Phys104  How Things Work
University of Maryland, College Park
Spring 2013, Professor: Ted Jacobson
Homework
examples of notation:
E1.4 means "Exercise 4 of Chapter 1"
P1.8 means "Problem 8 of Chapter 1"
C1.11 means "Case 11 of Chapter 1"  for these see Cases,
at 4th edition Textbook Companion Website
S5.1 means "Supplementary problem 1 for homework 5, written
out here".
GRADING POLICY:
Your solution must explain your reasoning and show your method
of computation in order to earn credit.
Explanations can be very brief as long as they are clear.
Numerical answers without explanation will receive no credit.
HW11  due at the beginning of class,
Thursday 5/09/13
On material already covered by Thursday,
5/02
E14.36 (Maser1)
E14.37 (Maser2)
E14.41 (LED1)
E14.42 (LED2)
C15.7 (optical fibers) [See
p. 4956]
On material to be covered Tuesday, 5/07.
You may ask about them in class.
E16.21 (lead and Xrays)
E16.24 (MRI electromagnetic radiation)
E16.25 (MRI and bone)
E16.28
(magnetic field strength and MRI)
S11.1 (a) How do Xrays and gamma rays for radiation therapy
differ
from Xrays for imaging?
(b) How do radiation therapy photons kill cancerous cells?
(c) Name two ways that radiation therapy photons can be
produced.
HW10  due at the beginning of class, Thursday 05/02/13
E14.10 (refraction of diamond)
E14.13 (colored oil
films) [See p. 4512]
E14.20 (yellow paint)
E14.24 (light emission from excited state of sodium)
E14.28
(incandescent vs. neon lamp colors)
E15.28 (color of DVD surface) [See p. 489; also,
this is basically the same as the diffraction grating I
explained in class.]
C14.1
(color of sky) [See section 14.1]
C14.2
(electronic flash) [See section 14.2]
C14.4a,c,e only (interior house paint) [See section 14.2]
S10.1 In order to fold a long optical path in binoculars into a
small space the light must be reflected several times. This is done,
for example, by a "double Porro prism" shown here:
http://en.wikipedia.org/wiki/Image:Doubleporroprism.png
(taken from http://en.wikipedia.org/wiki/Binoculars).
There are no mirrored (metallic reflecting) surfaces  only glass
prisms are used. How are the reflections accomplished without
mirrors? [See p. 495]
HW9  due at the beginning of class, Thursday 04/25/13
E13.14 (spinning
magnet) Make this two parts, (a) in the horizontal plane in
which the magnet spins, and (b) above the plane. (Hint: Think of how the
magnetic field wiggles to infer the direction of the magnetic
field in the wave, by analogy with the electric case (see the
applet in the notes for 04/11/13). Use the relation between
electric and magnetic fields in an electromagnetic plane wave,
p. 428, to find the direction of the electric field.)
E13.16 (AM
vs. FM fadeout)
E13.22 (oven vs. microwave cooking of a potato) Take the question to be this:
how is heat deposited in the potato using the two cooking
methods?
E13.28
(synchrotron radiation)
C13.6 (cordless microphone)
S9.1 Polarizing sunglasses,
or a polarizing filter over a camera lens, can enhance the
contrast between the sky and clouds, by darkening the sky more
than the clouds. This and other uses of polarizing filters in
photography is explained here:
http://en.wikipedia.org/wiki/Polarizing_filter_(Photography)
It states but does not explain in this article why the light
from the blue sky is somewhat polarized. Try to explain why.
Consider the following situation:
sunlight molecule




viewer
The dashed lines represent sunlight that scatters from a
molecule into the perpendicular direction towards the
viewer. Explain why the light that reaches the viewer is
100% linearly polarized,
and say what the direction of polarization is. (Hint:
Remember this key fact about polarization: the electric
field vector is always perpendicular to the direction the
light is traveling. Consider two different cases for the
incoming sunlight: (i) polarized vertically on this page,
and (ii) polarized perpendicular to this page. Think of the
molecule as an antenna whose charge is shaken by this
incoming electric field, and then emits its own waves like a
dipole antenna.)
