Physics 123 Homework Problems, Spring 2011
1-1. The small piston of a hydraulic lift has a cross-sectional area
of A1 = 3.24 cm2 , and its large piston has a cross-sectional
area of A2 = 235 cm2 (see figure). What force F1 must be
applied to the small piston for it to raise a load of
[01]
kN? (In service stations, this force is usually
generated with the use of compressed air.)
1-2. Suppose that the Earth’s atmosphere were condensed from the air that’s around us down
to solid air. (a) How thick in meters would that layer be where the atmospheric pressure
atm? Use 1 atmosphere = 1.013 × 105 Pa, density of solid
was [02]
air = 1050 kg/m3 , and the acceleration of gravity g = 9.8 m/s2 . (b) What would be the
thickness of CO2 at a partial pressure of 400 ppm (parts per million)? Density of solid
CO2 = 1560 kg/m3 .
kg/m3 . When this block is floating in
1-3. The density of a block of wood is [03]
water, what fraction of its volume is submerged?
1-4. The density of a block of wood is [04]
kg/m3 . Its mass is 689 g. We tie the
block to the bottom of a swimming pool using a single strand of string so that the block
is entirely submerged. Find the tension in the string.
2-1. A glass of water sits on a scale. The scale reads 4.78 N. A steel bolt weighs
[01]
N. The density of steel is 7.86 g/cm3 . We tie the bolt to a string and
lower the bolt into the glass of water so that the bolt is fully submerged in the water but
is not touching the bottom or side of the glass. (a) How much does the scale read now?
(b) What is the tension in the string?
2-2. A raft is made of solid wood and is 2.31 m long and 1.59 m wide. The raft is floating in a
lake. A woman who weighs [02]
lb steps onto the raft. How much further into
the water does the raft sink? You do not need the thickness of the raft or the density of
the wood to solve this problem.
g/cm3 . Its
2-3. A block of wood floats on water. The density of the wood is [03]
mass is 243 g. Find the minimum mass of lead we must attach to the block so that it will
sink, along with the lead. The density of lead is 11.3 g/cm3 . Caution: you must take into
account the buoyant force on the lead, as well as on the wood.
2-4. Consider a man whose weight is w = [04]
lb. (a) Find the minimum radius of
a helium balloon that will lift him off the ground. The density of helium gas is
0.178 kg/m3 , and the density of air is 1.29 kg/m3 . Neglect the weight of the deflated
balloon itself. Assume that the shape of the balloon is a sphere. Neglect the buoyant
force of the air on the man. (b) If we replace the helium with hydrogen gas, how much
more weight can the balloon lift? Give the answer in units of pounds. The density of
hydrogen gas is 0.089 kg/m3 . (Find how much weight in excess of w the same balloon
inflated to the same volume can lift.) Caution: the answer is not w anymore. The
buoyant force is the same. Only the weight of the gas has changed.
3-1. I find that I can blow 1000 cm3 of air through a drinking straw in [01]
s. The
diameter of the straw is 5 mm. Find the velocity of the air through the straw.
3-2. A water pipe goes down a hill. The level of the pipe at the bottom of the hill is
[02]
m below the level of the pipe at the top of the hill. The diameter of a
pipe is 2.7 cm at both the top and bottom of the hill. Water is flowing through the pipe.
m/s, and its gauge
At the top of the hill, the velocity of the water is [03]
pressure is 58.3 psi (lb/in2 ). (a) Find the flow rate (volume per unit time) of the water
through the pipe. (b) Find the velocity of the water at the bottom of the hill. (c) Find
the gauge pressure (in psi) of the water at the bottom of the hill.
3-3. Suppose the wind speed in a hurricane is [04]
mph (mi/h). (a) Find the
difference in air pressure outside a home and inside a home (where the wind speed is
zero). The density of air is 1.29 kg/m3 . (b) If a window is 61 cm wide and 108 cm high,
find the net force on the window due to the pressure difference inside and outside the
home.
3-4. Examine the figure shown. A pilot tube is a device
used to determine the velocity of airflow (density
1.25 kg/m3 ) by measuring the difference in pressure
between two holes on the tube, one exposed to air
which comes to rest with respect to the tube (point A)
and the other exposed to air rushing past (the hole on
the top). The two holes are connected only through a
U-tube filled with mercury (density 13.6 g/cm3 ). A
difference in pressure causes the mercury column on
either side of the U-tube to be different in height by
∆h =[05]
cm. Find the speed of the airflow.
4-1. Find the wavelength of a sound wave which has a frequency of [01]
Hz. The
speed of sound is 343 m/s.
4-2. Consider light with a wavelength equal to [02]
nm. Find (a) the frequency
and (b) the period of the light wave. The speed of light is 3.00 × 108 m/s.
4-3. A wave has the form, y(x, t) = A sin(kx − ωt − φ), where A = 10.0 cm,
k =[03]
cm−1 , ω =[04]
s−1 , and φ = 1.00 rad.
(a) What is the amplitude?
(b) What is the wavelength?
(c) What is the period?
(d) What is the magnitude of the velocity?
(e) What is the direction of the velocity?
(f) Draw y(x) at time zero and at a time one period later on the same graph. Do not
turn in this part, but be ready to refer to your drawing during an in-class quiz.
4-4. (a) An AM radio station transmits at [05]
kHz. What is the wavelength of
these radio waves? Radio waves travel at the speed of light, 3.00 × 108 m/s. (b) Repeat
for an FM radio station which transmits at [06]
4-5. A 25.3-ft rope weighs [07]
MHz.
lb. I tie this rope between two trees which are
10.8 ft apart. I pull the rope as tight as I can, resulting in a tension of 73.7 lb. Find the
speed of the waves that travel along this rope from one tree to the other.
