

Einste in ' s

, theory

o f

the photo

electr ic

ef fec t the

Bohr model o f

hydrogen

This

chapter

depicts the

quantum theory in i t s

early

years, when t was based on empir ical ly successful

but

arbi t ra ry assumptions. I f

a student

complains

that he

doesn' t get the connections between a l l

these

ideas,

point

out that

th is i s an accurate reflect ion of

the a t -

t i tude of

the

phys ic is ts

he s reading about.

-The Planck theory i s best sloughed off as quickly as

possible .

I f

you

wish to

go

in to t

a t somewhat

greater

depth, the treatment in Gamow and Cleveland, Physics:

Foundations and Frontiers

(Prentice-Hall,

1960), p. 378.,

i s suitable for

students

on th is level . The photoelectric

ef fect

is pre t ty

straightforward.

The

Bohr theory,

13


11/22

however, is

more

d i f f icu l t and must be

gone

over

slowly.

Keep

the

diagram a t

the

top of page 190

in

mind

as you

plan

your

lec tures ,

as t is

easy

for the students

to

lose the thread

of the ra ther

complex paths

of

reasoning

leading to the

Bohr theory. I t is also

wise, in

terms of

the future

development

of

the

theory,

to emphasize the

difference

between the idea of s tationary

sta tes , which

survives in

the

la ter

vers ions

of the

theory,

and Bohr's

c i rcula r

orbi ts ,

which do

not.

This

i s

also a good point

a t

which

to

begin working

numerical examples in

c lass to give

the students

a

feel

ing for the

magnitudes

of the

quant i t ies

involved.

CH PTER

6

3

lectures)

Topics:

The

DeBroglie hypothesis; Shroainger's equation;

wave equivalent

o f Bohr orbi ts ; expansion

o f

the

wave

packet

In

th is

chapter

the

quantum

theory advances

one

level

deeper; the wave

theory appears, removing

the arbi t ra ry

character of the ear l i e r

theories ,

but t s t i l l

remains

to be interpreted.

The

only dif f icul ty students tend to have with t h i s

par t o f the story of

quantum

mechanics comes

from

the

fact

that

t

is hard

to visualize three-dimensional

s tanding

wave patterns such

as are obtained in the hydro

gen atom. e have found the following

derr,onstration

helps a great deal . Mount

on

a drum a

loose

rubber drum

head.

Drive t

with

a speaker inside the drum and ob

serve t with

a

strobe

l ight . The resu l t ing

undulations

are very s t r iking.

CH PTER

17 (3 lectures)

Topics:

The probabil i ty interpretation o f the wave

function; the uncertainty relations;

consequences

o f

the uncertainty re la t ion for

behavior

o f free part i

cles and electrons in Bohr orbi ts

This chapter is the real heart of the sect ion on the

quantum theory.

The probabi l i ty

interpretat ion should

pose

no

d i f f i cu l t i e s , but the

uncerta inty

re la t ions

are

more of a problem, not because

they are

mathematically

d i f f icu l t ,

but because

students

may have a hard time

14

understanding what

they

are

a l l about. I t may

be

neces

sary

to carefully explain what you mean by error

and

deviat ion.

The more examples

you

can give in class,

the bet ter .

I f

you

have an unusually bright group of students, the

wave interpretat ion of

the uncerta inty

pr incip le can be

explored.

Show how a

f in i te

wave

packet can be construc

ted

from

a

spread

o f

close

wavelengths. The eas ies t way

to do t h i s

i s

to s ta r t

with

two

close

wavelengths.

The

resu l t ing

beat

pat tern

i s

a str ing

of

wave

packets.

The wave halfway between

them

in wavelength

suppresses

the odd

wave

packets,

and further

in-between wave

lengths

suppress others , unt i l but one

i s

l e f t . Then

you

can

re la te

the

spread

in

wavelength

momentum) to

the

s ize of the

packet

(position).

CH PTER

18

( l o r

more lectures)

Topics:

Quantum-mechanical interpretation o f a two-s l i t

interference experiment with

electrons;

the

Copenhagen

interpretation; disagreements

with

th is interpretation

The

two-s l i t interference experiment is

used

as

a

gedanken

experiment to

show

the dis t inc t ion

made

in

quan

tum mechanics between what i s

knowable

in pr incip le and

what

i s actually known

from

measurement. I f

you

have

some

philosophical ly sophisticated students

in

your c lass ,

t h i s can lead to some l ively discussions. But

the

weaker

students

wil l simply

learn nothing from th is chapter.