S9.2 View (a) the LCD Monitor Teardown video, and (b)
the "Creating Electronic Images" and Components of an LCD"
sections of the Optics101 link (use the Navigation button),
linked below. Then write a brief description (a few
sentences) of how an LCD works. (I will also discuss this
briefly in class on Tuesday.)
LCD
Monitor Teardown
http://www.youtube.com/watch?v=jiejNAUwcQ8
Optics101
http://solutions.3m.com/wps/portal/3M/en_US/NA_Optical/Systems/BehindTheScenes/Optics101/
HW8  due at the beginning of class, Thursday 4/18/13
E11.29 (compass
"motor") (The answer is in the back of the book...)
C11.12 a,b,c only (electric shavers)
S8.1 An induction stovetop
puts heat directly into a cooking pan, without even making the
stovetop hot (a small amount of heat transfers by conduction
from the pan to the stovetop). Read the Wikipedia article http://en.wikipedia.org/wiki/Induction_cooking,
and then explain how the induction stovetop works.
S8.2 Read the section in the textbook on induction motors, and
watch this video: http://www.youtube.com/watch?v=HWrNzUCjbkk.
Then write a brief explanation of the principle of operation of
an induction motor. (A few sentences will suffice.)
S8.3 Read (all four panels of) this explanation of the Hall
effect: http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/hall.html.
You can ignore the equations.
[I had a copy of this web page,
in case this site is unavailable...]
HW7  due at the beginning of class,
Thursday 4/11/13.
Note: Some of these problems involve
material that will be covered in class Tuesday. I suggest you
read ahead in the book,
think about the problems, and come to class Tuesday with any
questions you have.
E11.2 (distance
dependence of magnetic force between button magnets)
Note: What this question is asking is why does the
force between dipoles decrease FASTER than the inverse of the
square of the distance between them?
E11.4 (why don't magnet and iron repel?) Expand
question: Explain why they attract no matter which pole of the
magnet is next to the iron pipe.
E11.6 (hammering or heating a magnet) Expand question: In the case of heating,
address two cases:
(a) if the magnet temperature is raised above the Curie point,
and (b) if the temperature remains below the Curie point.
E11.8 (net force on a compass in a uniform field)
E11.19
(magnetic strip reader)
E11.24 (transformer in amplifier)
E11.26 (current in transformer coil) Note: The
book gives a formula for this, but I don't quite like the
accompanying explanation.
Perhaps
a
better
way
to
say
it
is that the work done by the power supply on the charges in the
primary coil is transferred
via
the
magnetic
field
to
the
secondary
coil, where the same amount of work is done on the charges
there. As with DC
circuits, the instantaneous power is VI, where V
is the induced emf (see
p. 361), which plays the same role as the voltage.
Setting
the
power
in
the
primary
equal
to the power in the secondary gives you the answer to this
question.
C11.2 (electromagnetic trash sorter) (Hint for (b): See
Check your understanding #4 of section 11.2, p.362.)
C11.5 (audio speaker)
S7.1 A substation transformer steps down the 500,000 V AC
transmission line voltage to 5000 V for delivery to neighborhoods.
If the primary coil has 2000 turns of wire, how many turns must the
secondary coil have?
A) 20
B) 100
C) 250
D) 20,000
E) 200,000
HW6  due at the beginning of class,
Thursday 4/4/13.
E10.14
(car battery voltage) To be specific, compare the energy
of one Coulomb of charge.
E10.20 (electric field at battery terminal)
E10.32 (half a plug)
E10.40
(battery testing)
P10.2 (electrostatic force on socks)
P10.23
(voltage drop in extension cord) (Answer at back of
book  you must supply the reasoning.)
P10.24 (wasted power in extension cord) ("is wasted" means
"goes into heating the wire instead of the oven")
C10.2 (Van
de Graaff generator)
C10.3 (spark lighters)
S10.1 A
balloon rubbed on your hair will acquire negative
charge, and will then stick to a neutral surface like a
wall.
Explain the origin of the force of attraction between
the charged balloon and the neutral wall.