5-1. At position x = 0, a water wave varies in time as shown in the figure. (The curve is at
the 10-cm mark at both edges of the figure.) If the wave moves in the positive x direction
with a speed of [01]
cm/s, write the equation for the wave in the form,
y(x, t) = A sin(kx − ωt − φ).
Give the values of (a) A, (b) ω, (c) k, and (d) φ. (Give the value of φ between 0 and 2π
rad.) HINT: When taking an inverse sine to find φ, you must be careful to use the right
quadrant. Your calculator by default will use the 1st and 4th quadrants. Check your
final answer to make sure that it actually fits the curve everywhere. To change
quadrants, use sin−1 x → π − sin−1 x.
5-2. (a) The intensity of a sound wave is [02]
decibels. (b) The sound level of some music is [03]
W/m2 . Find the sound level in
dB. Find the intensity in
units of W/m2 .
5-3. I am sitting 2.37 m from a speaker listening to some music. How close to the speaker
should I sit if I want the music to be [04]
dB louder?
5-4. A 60-W light bulb consumes 60 W of electrical power. It radiates almost all of this
power, some of it in the form of visible light and some of it in the form of heat. Find the
intensity of the total radiated energy (light and heat) at a distance [05]
from the light bulb.
m
6-1. We stand near a railroad track as a train passes. The train is traveling at
[01]
mph (mi/h). The train blows its horn as it approaches us and continues
to sound the horn until it is well past us. When the train is standing still, the pitch of
the horn is 124.00 Hz. (a) What frequency do we hear as the train is approaching us?
(b) What frequency do we hear as the train is moving away from us? The speed of sound
is 343 m/s.
6-2. One day as I stepped out onto the street, I was very nearly hit by a car. Fortunately, the
car honked its horn and I jumped out of the way. But I noticed that the frequency of the
horn as the car approached me was a factor [02]
higher than its frequency
after the car passed me and was moving away from me. Calculate the velocity of the car.
The speed of sound is 343 m/s.
6-3. When we analyze the light coming from a distant galaxy, we find a particular absorption
line with a wavelength of [03]
nm. This same absorption line in light from the
sun has a wavelength of 625 nm. (a) Is the galaxy moving towards us or away from us?
(b) Calculate the magnitude of the velocity of the galaxy relative to us. Note that for
light waves, the Doppler shift is given by
0
f =f
r
c±v
c∓v
where c is the speed of light and v is the relative velocity of the source and observer. Use
the upper signs when the source and observer are moving towards each other and the
lower sign when the source and observer are moving away from each other.
6-4. We are in an automobile traveling at [04]
mph (mi/h) down a street. We
approach a tall brick wall and honk our horn which has a pitch of 245.0 Hz. Find the
frequency of the sound we can hear reflected off the wall and coming back to us. The
speed of sound is 343 m/s.
7-1. A jet airplane flies with a speed of 1120 mph (mi/h) at an altitude of [01]
ft.
It passes directly over my head. How soon after it passes directly above me will I hear
the sonic boom? The speed of sound is 343 m/s. (Caution: I am not asking how much
time it took for the sound to travel from the airplane when it was directly overhead. The
sonic boom originates from the airplane sometime before it reached the point directly
overhead.)
7-2. Two speakers emit sound waves with frequency [02]
kHz. They are driven by
the same oscillator so that they are in phase with each other. I place the speakers
side-by-side, and I stand across the room from them. If someone moves one of the
speakers towards me, I hear the total intensity drop and then rise again. How far did he
move the speaker to the point where I heard a minimum intensity due to destructive
interference of the sound waves from the two speakers? The speed of sound is 343 m/s.
7-3. Two speakers emit sound waves with frequency [03]
Hz. They are driven by
the same oscillator so that they are in phase with each other. We place the speakers so
that they are a few meters apart and facing each other. Along the line joining the two
speakers, the sound waves from the two speakers are traveling in opposite directions.
This creates a standing wave between the two speakers. How far apart are the antinodes
in that standing wave? Neglect the effect of reflection of waves from the speakers. The
speed of sound is 343 m/s.
7-4. A long spring is stretched and attached to two walls 5.42 m apart. The mass of the
spring is 276 g. The tension in the spring is [04]
N. What will be the
frequency of a standing wave with three loops (three antinodes)?
7-5. Suppose we excite a two-loop standing wave in a rope using a tension of
[05]
N. What tension should we apply to the rope if we want to excite a
one-loop standing wave with the same frequency?
8-1. The speed of sound in aluminum is 5000 m/s. We excite standing waves in a rod of
aluminum [01]
m long such that there is an antinode at each end of the rod
and only one node half-way between. Find the frequency of the standing wave.
8-2. We place a speaker near the top of a drinking glass. The speaker emits sound waves with
a frequency of [02]
kHz. The glass is 14.1 cm deep. As I pour water into the
glass, I find that at certain levels the sound is enhanced due to the excitation of standing
sound waves in the air inside the glass. Find the minimum depth of water at which this
occurs (distance from surface of water to bottom of glass). The standing sound wave has
a node at the surface of the water and an antinode at the top of the glass. Assume that
the antinode is exactly at the top of the glass. The speed of sound in air is 343 m/s.
8-3. A tuning fork oscillates with a standard frequency of 440.0 Hz. When I draw a bow
across a violin string, I find its frequency to be a little higher than that of the tuning
fork. In fact, when I superimpose the two sound waves (one from the tuning fork and one
from the violin), I can hear beats with a frequency of [03]
Hz. What is the
frequency of the violin string?
8-4. The wavelength of one sound wave is 0.81 m. The wavelength of a second sound wave is
a little bit longer. When the two sound waves are superimposed on each other, we hear a
[04]
-Hz beat. Find the difference in their wavelengths. The speed of sound is
343 m/s.