CH PTER

19 (4 lectures)

Topics: Quantum f ie ld

theory;

accelerators; the

quark

model;

cosmological

implicat ions

Ins t ructors who are not themselves

par t ic le

o r

nuclear

physicists ,

or who

do not a t least

follow

par t ic le

physics on

a

Scient i f i c American

level , may

have

some

t rouble

teaching

th is

chapter and may be well-advised

to

omit

i t .

The

exciting par t is

the poss ibi l i ty

of ex

plaining subsequent

developments in

the

f i e ld ,

giving

students a sense of the swiftness of scient i f ic progress

once a breakthrough

is

made. The

hardest

par t

of

the

chapter

is the quantum

f i e ld

theory; the

fact that

the

Heisenberg re la t ions

allow

the

f ie ld to

borrow

energy

to create

f ie ld quanta.

Once over

th is

hump, the

r es t

of

the materia l is stra ightforward.

15


12/22

E X A MIN A T

I ON

S

AND

T E R M PAP E R S

For the type of student who takes t h i s course , the

t radi t iona l physics examination consist ing

exclusively

of

mathematical

problems

is simply not suitable. While

such

students

can

often

work

quite challenging problems, they

can

rarely do

so within the time

l imits imposedby

an

exam. Most problems suff ic ient ly simple to put on

an

exam

for th is

course

t e s t

very

l i t t l e of s igni f icance .

When the

course

a t

Wisconsin

i s not too

large,

we use

exams

consist ing of

a

mixture

of three

kinds

of questions.

First , the re a re problems, usually closely

r e l a t ed to

ones given as homework and

broken

down i n to s t eps to help

lead

the s tudent

to the correct route to

solution.

Then

the re a re short-answer,

multiple-choice,

etc . ,

questions

designed to

t e s t qu l i t t ive understanding

of the predic

t ions of

physical

laws

or

the logical

in ter re la t ionships

of

those laws.

Finally,

the re a re shor t essay questions,

similar to those

given in

the Appendix

of

the text. Of

course , the

grading

of such questions

tends

to be ra ther

subjective.

In a school

with

an honor

system,

take-home exams

are

a

useful

device.

At

Wisconsin we have evolved a "semi

take-home" exam. In

th is

type of exam,

the student is

given a set of

problems

to

solve

or questions

to answer.

e then

i s given a

multiple-choice

or

short-answer

exam

in class

to

t e s t

his

knowledge

of the

areas he has

studied.

Regardless of the type of exam used, t is the author 's

personal

incl inat ion to make a l l examinations open-book,

i f

only to persuade t he s tuden t that learning physics i s

not just a matter

of

memory work.

When

the course i s not too large a t

Wisconsin,

we

assign

term papers.

At

our

inst i tu t ion, most

humanities

and social science majors do a great deal

of

writ ing for

courses in thei r own discip l ine and feel confident of

thei r abiLity

to

tackle suchprojects.

The

termpaper

also serves to

st imulate

the

student

to

think

more deeply

16

about some

topic

in

the

course.

The

technique

used was

to

leave the topic open but in-

form

the

student that

the

paper

was supposed to show

that

he

could

incorporate

something

from the

course into

his

own

personal

frame

of

reference.

This is

too vague

a

charge for most students,

so t was i l l u s t r a t ed

by giving

out abs tracts of some of the more

successful

term papers

from previous

years as examples. A group of such

ab

st racts appears

after

the sample exam questions.

S MPLE EX M

QU STIONS

The questions below have al l

been used

with success

a t

Wisconsin.

Five

to

seven such

questions, suitably

bal -

anced

for dif f icul ty ,

cons t i tu te an hour-long exam. We

generally st r ive for

an exam which, given

generous par t ia l

credi t ,

gives average scores of 70 to 75 high

enough

to

avoid

discouragingmost students,

while

low enough

to make

the bet ter students stand out.

Some of

the quest ions and

exercises from

the text

have

been used

as examination questions

also.

lassicalMechanics

1) Ga1i1eo found a bal l

ro l led

down

an

incl ined plane

a dis tance propor tional to __ ___________________

whereas had

Aris to t le been correct,

the d is tance

would have

been

proport ional

(2 ) Newton's

law

of gravi ta t ion

can be reduced

to

the

following

four

statements:

(a) A fa l l ing body experiences a force proport ional

to i t s mass.

(b) And also proport ional to the mass of the body

withwhich t

i s in teract ing .