S10.2 You stick two pieces of adhesive tape on a glass window
and then pull them off suddenly. If you now hold the tape pieces
near each other, will they attract, repel, or do nothing to each
other. Why? (Try it!
Use 3 inch pieces of tape.)
S10. 3 Suppose you have two identical metal spheres on
insulating stands and a balloon. You rub the balloon on your
hair and then touch it to one sphere, charging the sphere. Then
you place the two spheres in contact. As a result of these
operations, which of the following will happen, and why:
A) the two spheres will wind up neutral
B) the first sphere will remain charged and the second sphere
neutral
C) the second sphere will wind up charged and the first sphere
neutral
D) the second sphere will pick up a small fraction of the charge
from the first
E) the two spheres will wind up equally charged
S10.4 Suppose you have the same two spheres of S10.3, both
initially neutral. You place the spheres in contact, rub the
balloon on your hair, and then bring the balloon near to but not
touching one of the spheres. You then separate the spheres, and
then remove the balloon. As a result of these operations which
of the following will happen, and why:
A) the two spheres will each wind up neutral
B) the two spheres will wind up oppositely charged
C) the two spheres will wind up with equal charges
D) the sphere closer to the balloon will become charged and the
farther sphere will not
E) the sphere farther from the balloon will become charged and
the closer sphere will not
S10.5 One month PEPCO billed me for $112.46 for 920 kWh of
electrical use. (a) How many joules of electrical energy did I
use? (b) How much am I paying per million joules?
(Food for thought: A
million joules is about equal to the work (mgh) it takes to
vertically lift 100 kg (220 pounds) a distance of 1 kilometer
(0.6 miles). Does this price for a million joules seem high or
low to you?) (Note: 1 kWh = 1
kilowatthour)
HW5  due at the beginning of class,
Thursday 3/7/13.
E8.8 (airplane air conditioning)
E8.20 (plant growth and the second law of thermodynamics)
P8.6 (freezer work) Modify the problem:
a. By how much does the entropy of the food decrease?
b. By how much does the entropy of the room increase?
c. How much heat is added to the room?
d. The answer to c is greater than 100 J, since 300K is
greater than 260K.
Energy is conserved, so the source of the extra heat must be
the work done by the compressor. How much work is that?
P8.8 (heat pump work) Modify the problem:
a. How much does the entropy of the room increase?
b. How much does the entropy of the outdoor air decrease?
c. How much heat is extracted from the outdoor air?
d. The answer to c is less than 1000 J, since 260K is less
than 300 K. The source of the extra heat must be the work done
by the compressor. How much work is that?
P8.10 (airplane engine work) Modify the problem:
a. What fraction of the heat leaving the burned gases is
discarded as heat to the air?
b. What fraction of
the heat leaving the burned gases is converted to work?
(Hint: Let Q represent the heat that flows from the
burned gases, and use algebra...)
C8.2 (refrigerator)
S5.1 If a car engine operates at 600 K in ambient air at 300
K, what is the maximal work it could possibly obtain from 1000
J of heat at 600 K?
Note on
P8.6,8,10,S5.1: Solve these problems using the
fact that the entropy change is given by Q/T,
and the fact that in the operation an ideal heat pump or
engine, the total entropy is unchanged.
Refer to the lecture notes of 2013 and 2010 for a
discussion of these things. (The textbook has equations
(8.1.2) and (8.2.1) that refer to work consumed in pumping
heat and work provided by a heat engine,
depending on the temperatures involved. The equations are
derived using the entropy change Q/T. I
think it is more instructive to solve these problems making
direct use of the entropy changes.
HW4  due at the beginning of class,
Thursday 2/28/13.
E9.2 (period of swinging clothing rack)
E9.9 (pitch of guitar string) Modification:
Explain, in terms of inertia and/or restoring force as
appropriate, why the pitch is higher for the cases of
(a) smaller mass, higher tension, and (c) shorter length.
E9.14 (organ pipe filled with helium)
E9.30 (gong overtones)
E9.32 (string bass body)
C9.9 (trumpet) Omit part (d).