9-1. A nylon guitar string is 92.4 cm long. Its linear mass density is 7.28 g/m, and its tension
is [01]
N. Find the pitch of the musical note produced when this string is
plucked. (The pitch is the fundamental frequency of the standing waves produced.)
9-2. A steel piano string is [02]
inches long. The diameter of the string is
0.0421 inches. When struck, this string produces the musical note B which has the pitch
of 123 Hz. (a) Find the tension of this string. Give the answer in pounds. The density of
steel is 7.86 g/cm3 . (b) There are 228 strings in a piano. (Some notes use more than one
string.) If we assume that the tension in every string is the same, find the total force (in
tons, 1 ton = 2000 lb) exerted on the frame of the piano. (Add together the tensions of
all of the strings.) Piano frames are made of steel so that they can withstand this kind of
force.
9-3. A violin string, which is 30.4 cm long, is tuned so that its pitch is concert A which is
440 Hz. I can effectively shorten the string by placing my finger on it and pressing it
down. How far from the end of the string should I put my finger if I want the pitch of the
note to be [03]
Hz? (Give the distance from the end where the wooden tuning
pegs are located.) Assume that the tension in the string remains the same.
9-4. A pipe is open at both ends. Its length is 22.81 cm. If I excite standing waves in the pipe
by blowing air over one of its ends, I hear a pitch of [04]
Hz. (a) Find the
distance between the antinodes at the two ends of the pipe. This is not the same as the
actual length of the pipe, since the antinodes are not exactly at the ends of the pipe. The
speed of sound is 343 m/s. (b) How far past the physical ends of the pipe do the
antinodes extend? Assume that it is the same amount for each antinode. (c) If I close
one end of the pipe, what pitch will I hear? The node at the closed end is exactly at the
position of the closed end. The antinode at the open end extends past the physical end of
the pipe by the same amount found in part (b).
9-5. We are in an automobile traveling at [05]
mph (mi/h) down a street. We
approach a tall brick wall and honk our horn which has a pitch of 245.0 Hz. (a) Find the
frequency of the sound we can hear reflected off the wall and coming back to us. (b) We
can hear beats from interference between the reflected sound and the sound directly from
the horn. Find the beat frequency. The speed of sound is 343 m/s.
9-6. A wave traveling to the right has the form y = y0 sin(kx − ωt) and another wave traveling
to the left has the form y = y0 sin(kx + ωt). The two waves are superimposed.
(a) Using trigonometric identities, show that together they form a standing wave which
can be written as y = 2y0 sin kx cos ωt.
(b) Make a sketch of the standing wave for several arbitrary times. (Use any value of ω.)
Plot them on the same graph. See Fig. 18.10 in the textbook as an example. (Fig. 18.7 in
5th edition) Take the amplitude y0 to be 10 cm and the wavelength to be 1 m.
Turn in this problem on paper using the 10 lower bins near our classroom. Use the
bin that corresponds to the first digit of your class ID number.
10-1. The inside diameter of a steel ring is 0.2500 inch at 20◦C. If we heat the ring to
[01]
◦
C, what will its inside diameter be?
10-2. Inside the house where the temperature is 20◦C, we measure the length of an aluminum
rod with a micrometer made of steel. (A micrometer is a device which measures
distances very accurately.) We find the rod to be 10.0000 cm long. If we repeat this
measurement outside where the temperature is [02]
◦
C, what result would we
obtain? Caution: the size of the micrometer is also affected by the temperature, so we no
longer obtain the true length of the rod when we measure it with the micrometer. We
want to find the length of the cold rod according to the cold micrometer.
10-3. We measure the pressure in an automobile tire early in the morning when the
temperature is 60◦F. We read 35.1 psi (lb/in2 ) on the pressure gauge. This is the
pressure with respect to atmospheric pressure. To obtain the absolute pressure of the air
in the tire we must add to this the pressure of the atmosphere. On that day, the
atmospheric pressure is 0.87 × 105 Pa. Later in the day, the temperature is
[03]
◦
F but the atmospheric pressure is unchanged. What will we read on the
pressure gauge if we measure the pressure in the tire then? Assume that the volume of
the tire remains the same.
10-4. Consider a hot-air balloon. The deflated balloon, gondola, and two passengers have a
combined mass of 315 kg. When inflated, the balloon contains [04]
m3 of hot
air. Find the temperature of the hot air required to lift the balloon off the ground. The
air outside the balloon has a temperature of 20.2◦C and a pressure of 0.916 × 105 Pa.
The pressure of the hot air inside the balloon is the same as the pressure of the air
outside the balloon. The molar mass of air is 29 g/mol. Hint: First find the density of
the air outside the balloon. Then use Archimedes’ principle to find the density required
for the air inside the balloon. Then find the temperature of the air inside the balloon.
11-1. How much heat is required to raise the temperature of 12.7 g of water from 18.3◦C to
[01]
◦
C?
g of lead which we have cooled down in the freezer to −5.28◦C.
11-2. We have [02]
We also have a jar containing 1000 g of water at room temperature, which is 21.32◦C. If
we drop the lead into the water, find the final temperature of the water when the lead
and water have come to a common temperature. Neglect any flow of heat to or from the
environment.
11-3. We drop a cube of ice into a glass of water. The mass of the cube of ice is
[03]
g and its initial temperature is −10.2◦C. The mass of the water is 251 g
and its initial temperature is 19.7◦C. What is the final temperature of the water after all
of the ice has melted?
11-4. Repeat problem 3 above using [04]
g of ice. This time, not all of the ice will
melt. (a) What is the final temperature of the water-ice mixture? (b) How much ice is
left?