(c)

The

force

acts along

the

l ine

joining

the

cen

ters

of

the objects .

(d) And i s

inverselyproport ional

to

the

square of

the

distance.

Ga1i1eo's lawof fa l l ing

body

motion

supports

statement

17


13/22

Kepler 's laws

of

planetary

motion support

s ta te

ments and

The

agreement of

the moon's

observed

accelerat ion

with that

predicted from

the accelerat ion of fa l l

ing

bodies supports

and

(3 ) Consider

the

formula

1 2

mv

+

mgh E

This formula

represents:

(a)

The law

of

momentum conservation.

(b)

The law of energy conservation

for

an object

moving

subject to gravity.

(c)

The law of energy conservation for an object

moving

subject

to any

form

of

potent ia l

energy.

(d)

A combined statement of Newton's

f i r s t

and

second

laws.

The

term

1 2 i s cal led , and mgh i s

2

mv

cal led

The

formula can

be used

to calculate

the maximum

height to which an object can r i se

by

set t ing

the

variable equal

to

( 4)

A fal l ing object

has reached

terminal velocity

when two forces are equal. What are these forces?

(5) F i l l

in

the

blanks in the

statements below with

the

l e t t e r s corresponding to the appropriate points

on

Graph

1.

I

l

c

; JI ~ ~ /F

J

l 1

It

r

"

; - ;

rn

18

(a)

The velocity

i s pos i t ive

between

and

, and also between and

(b)

The accelerat ion is

positive

a t

and

(c)

The accelerat ion i s negative at

and

(d)

The motion (instantaneously)

comes to a

hal t a t

and

(e)

The highest velocity i s found a t

(6 )

The

Fairmont

Hotel

in

San Francisco has

an

outside

elevator

with one t ransparent wall . Suppose

that

while

the

elevator is r ising a t constant speed, a

passenger drops a cigaret te l ighter , which drops

st ra ight to the f loor

of

the elevator.

Describe

the motion

of

the l ighter :

(a)

s

seen by

the

passengers on the

elevator.

(b) As

seen

by a

nosy resident of an adjoining

building.

( 7)

The following two statements

could

not

be

directly

tes ted

a t the

time they

were

or ig inal ly

made. Cite

indire t evidence or plausible arguments for thei r

validi ty:

(a) Galileo's assertion that al l bodies fa l l

a t

the

same

rate in

a vacuum.

(b) Newton's assertion that

the

force of gravity on

a fal l ing rock i s

proportional

to

the mass

of

the ear th .

(8 ) A bal l dropped from a

height

qf 9 meters rebounds

to a height of 4 meters.

(a) What

fraction of

i t s

energy

is

l o s t

in the

re

bound?

(b)

I t s speed immediately

af ter

leaving

the

f loor

is what fraction of i t s speed just before

str iking the floor?

(9 ) A pendulum consist ing

of

a str ing and a sticky clay

bal l is

raised to

a height 4

meters

above i t s

normal

horizontal

position

and

allowed

to

swing.

At the

bottom of i t s swing t st r ikes and

s t icks

to an

ident ical

clay bal l , carrying t up on

the

other

side.

(a) Which conservation laws apply during (i) the

downswing, ( i i) the coll ision, and

( i i i )

the

19


14/22

- - - -

upswing?

(b)

How

fa r does

the pendulum r i se on

the

upswing?

(10) How long does

it

take a freely

fa l l ing

body to fa l l

125 meters?

How

fas t i s it then going? (Use g

10 m/sec

2

.)

(11) A

car

drives off a

ver t ica l c l i f f . Two seconds

l a te r it hits the

ground, 30

meters from the

base

of

the cl i f f .

(Use g 10 m/sec

2

.)

(a) How

high was

the c l i f f?

(b) What

speed

was the car

going?

(c) Draw a vector

diagram

to find the velocity

vector for the car a t

the ins tant

it

hi t

the

ground.

(12) A

body

of mass 5 kg, speed 6 m/sec

st r ikes

a

s ta

t ionary body of

mass

1 kg.

This

coll ision slows it

down

to

4 m/sec.

(a) How

fas t i s

the

1 kg

body

moving

a f te r

co l l i

sion?

(b) I s

the

coll ision elast ic? Explain why

or

why

not.

(c) Suppose the bodies

had

instead

stuck

together .

What speed

would

the

combined mass

be moving?

