Phys104 - How Things Work
University
of Maryland, College Park
Fall 2010, 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 chapter 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.
HW12
-
NOT DUE: this is for your learning experience. Some of the material
will be on the exam,
so
I strongly suggest that you try to do the problems. Solutions are
posted.
E16.2 (separating Cu-63
and Cu-65)
E16.4 (atomic structure of Fe-58 vs. Co-59)
E16.6 (alpha decay)
E16.8 (beta
decay) Add part (b): Answer the second part of the written problem for
the specific example of carbon-14.
(Note
"Exercise 9" should be "Exercise 7" in the text of this problem.)
E16.10 (size matters) (The
question is, what sets the lower limit on
the size?)
E16.28 (magnetic field strength and MRI)
P16.1
(gallium-67 decay after two days) (The numerical answer is in the book.
(a) Show how this number is obtained.
(b) How much
gallium-67 remains
after two weeks?)
C16.5 (applications of neutron activation)
S12.2 An MRI
machine could operate with a weaker magnetic
field
if it could
employ more sensitive
radio frequency electromagnetic wave detectors.
How would the use of more sensitive detectors compensate
for the use of
a weaker magnetic field? (Use of a weaker field could lower
costs, save space and weight,
and operate more safely and with patients
that have ferromagnetic metal inside them.)
S12.3 Plutonium-239 is produced in nuclear reactors, and can be used to
make a bomb. Why is it much easier
to separate out Pu-239 from the rest of the elements in reaction
products than it is to separate out uranium-235 from uranium-238?
HW11
-
due
at the beginning of class, Friday 12/10/10
E14.13 (colored oil films) [See p. 451-2]
E15.24 (beam waist of blue vs. IR light) [See p. 493-4]
E15.28 (color of DVD surface) [See p. 489]
C15.7 (optical fibers) [See p. 495-6]
S11.1 If you are
20 years old how is your age written in binary numbers?
S11.2 Blu-ray discs use laser light with
wavelength 405 nm in vacuum. (a) What is the wavelength of this
light in plastic with an index of refraction n = 1.55? (b) What index
of refraction would be required if the
wavelength in the plastic were to be 215 nm? (Reminder: you must show your calculations
to receive credit.)
[See p. 492, and eqn. (13.2.1).]
S11.3 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:Double-porro-prism.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]
S11.4 (a) How do X-rays and gamma rays for radiation therapy differ
from X-rays 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, Friday 12/03/10
E14.10 (refraction
of diamond)
E14.20 (yellow
paint)
E14.24 (light emission from excited state of sodium)
E14.28
(incandescent vs. neon lamp colors)
C14.1 (color of
sky)
[See section 14.1]
C14.2
(electronic flash) [See section 14.2]
S10.1 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.
HW9
- due at
the beginning
of class, Monday 11/22/10
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 11/08). 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)
C13.4 (cell phones) (Note:
this case has eight parts, so start early!)
S9.1 An induction stovetop puts heat directly into a cooking pan,
without even making the stovetop hot (until heat transfers by conduction
from the pan to the stovetop). Steel or some other ferromagnetic
material must be used for the bottom of the cooking pan.
Based on what you know about electromagnetic induction and
ferromagnetic materials, explain two different mechanisms
that contribute to the heating effect. (Hint:
I discussed this in class, and it may even be in the notes...)
HW8
- due at
the beginning
of class, Monday
11/08/10
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.
C11.5 (audio
speaker)
C11.2 (electromagnetic trash
sorter) (Hint
for (b): See Check your understanding #4 of section 11.2, p.362.)
C11.12 (electric shavers)
HW7 - due at
the beginning
of class, Friday 10/29/10.
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)
P10.23 (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")
S10.5 If lightbulb consumes 60W of power when operating at 120V,
(a) how much current flows through the filament, and (b) what is the
resistance of the filament?
S10.6 A rear
window defroster strip generates heat due to its electrical resistance
when a current flows
through it. If you double the voltage across the strip, what then would
be the rate at which it generates heat,
compared to the original rate P?
S10.7 A clothes dryer can be set to run until the clothes reach a
certain level of dryness.
To measure the dampness of the clothes the dryer employs a pair of
electrical temperature
sensors, one located before where the heated air enters the drying
drum, and the other located
downstream, where air heads out to the vent.
(a) How can temperature be sensed electrically?
(b) How can the two temperature measurements be used to determine the
dampness of the clothes?
(Hint: For (a) see p. 333. For
(b) look back at Ch. 7, pp. 218-219.)
S10.8 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
kilo-watt-hour)
HW6 - due at the
beginning of class, Friday 10/22/10.
E10.26 (electric field at tree top) (Hint: Read pp. 321-22.)