12-1. We have some gas in a cylinder like that in the figure. The diameter of the
cylinder is 8.1 cm. The mass of the piston is [01]
kg. The
4
atmospheric pressure is 9.4 × 10 Pa. (a) Find the pressure of the gas. (Both
the weight of the piston and the pressure of the atmosphere on top of the
piston contribute to the pressure of the gas inside the cylinder.) (b) If we
heat up the gas so that the piston rises from a height of 12.3 cm to 15.6 cm
(measured from the bottom of the cylinder), find the work done on the gas.
Note that the pressure of the gas remains constant as it is heated up.
12-2. We have some gas in a container at high pressure. The volume of the container is
[02]
cm3 . The pressure of the gas is 2.52 × 105 Pa. We allow the gas to
expand at constant temperature until its pressure is equal to the atmospheric pressure,
which at the time is 0.857 × 105 Pa. (a) Find the work done on the gas. (b) Find the
change of internal energy of the gas. (c) Find the amount of heat we added to the gas to
keep it at constant temperature.
12-3. A pond is frozen over with a layer of ice [03]
cm thick. The water under the
ice is at 0◦C. The temperature of the air above the ice is −15◦C. This difference in
temperature causes heat to flow through the ice from the water below to the air above.
As heat is removed from the water, it freezes, adding to the thickness of the layer of ice.
At what rate does the thickness of the ice layer increase? Give the answer in centimeters
per hour. You only need to consider the freezing of the water. You may neglect any
additional cooling of the ice to temperatures below 0◦C.
12-4. Water is being boiled in an open kettle that has a 0.52-cm-thick circular aluminum
bottom with a radius of 12.0 cm. If the water boils away at a rate of
[04]
kg/min, what is the temperature of the lower surface of the bottom of
the kettle? Assume that the top surface of the bottom of the kettle is at 100.0◦ C.
12-5. At a certain time of day, the Sun delivers [05]
W to each square meter of a
blacktop road. If the hot asphalt loses energy only by radiation, what is its steady-state
temperature? (Assume e = 1.)
13-1. We have a container of a hot ideal monatomic gas. The volume of the container is
25 liters. The temperature of the gas is [01]
◦
C, and its pressure is
5
0.858 × 10 Pa. We allow the gas to cool down to room temperature, which at the time is
21◦C. We do not allow the volume of the gas to change. (a) Find the final pressure of the
gas. (b) Find the amount of heat that passed from the gas to its surroundings as it
cooled. (c) Find the change of internal energy of the gas.
13-2. We have a container of an ideal diatomic gas. The volume of the container is 1.000 liter.
The temperature of the gas is 20.2◦C, and its pressure is 0.853 × 105 Pa. We drop a piece
of hot copper into the container and stop up the opening so that the gas is kept at
constant volume. The mass of the copper is [02]
g, and its temperature is
100◦C. After a while, the gas and copper finally come to a common temperature. Find
this final temperature. Neglect any flow to heat to the surroundings.
13-3. We have some air in a cylinder like that in the figure. Assume that air is an
ideal diatomic gas. The diameter of the cylinder is 5.3 cm. The mass of the
piston is negligible so that the pressure inside the cylinder is maintained at
atmospheric pressure which is 1.00 atm. The height of the piston is 9.7 cm,
measured from the bottom of the cylinder. The temperature of the air is
[03]
◦
C. (a) Find the number of moles of air in the cylinder.
(b) We heat the gas so that the piston rises to a height of [04]
cm.
The pressure of the air remains constant. Find the final temperature of the
air. (c) Find the amount of heat that was put into the air.
13-4. We heat up 2.43 mol of some gas from 21.7◦C to [05]
◦
C, holding the pressure
constant. The molar specific heat at constant volume for this gas is
CV = [06]
J/mol · K. (a) Assuming that this gas behaves like an ideal gas,
find the value of the molar specific heat at constant pressure CP . (b) Find the amount of
heat that flows into the gas. (c) Find the amount of work done on the gas. (d) Find the
change of internal energy of the gas.
14-1. We have a container of [01]
moles of an ideal monatomic gas. The volume of
the container is 15.0 liters, and the temperature of the gas is 21.7◦C. We compress the
gas adiabatically to [02]
liters. (a) Find the final temperature of the gas.
Neglect any heat flow into the surroundings. (b) Find the change in internal energy of
the gas. (c) Find the work done on the gas. Find (d) the initial and (e) the final
pressures of the gas.
14-2. We have a container of compressed air. Assume that air is a diatomic ideal gas. The
volume of the container is 1.35 liters. The pressure of the gas is [03]
atm, and
its temperature is 19◦C. We allow the gas to expand adiabatically to a final pressure of
1.00 atm. (a) Find the final volume of the gas. (b) Find the final temperature of the gas.
(c) Find the change of internal energy of the gas. (d) Find the work done by the gas.
14-3. We have a cylinder and piston similar to the one in the figure. The diameter
of the piston is [04]
cm. The distance from the bottom of the
cylinder to the piston is 12.6 cm. The cylinder is filled with an ideal diatomic
gas at room temperature (23.8◦C) and room pressure (1.00 atm). (a) If we
push down on the piston with a force equal to 119 lb, how far can we move
the piston? Consider the compression to be adiabatic, and neglect the flow of
heat to the surroundings. Also neglect the weight of the piston. Caution:
remember that atmospheric pressure also pushes down on the piston. The
total force is 119 lb plus the force of atmospheric pressure. Be sure to give
the distance the piston moves, not just the final height of the piston.
(b) Repeat for an ideal monatomic gas.