Waves

(1) Cross

out from

the

l i s t

below

those

wavelengths

that

cannot exist

as standing

waves on

a

st r ing

1

meter long:

1/4 m

2/3 m 11.: m

1/3

m

3/4

m 2 m

1/2 m

1 m 3 m

(2)

In

the

two-sl i t interference experiment,

the

point

direct ly opposite

the

speakers and

halfway

between

them:

(a)

i s always a maximum.

(b) i s always a minimum.

(c) can be

ei ther

a maximum or minimum, depending

on wavelength.

(d) cannot

be

ei ther a maximum

or

minimum.

20

,

i

,

.

1

1

.,

.

,

.'

.

,

t:,

t

, ,.

The speed of sound i s about 330 m/sec. The Abelow

(3)

middle C has a frequency of 220 Hz. What is

the

wavelength of A below middle C?

Two hi - f i speakers

sounding

the same sustained note

(4)

are 3 m

apart. An

observer walking along a l ine

4 m

from the

speakers

hears

a maximum when

he

i s

halfway between

the

two

speakers, but

di rec t ly in

front of

ei ther

he hears a minimum. What i s

the

wavelength of the note?

elativi ty

(See also the "semi-take-home" exam in the next

section.)

(

1)

A

spaceship passes an ob

@

server

S

a t

a speed of

6/10 the velocity

of

\

@

/

l ight . There

are

three

clocks on

board

the

spaceship - - A, B, and C,

as

shown. They

have been

synchronized by

the

crew

of

the

spaceship.

As

clock

C

passes the observer, he

se t s his

clock by

it. Answer

the

next three questions from the

point

of

view of observer S,

at

the instant depicted in

the picture.

(a) How do the readings of clocks

A and B

compare?

A i s

fas te r

B is faster

same

How do the

readings of clocks A and C

compare?

(b)

A

i s

fas te r

C

i s

fas te r

same

(c) How

do

the readings of clock A and S's

clock

compare?

A i s faster

S i s

faster

same

On the l i s t below, check those

quant i t ies

on which

(2)

S and

the

spaceship crew agree (there i s more

than

one correct

answer).

21


15/22

-----

_____The length of the spaceship

The width

of

the

spaceship

The

time

elapsedwhile the spaceship

is

passing S

_ _ _ _ The

relat ive

speed

(0.6 c)

The rate

a t which clock

S

is

running

The ra te a t which

clocks

A, B,

and

Care

running

The veloci ty of l ight

The mass of

the spaceship

(3) One or more of

the

following

statements is an

in -

correct applicat ion

of

the

mass-energy

equivalence.

Mark

each one

"T" or

"F" and

explain

below the

flaw

(

in

the

one or ones

marked

"F".

(a)

The combination products of a f i re weigh less

than the fuel

and

oxygen

tha t

went

into

i t .

(b) I f a

f i re

takes

place

in a

sea led insula ted box

so tha t neither

heat normater ial can escape,

the weightwill not

change.

(c)

By

vir tue of i t s motion around

the

sun,

the

earth appears (to an

observernot sharing th is

motion)

heavier than

it would i f standing s t i l l .

(d) All

objects on

the ear th share in

the

mass in -

crease mentioned in

(c)

above, and a very

l ight

absorptions,

or

a mixture?

On

the bas is o f

the

Ritz pr incip le ,

the follow

(b)

ing

relat ion holds

for the

frequency of l ight

in

t rans i t ions A, B, and F:

=

VB + VF

VA

write

down

at least four

more correct re la t ion-

ships

of t h i s type.

Einstein 's

formula

for the photoe lec t r ic ef fect i s

(

2

= hv

-

W

(a) The symbol stands for :

(i) The average

energy

of e lec t rons emitted.

(i i ) The maximum

energy of electrons

emitted.

( i i i )

The

energy

of the

l ight

quantum.

(b) The symbol W stands

for the

work

required

to:

(i) Produce one quantum of l ight .

( i i) Create

an

electron.

( i i i )

Overcome

the

forces

holding the e lec tron.

Rank

the

following developments

in the

his tory of

( 3

the quantum theory in the

order

they happened

(1

for

the ear l iest , etc . ) .

sensitive

scale on the

earth

could detect th is .

J ~ ~

Bohr 's theory of the hydrogen atom.

(e) Light

can be used to t ransport mass from

one

The Geiger-Marsden experiments.

place

to

another.

:

Planck's theory of

incandescent

l ight .

Robert March - Instructor's Manual Physics For Poets.pdf

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