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8/11/2019 Robert March - Instructor's Manual Physics For Poets.pdf
1/22
INSTRUCTOR'S MANUAL
T
ACCOMPANY
SECOND EDITION
oi Pli J. Ma ltk
8/11/2019 Robert March - Instructor's Manual Physics For Poets.pdf
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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
http:///reader/full/A1a!1.Ckhttp:///reader/full/A1a!1.Ck8/11/2019 Robert March - Instructor's Manual Physics For Poets.pdf
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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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8/11/2019 Robert March - Instructor's Manual Physics For Poets.pdf
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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.
3
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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 .
9
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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
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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,
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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.
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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
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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
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- - - -
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).
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-----
_____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 .