14-4. With specialized equipment, it is routine to achieve vacuums with pressures below
10−10 torr (1 torr = 1 mm of Hg = 133.3 Pa). However, special care must be taken in
cleaning and baking the walls of the stainless steel chamber, or “outgassing” of
contaminants will seriously increase the pressure (by orders of magnitude). If the
pressure is 1.00 × 10−10 torr and the temperature is [05]
number of molecules in a volume of 1.00 m3 .
◦
C, calculate the
14-5. What are the number of degrees of freedom for
(a) helium at room temperature?
(b) oxygen at room temperature?
(c) water vapor at 200◦C?
(d) hydrogen at a few thousand Kelvin?
15-1. We supply 132.4 J of heat to an engine with [01]
% efficiency. (a) How much
work can the engine do? (b) How much heat must the engine exhaust?
15-2. A particular engine has [02]
% efficiency and is capable of doing work at a rate
of 253 hp. (a) At what rate must we provide heat to this engine? (b) At what rate will
this engine exhaust heat?
15-3. A refrigerator keeps its freezer compartment at −10◦C. It is located in a room where the
temperature is 20◦C. The coefficient of performance (heat pump in cooling mode) is
[03]
. How much work is required to freeze one 26-g ice cube? Assume that we
put 26 g of water into the freezer. The initial temperature of the water is 20◦C. The final
temperature of the ice cube is −10◦C. The refrigerator removes the heat from the freezer
compartment, maintaining its temperature at about −10◦C.
15-4. Consider a heat pump which is used to cool down a home during the summer. Its
coefficient of performance in cooling mode is [04]
. On a particular hot day,
the temperature outside the home is 90◦F, and the temperature inside the home is
maintained at 70◦F. If the heat pump consumes 500 W of electrical power, at what rate
does it remove heat from the home?
16-1. A reversible engine draws heat from a reservoir at [01]
◦
C and exhausts heat
to a reservoir at 19◦C. (a) Find the efficiency of the engine. (b) Find the heat required to
do 100 J of work with this engine.
16-2. A reversible refrigerator maintains the temperature of its freezer compartment at
[02]
◦
C. It sits in a room at 20◦C. Find the work required to remove 100 J of
heat from the freezer compartment.
16-3. We have 2.451 moles of air in some container at 25.2◦C. Assume that air is an ideal
diatomic gas. We put [03]
J of heat into the air. (a) Find the change of
entropy of the air if we hold the volume constant. (b) Find the change of entropy of the
air if we hold the pressure constant.
-g ice cube (0◦C) into 1000 g of water (20◦C). Find the total
16-4. We drop a [04]
change of entropy of the ice and water when a common temperature has been reached.
Caution: calculate the common temperature to the nearest 0.01◦C.
16-5. A sample of a monatomic gas is taken through the Carnot cycle ABCDA. For your
convenience, the cycle is drawn with the mathematical relationships of each part shown.
Complete the table for the cycle.
A
P
1400 kPa
V
10.0 L
T
720 K
B
C
24.0 L
D
15.0 L
Avoid rounding intermediate steps so that errors do not accumulate. You may find it
beneficial to solve for the unknowns in the order requested below.
First determine the number of moles from the data in row A.
(a) Find PD .
(b) Find the value of TD and TC , which are equal.
(c) Find PC .
(d) Find TB .
(e) Find VB .
You should then be able to find that PB = 875 kPa (provided here as a check).
16-6. Two 1.00-kg pieces of silver are brought into thermal contact while insulated from the
environment. If initially one piece is at [05]
the change in entropy for the system?
◦
C and the other at 0◦C, what is
16-7. In the figure is shown the Otto cycle. Paths A and C are adiabatic (Q = 0), and paths B
and D are at constant volume (∆V = 0). Consider the working substance of this engine
to be an ideal gas. For each path, indicate on the chart below whether the work W done
on the gas is positive (+), negative (−), or zero (0). Also indicate the sign of the net
work for the entire cycle. Repeat for the heat Q put into the gas, and the change of
internal energy ∆Eint of the gas. Bring the completed chart to class.
P
A
B
C
D
net
W
B
C
Q
A
D
∆Eint
V
17-1. A ray of light passes through a pane of glass which is 1.0 cm thick. The index of
refraction of the glass is 1.53. The angle between the normal to the surface of the pane
and the ray in the air as it enters the pane is [01]
◦
. (a) Find the angle
between the normal to the surface of the pane and the ray inside the glass. (b) Find the
angle between the normal to the surface of the pane and the ray in the air after it exits
the pane.
17-2. Light passes through a glass prism, as shown in the figure.
The cross-section of the prism is an equilateral triangle. (a)
Find the incident angle, if we want the light ray inside the
prism to be parallel to the base of the prism. Use
[02]
for the index of refraction of glass. Remember
that the incident angle is measured with respect to a line
normal to the surface of the prism. You may use n = 1 for the
index of refraction of air. (b) The index of refraction of glass for blue light is 1.528.
Using the incident angle from part (a), find the angle at which blue light exits the prism.
This is not the angle of deviation δ shown in the figure. We want the angle between the
light and a line normal to the surface from which the light exits. (c) Repeat part (b) for
red light, for which the index of refraction is 1.511. Caution: In parts (b) and (c), the
light ray inside the prism is no longer parallel to the base of the prism.
17-3. In the diving pool in the Richards Building, there is a glass window under the water.
There is a room full of air on the other side of the glass window pane. If I dive under the
water and look at the window, I notice that I can see the room on the other side of the
window only through a circular area. Outside that circle, light undergoes total internal
reflection at the surface between the glass and the air, and the window appears like a
mirror. If I am [03]
m from the window, find the radius of the circle. The
index of refraction of water is 1.33, and the index of refraction of glass is 1.52. Be sure to
take into account that the light ray which is refracted at the glass-air surface is also
refracted at the glass-water surface and changes direction there too.