(Part (d) is interesting, but
difficult to answer well, I think.)
S9.1 What is the role of the escapement mechanism in a pendulum
clock or spring wound wristwatch?
S9.2 A bat can hear sounds at 100,000 Hz. (a) What is the period
of one sound vibration at this frequency? (b) Approximately what
is the wavelength of this sound?
S9.3 Figures 9.2.3,4 illustrate the string motion
in the first three vibrational modes (the fundamental and the
next two) of a vibrating string. Draw similar diagrams for the
air pressure deviations in the first three modes of (a) a pipe
open at both ends, and (b) a pipe closed at one end and open at
the other.
Bonus extra credit part for those who want a
challenge: (c) Suppose the pipes in (a) and (b) have the same
length, and let f_0 denote the frequency of the fundamental mode
of the pipe that is open at both ends. What are the frequencies
of the first three modes of the pipes in (a) and (b)? Explain
your answer.
S9.4 A guitar string that normally vibrates
with a fundamental frequency of 110 Hz is also capable of
vibrating at 330 Hz without changing the length or tension.
When that higher frequency vibration occurs, the string is
vibrating
A) with 3 times its normal amplitude of oscillation.
B) with 1/3 of its normal amplitude of oscillation.
C) as the fundamental mode of a string that is 3 times as
long.
D) as the fundamental mode of a string that is 1/3 as long.
S9.5 If you blow across the end of a tube open
at both ends it will sound a tone with some characteristic
pitch. If you then cover one end with your hand and again blow
across the other end the pitch will be
A) one octave higher because the closed end becomes a pressure
node
B) one octave higher because the closed end becomes a pressure
antinode
C) one octave lower because the closed end becomes a pressure
node
D) one octave lower because the closed end becomes a pressure
antinode
E) the same because the length is the same
HW3  due at the beginning of class,
Thursday 2/21/13.
E5.16 (lowest thermometer readings)
E7.7 (fireplace convection)
E7.12 (how space shuttle dumps heat)
E7.20 (wine bottle in ice water)
E7.24 (steamed vegetables)
E7.30 (disappearing ice)
P5.6 (net force on submerged log)
C7.3 (electric oven)
http://www.keidel.com/design/select/ovensconvection.htm and/or
http://en.wikipedia.org/wiki/Convection_oven
C7.8 (duck warmth) (It's important for this case that both fat
and oil are relatively poor heat conductors, compared to water
or body tissue.)
C7.9 (tightfitting metal parts) (See page 229 for a discussion
of thermal expansion, and the demo, I111
THERMAL
EXPANSION  BALL AND HOLE)
S3.1 Air is mostly composed of oxygen molecules and nitrogen
molecules. The mass of a nitrogen molecule (N_2) is 7 times the
mass of a helium atom. If the average speed of a nitrogen
molecule at room temperature is v, what is the average speed of
a helium atom at room temperature?
S3.2 Why do metals tend to conduct heat better than nonmetals?
HW2  due at the beginning of class,
Thursday 2/14/13.
E2.12 (wire cutter)
E5.4 (grocery freezer displays)
P2.6 (nutcracker)
P5.4 (air compressor pressure)
P5.5 (fridge pressure change) To simplify this problem, instead
of finding the change of
the pressure, find the ratio
of the cold
pressure to the room temperature pressure. (Note: Don't forget to use
the absolute temperature scale!)
C1.5 (takeoff and landing on aircraft carrier)
C5.2 (bass air bladder) Assume the fresh and saltwater
bass have the same mass.
S2.1 If a car's engine does work W to
accelerate it to a speed of 10mph, how much more work would be
required to reach a speed of 30mph, assuming perfect efficiency,
i.e. neglecting wasted heat, friction, and air
resistance?
S2.2 In a classroom demonstration, I broke a 2x4 piece of
wood using a hydraulic press. If the force applied to the
wood must be 5000 N to break the wood, the point of
application of the press on the wood moves through 5 mm, and
my hand applying the force on the lever moves through 50 cm,
how much force must I apply?