P10.10 (electric field from force) Consider the stated problem part
(a), and give the answer in units of both N/C and V/m.
Add
(b) If the electric field is constant along a vertical line 1 cm long,
what is the voltage drop from one end of the line to the other?
C10.2 (Van de Graaff generator)
C10.3 (spark lighters)
S10.1 A certain compact fluorescent bulb operates on a potential
difference of 120 volts between the ends of a (twisted)
40 cm long tube. If the voltage drops unifromly along the length along
the tube from one end to the other, what is the magnitude
of the electric field at any point inside the tube? Give your answer
both in N/C and in V/m.
(Hint: See "Check your figures #2" on p. 321.)
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.
Explain your answer.
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
HW5 - due at
the beginning
of class, Friday 10/15/10.
E9.2 (period of swinging clothing rack)
E9.9 (pitch of guitar string) Note that this is an odd-numbered
problem, so the "answer" is in the back of the book.
For this assignment
explain WHY this is the answer, for the case of
mass, tension, and length. Refer to the role
of the the restoring
force and the inertia in determining the frequency of a vibration.
E9.14 (organ pipe filled with helium)
E9.16 (trumpet vs. tuba)
E9.30 (gong overtones)
E9.32 (string bass body)
S9.1 Figures 9.2.3,4 illustrate the string motion in the first
three vibrational modes (the fundamental, second and third harmonic)
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. (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 then are the frequencies of
the first three
harmonics of the pipes in (a) and (b). Explain your answer.
E10.4 (bowling balls
and charges)
P10.2 (electrostatic force on socks)
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.
HW4
-
due
at
the
beginning
of
class,
Friday
10/1/10.
E7.20 (wine bottle in ice water)
E7.24 (steamed vegetables)
E8.6 (car knocking on a hot day)
E8.8 (airplane air conditioning)
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.
The source of the extra heat must be the work done by the freezer. 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 heat pump. 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?
C8.2 (refrigerator)
Note on P8.6,8,10: 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 for a
discussion of these things.
HW3 - due at
the beginning
of class, Friday 9/24/10.
E5.4 (grocery freezer displays)
E5.16 (lowest thermometer readings)
P5.2 (force of air on book cover)
P5.4 (air compressor pressure)
P5.5 (fridge pressure change) To simplify this problem, instead of
finding the change of the
pressure, just find the ratio
of the cold pressure
to
the room temperature pressure. (Note: Don't forget to use the
absolute temperature scale!)
P5.15 (submarine pressure) Express your answer both in pascals and in
"atmospheres" (1 atm = 100,000 Pa).
E7.12 (how space shuttle dumps heat)
C7.3 (electric oven)
http://www.keidel.com/design/select/ovens-convection.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 (tight-fitting metal parts) (See page 229 for a discussion of
thermal expansion, and the demo,
I1-11
THERMAL EXPANSION - BALL AND HOLE)
HW2 - due at
the beginning
of class, Friday 9/17/10.
C1.5 (takeoff and landing on aircraft carrier)
C1.12 (cable cars in San Francisco)
E2.16 (bottle opener)
E2.22 (horse and cart)
E2.26 (force on bicycle) This is could be phrased more precisely. Let's
make it:
"What is exerting the forward force that accelerates the
system consisting of you and the bicycle?"
E2.28 (friction on sled) Make this two parts: (a) if you are pulling
horizontally, (b) if you are pulling diagonally upward.
P2.6 (nutcracker)
P5.7 (water displaced by boat) (Note:
Give both the mass and the volume of the displaced water.)
C5.2 (bass air bladder) Assume the fresh and saltwater bass
have the
same mass.
S5.1 (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
intially on land slides into the ocean and melts, then of course the
sea level rises.)
HW1 - due at the beginning
of
class, Friday 9/10/10.
E1.8 (carousel velocity)
(Book: Why is your velocity
continuously changing as you ride on a carousel?)
Let's make this problem four parts: (a) How is
your velocity vector is changing?
(b) What is the direction of your
acceleration vector at any moment?
(c) What agent is exerting the force
on your body making your velocity change?
(d) What is the direction of
that force vector?
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?
E1.34 (work when
sawing)
(Book: You're cutting wood with a
handsaw. You have to push the saw away from you as it moves away from
you
and pull the saw toward you as it moves toward you. When are you doing
work on the saw?)
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 agent exerts the horizontal force that decreases your horizontal
velocity?
(b) What agent exerts the vertical force that initially
increases your upward, vertical velocity as you start rollling 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/s2.)
P1.18 (hydroelectric
power)
(Book: As water descends from the top
of a tall hydroelectric dam, its gravitational potential energyis
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 1000 J/s, how
long would it take a human 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?