17-4. A glass fiber (n = [04]
) is submerged in water (n = 1.333). What is the
critical angle for light to stay inside the optical fiber?
18-1. An object is placed [01]
cm in front of a concave mirror with a focal length
equal to 3.00 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 2.00 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
18-2. An object is placed [02]
cm in front of a concave mirror with a focal length
equal to 3.00 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 1.00 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
18-3. An object is placed [03]
cm in front of a convex mirror with a focal length
equal to −2.0 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 5.0 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
18-4. At the south end of the foyer in the Eyring Science Center, there is a demonstration
called “The Illusive Dollar.” A large concave mirror produces a real image of a dollar
bill. Suppose that both the object and the image are [04]
cm from the mirror.
(a) Find the radius of curvature of the mirror. (b) Draw a ray diagram on the next sheet
in this packet and turn it into the homework bins.
.
Physics 123
Homework Set 18, page 1 of 2
Identification number
out of 8 points
Score:
Do the following homework problems on this sheet of paper and submit it through the
Physics 123 slots outside our classroom. This part of the assignment is due at 1:00 pm on
the same day that the rest of the assignment is due. Late papers will receive half credit.
For each problem, draw a ray diagram to find the location and size of the image.
(Construct three rays. See examples in the section, “Ray Diagrams for Mirrors,” in the
textbook.) Use solid lines for the actual paths of the rays of light. Use dashed lines for
all other lines drawn to guide the eye. Draw the image. Do your work accurately and
neatly, using a ruler.
18-1 (d). In the figure below, a concave mirror and its focal point are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 2 cm
long). Then draw the ray diagram and the image.
F
18-2 (d). In the figure below, a concave mirror and its focal point are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 1 cm
long). Then draw the ray diagram and the image.
F
Physics 123
Homework Set 18, page 2 of 2
18-3 (d). In the figure below, a convex mirror and its focal point are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 5 cm
long). Then draw the ray diagram and the image.
F
18-4 (b). In the figure below, a concave mirror, an object (O), and an image (I) are
shown. (The object is the downward pointing arrow and the image is the upward
pointing arrow.) From the answer you obtained in part (a), indicate the position of the
focal point on the diagram. Then draw the ray diagram. Note that one of the usual three
rays cannot be drawn in this case. You can only draw two of them.
I
O
19-1. An object is placed [01]
cm in front of a converging lens with a focal length
equal to 2.00 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 1.0 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
19-2. An object is placed [02]
cm in front of a converging lens with a focal length
equal to 6.0 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 1.0 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
19-3. An object is placed [03]
cm in front of a diverging lens with a focal length
equal to −5.0 cm. (a) Find the location of the image. (b) Find the magnification. (c) If
the height of the object is 5.0 cm, find the height of the image. (d) Draw a ray diagram
on the next sheet in this packet and turn it into the homework bins.
19-4. Consider a lens which is convex on one side and concave on the other side. (a) If the
radius of curvature of the convex side is 8.00 cm, find the radius of curvature of the
concave side such that the lens will be diverging with a focal length equal to
[04]
cm. The lens is made of glass with an index of refraction equal to 1.58.
(b) The diameter of the lens is 5.0 cm. The lens is 1-mm thick at its center. Draw a
life-size cross-section of the lens on the next sheet in this packet and turn it into the
homework bins.
.
Physics 123
Homework Set 19, page 1 of 2
Identification number
Score:
out of 8 points
Do the following homework problems on this sheet of paper and submit it through the
Physics 123 slots outside our classroom. This part of the assignment is due at 1:00 pm on
the same day that the rest of the assignment is due. Late papers will receive half credit.
For each problem, draw a ray diagram to find the location and size of the image.
(Construct three rays. See examples in the section, “Ray Diagrams for Thin Lenses,” in
the textbook.) Use solid lines for the actual paths of the rays of light. Use dashed lines
for all other lines drawn to guide the eye. Draw the image. Do your work accurately and
neatly, using a ruler.
19-1 (d). In the figure below, a converging lens and its focal points are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 1 cm
long to the left of the lens). Then draw the ray diagram and the image.
F
F
19-2 (d). In the figure below, a converging lens and its focal points are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 1 cm
long to the left of the lens). Then draw the ray diagram and the image.
F
F
Physics 123
Homework Set 19, page 2 of 2
19-3 (d). In the figure below, a diverging lens and its focal points are shown. Each
division on the diagram is equal to 1 cm. Draw the object on the figure (an arrow 5 cm
long to the left of the lens). Then draw the ray diagram and the image.
F
F
19-4 (b). Draw the lens below. Use a ruler and compass if you want to receive full credit
for this problem.
20-1. I use my slide projector to project a slide onto a screen. The picture on the slide is
35 mm wide. The picture on the screen is [01]
m wide. The distance between
the screen and the lens on the projector is 4.42 m. Find the focal length of the lens.
20-2. Consider a camera with film in it. The focal length of the lens is [02]
mm.
(a) If we want to take a picture of some distant object, where should we put the film?
(Consider the distance to the object to be infinite.) (b) If we next want to take a picture
of an object a distance x = [03]
m away, by how much should we change the
distance between the film and the lens? (c) Suppose we didn’t change the position of the
film, but left it in the position for taking a picture of a distant object, as in part (a). A
“point” of light a distance x away would not be “focused” properly on the film but
instead would produce a “dot” on the film. Find the diameter of the dot. The diameter
of the lens is 1.0 cm. (d) If we cover up part of the lens so that light can only enter
through a hole 3 mm in diameter, find the diameter of the dot in part (c).
20-3. A near-sighted woman cannot focus on any object farther away than a distance
x = [04]
cm. Find the focal length of the lens which will correct her vision. (If
an object is very far away, the lens should produce an image a distance x in front of her
eyes so that she can focus on it.) Neglect the distance between the lens and the eye.