S2.3 The Mariana Trench is the deepest part of the earth’s
oceans, and lies around 10,000 meters below sea level. How
many times atmospheric pressure is the pressure at the
bottom of this Trench? (Hint: In class we computed
how many meters high a column of water must be if its weight
produces atmospheric pressure at the bottom.)
S2.4 Consider a block of stone with a mass of 2500 kg used
in building the Great Pyramid of Khufu in ancient Egypt. In
order to float that block on a raft on water across the
flooded Nile valley, what volume of water would have to be
displaced, neglecting the mass of the raft itself?
S2.5 (melting icebergs) Ice floats on water because when water
freezes and becomes ice, the density drops by about 10%. When a
floating iceberg melts, the sea level does not go up (or down),
but rather stays exactly the same. Explain clearly why this is
so. (By contrast, if ice initially on land slides into the ocean
and melts, then of course the sea level rises.)
HW1  due at the beginning of class,
Thursday 2/7/13.
E1.4 (toothbrush drying)
(Book: Why does tapping your toothbrush on the sink dry it off?)
E1.8 (carousel velocity)
(Book: Why is your velocity
continuously changing as you ride on a carousel?)
Let's clarify and expand the question: (a) How is your velocity
vector is changing?
(b) What is making your velocity change?
E1.10 (coffee grinder)
(Book: One type of home coffee
grinder has a small blade that rotates very rapidly and cuts the
beans into powder.
Nothing prevents the coffee beans from moving so why don't they
get out of the way when the blade begins to push on them?)
E1.14 (falling ball)
(Book: A ball falls from rest for
5 seconds. Neglecting air resistance, during which of the 5
seconds does the ball's speed increase most?)
E1.22 (force on Metro train cars)
(Book: What is the net
force on (a) the first car, (b) the middle car, and (c) the last
car of a metro train traveling at constant velocity?)
Hint : What is the
acceleration of the cars?
E1.38 (roller skating uphill)
(Book: When you're roller skating
on level pavement, you can maintain your speed for a long time.
But as soon as you start up a gradual hill, you begin to slow
down. What slows you?)
Let's make this problem two parts: (a) What external agent exerts
the horizontal force that decreases your horizontal velocity?
(b) What external agent exerts the vertical force that initially
increases your upward, vertical velocity as you start rolling up the
hill?
P1.8 (sprinter acceleration)
(Book: A sprinter can reach a
speed of 10m/s in 1 s. If the sprinter's acceleration is constant
during that time,
what is the sprinter's acceleration?)
P1.10 (mass and weight)
(Book: How much does a 60 kg
person weigh on earth?)
(Give your answer in Newtons. Use the approximate value g =
10m/s^{2}.)
P1.18
(hydroelectric vs. human power)
(Book: As water descends from the
top of a tall hydroelectric dam, its gravitational potential
energy is converted to
electric energy. How much gravitational potential energy is
released when 1000 kg of water descends 200 m to the
generators?)
Consider the book's problem to be part (a). Add two parts:
(b) If a human can do work at at rate of 400 watts over an extended
period, how long would it take them to deliver
the same total energy as the ton of water falling off the dam? (c)
How many pieces of cherry pie
(see page 30) would you have to consume to obtain the energy
required to do this much work?
P1.22 (work when
sanding)
(Book: You're sanding a table. You
must exert a force of 30 N on the sandpaper to keep it moving
steadily
across the table's surface. You slide the paper back and forth for
20 minutes, during which time you move it 1000 m.
How much work have you done?)
Consider the book's problem to be part (a). Add part: (b)
What is the average power you have supplied?
E2.22 (horse and cart)
(Book: A horse does work on a cart it's pulling along a
straight, level road at constant speed. The horse is
transferring energy to the cart,
so why doesn't the cart go faster and faster? Where is
the energy going?)
E2.28 (friction on sled)
(Book: If you are pulling a sled along a level field at
constant velocity, how does the force you are exerting on the
sled compare
to the force of sliding friction on its runners?)
Make this two parts: (a) if you are pulling horizontally, (b) if
you are pulling diagonally upward.