20-4. Suppose I want to focus on something [05]
cm from my eye, but my near
point is 25 cm. Find the focal length of a lens which, when held in front of my eye, will
produce an image 25 cm from my eye so that I can focus on it. Neglect the distance
between the lens and the eye.
21-1. (a) I hold a flat mirror [01]
cm in front of my face. There is a freckle on my
face 1 mm in diameter. Find the angular size of the freckle on the image of my face as
viewed by my eye. (b) Repeat for a concave mirror which has a focal length of 39 cm.
(c) What is the angular magnification of the concave mirror, as compared to the flat
mirror?
21-2. Find the focal length of a simple magnifier which has a magnification of [02]
Use 25 cm for the near point. Assume that the image is at infinity.
.
21-3. The focal length of an eyepiece on a microscope is 12 mm. The distance between the
eyepiece and the objective lens is [03]
cm. If the overall magnification of the
microscope is −600, find the focal length of the objective lens. Use 25 cm for the near
point.
21-4. A hobby telescope has an objective lens with a focal length of [04]
cm and an
eyepiece with a focal length of 8.2 mm. We view the planet Jupiter with this telescope.
We do this at the time of year when we are closest to Jupiter. Data about the solar
system can be found in the front inside cover of the textbook. (a) Find the diameter of
the image of Jupiter produced by the objective lens. (b) Find the angular size of Jupiter
as viewed through the eyepiece. (c) How far should I place a marble (1-cm diameter)
from my eye to obtain the same angular size as in part (b)?
22-1. Two loud speakers are 2.63 m apart. I am standing [01]
m from one of them
and 3.58 m from the other. The two speakers are driven by a single oscillator. If the
frequency of the oscillator is swept from 100 Hz to 1000 Hz, find the lowest frequency at
which I will hear an enhancement of the sound intensity due to constructive interference
of the waves from the two speakers. Use 343 m/s for the speed of sound. (DO NOT use
the double-slit equation, d sin θ = mλ. This equation is only valid for observations far
from the two slits, compared to the distance between the two slits.)
22-2. We pass a laser beam through a double slit. On a screen [02]
m away, we
observe a series of bright lines which are 3.4 mm apart. The wavelength of the laser light
is 633 nm. What is the distance between the two slits?
22-3. The figure shows an interference pattern from two slits. If
the slits are 0.17 mm apart and the observed picture is
seen on a screen [03]
m from the slits, find the
wavelength of the light used. Assume that the photograph
in the figure is life-size. To obtain an accurate value for
the distance between fringes, measure the distance
between the topmost and bottommost fringes and divide
by 4. Note: Sometimes printers do not faithfully reproduce
the actual size of a photograph. The box displayed below
should be 5.0 cm wide. If not, then scale the size of the
photograph accordingly.
5.0 cm
23-1. Consider the reflection of light from a soap bubble. The bubble is a thin film of water
with air on both sides. Find the minimum thickness of the bubble so that reflected light
constructively interferes when the wavelength is [01]
nm (in air). Assume that
the incident light is normal to the surface of the bubble. The index of refraction of soapy
water is about the same as that of water. Use n = 1.33.
23-2. A pool of water is covered with a film of oil which is [02]
nm thick. For what
wavelength of visible light (in air) will the reflected light constructively interfere? The
index of refraction of the oil is 1.65. Visible light (in air) has wavelengths between
430 nm (blue) and 770 nm (red) in air. Assume that the incident light is normal to the
surface of the oil.
23-3. Solar cells are often coated with a transparent thin film of silicon monoxide (SiO,
n = 1.85) to minimize reflective losses from the surface. Suppose that a silicon solar cell
(n = 3.5) is coated with a thin film of SiO for this purpose. If the thickness of the
coating is [03]
nm, find the maximum wavelength of ultraviolet light (in air)
for which the reflection will be maximized instead of minimized. (The wavelength of
ultraviolet light is shorter than that of visible light.)
23-4. Consider the circular interference pattern in Figure (b) caused by a thin film of air
between a flat plate of glass and a curved lens as shown in Figure (a). The radius of the
sixth dark ring (not counting the black dot in the middle) is 7.0 mm. Determine (a) the
radius of curvature of the lens and (b) the focal length of the lens. The index of refraction
of the glass is 1.5. Consider the wavelength of the light (in air) to be [04]
nm.
24-1. A laser beam passes through a single slit. We observe an interference pattern on a screen
[01]
m away. We find that the distance between the two dark lines (m = ±1)
on the two sides of the bright central maximum is 3.0 cm. The wavelength of the laser
light is 633 nm. Find the width of the slit.
24-2. The diameter of a laser beam is due entirely to the diameter of the hole through which it
passes as it exits the instrument. However, at large distances, the diameter of the beam
increases due to diffraction at that hole. Suppose that for a particular laser, the diameter
of the beam is [02]
cm at a distance of 11.5 m. The wavelength of the laser
light is 633 nm. Find the diameter of the hole through which the beam exits the
instrument. Caution: the value of θmin is measured from the center of the diffraction
pattern to the first dark ring.
24-3. A hobby telescope uses a concave mirror with a diameter of [03]
cm. Find the
distance between two points on the moon that can be resolved by this telescope. Use
550 nm for the wavelength of visible light.
24-4. In this problem, we will find the ultimate resolving power of a microscope. First of
all, in order to obtain a large magnification, we want an objective lens with a very
short focal length. Second, in order to obtain maximum resolution, we also want
that lens to have as large a diameter as possible. These two requirements are
conflicting, since a lens with a short focal length must have a small diameter. It is
not practical for a lens to have a diameter much larger than the radius of curvature
of its surfaces. Otherwise, the lens starts looking like a sphere. So, let us assume
that the objective lens has a diameter D equal to the radius of curvature of the two
surfaces, like the lens in the figure to the right. (a) If the lens is made of glass with
index of refraction [04]
, find the focal length f in terms of the diameter
D of the lens. (b) The distance between the sample to be observed and the
objective lens is approximately equal to the focal length f . Find the distance
between two points on the sample which can be barely resolved by the lens. Use the
result from part (a) to eliminate f from the expression. You should find that D is
also eliminated from the expression and that the answer is given entirely in terms of
the wavelength λ of the light. You may use the small angle approximation,
sin θ ≈ tan θ ≈ θ.
24-5. A diffraction grating contains 15,000 lines/inch. We pass a laser beam through the
grating. The wavelength of the laser is 633 nm. On a screen [05]
m away, we
observe spots of light. (a) How far from the central maximum (m = 0) is the first-order
maximum (m = 1) observed? (b) How far from the central maximum (m = 0) is the
second-order maximum (m = 2) observed? DO NOT use the “small-angle
approximation,” ybright = (λL/d)m. The angles are too large for sin θ ≈ tan θ to be a
very good approximation.
25-1. You wish to attenuate a polarized laser beam by inserting two polarizers. The second
polarizer is oriented to match the original polarization of the beam to ensure that the
final polarization remains unchanged. The first polarizer is then rotated through various
angles to control the intensity. Through what angle should the first polarizer be rotated
to reduce the final intensity by a factor of [01]
with no losses.
? Assume perfect polarizers
25-2. A prism is inserted into a polarized laser beam. The apex
angle φ is chosen so that the beam enters and leaves close to
Brewster’s angle. If the index of refraction is
n =[02]
, what should be the apex angle φ?
26-1. Suppose we want to put ourselves several years into the future and spend only one month
doing it. We can accomplish this by taking a trip into space at high speed and returning
again. It doesn’t matter where we go. If we go fast enough, time on board the space craft
will pass considerably more slowly than time on Earth. Find the speed we should travel
so that one month on board the space craft will equal [01]
26-2. A jet plane is [02]
years on Earth.
m long. How much shorter is the plane when it travels at
the speed of sound, 343 m/s? You will find the following approximation useful:
√
1 − x ≈ 1 − 12 x when x 1.
26-3. How fast must a meter stick move for it to appear to be only [03]
cm long?
26-4. We plan a trip to the nearest star, Proxima Centauri, which is 4.2 ly (light years) away
(in the reference frame of the earth). We travel on a space ship at a speed of
[04]
c. While at Proxima Centauri, we spend one year exploring its planetary
system before returning to earth. (a) How long does the entire round trip take according
to our clocks? Assume that while at Proxima Centauri our velocity relative to earth is
negligibly small. (b) How long does the entire round trip take according to clocks on
earth?
27-1. Suppose we are on our way to Proxima Centauri, which is 4.2 ly away (in the reference
frame of the earth). We are in a space ship which is traveling with a speed of
[01]
c. When we are half-way there, we send a signal to both the earth and
Proxima Centauri. The signals travel at the speed of light c. In the reference frame of
the earth and Proxima Centauri, both signals travel 2.1 ly and thus arrive at their
destinations at the same time. (a) In our reference frame, how long does it take for the
signal to reach earth? Remember that in our reference frame, the distance between earth
and Proxima Centauri is less than 4.2 ly because of length contraction. (b) In our
reference frame, how long does it take for the signal to reach Proxima Centauri?
(c) These two events (the signal reaching earth and the signal reaching Proxima
Centauri) are simultaneous in the earth’s reference frame. How much time elapses
between these two events in our reference frame?
27-2. If two objects are both traveling at [02]
c but in opposite directions, find the
speed of one object in the reference frame of the other object.
27-3. Suppose we are on a space ship generating a beam of electrons. In our reference frame,
the electrons are traveling in the +x direction with a speed of 0.87c. Our space ship
passes by the earth. In the earth’s reference frame, the space ship is traveling in the +x
direction with a speed of [03]
c. Find the speed of the electrons in the earth’s
reference frame.
27-4. Suppose we observe two space ships, one with a speed of 0.9900c and the other with a
speed of [04]
c. The faster ship overtakes and passes the slower ship. Find the
speed of the faster ship in the reference frame of the slower ship.
28-1. If a particle’s kinetic energy is equal to [01]
times its rest energy, find its
velocity.
28-2. Find the work required to increase the velocity of an electron by 0.010c (a) if its initial
velocity is [02]
c and (b) if its initial velocity is [03]
c. Remember
that the work done is equal to the change of kinetic energy.
28-3. (a) According to Newtonian physics (kinetic energy = 21 mv 2 ), how much work is required
to accelerate an electron from rest to [04]
c? (b) If we do that much work on
an electron, what will its final speed actually be?
28-4. We accelerate electrons between two parallel plates a few cm apart. We apply
[05]
MV across the plates. When an electron begins at rest at one plate, it
arrives at the other plate with a kinetic energy of [05]
MeV. (a) Find the
velocity of the electron. (b) Find the momentum of the electron. (c) The electric field
between the plates is equal to 2.15 MV/m. This produces a constant force of
3.44 × 10−13 N on the electron as it travels from one plate to the other. Find the amount
of time it takes for the electron to travel from one plate to the other. Remember that the
force is the time derivative of the momentum.
29-1. Find the energy of a photon in light with a wavelength of [01]
29-2. The energy of photons in a gamma ray is [02]
this radiation.
nm.
MeV. Find the wavelength of
29-3. Consider the photoelectric effect in some metal where the work function is
[03]
eV. If we shine yellow light (λ = 550 nm) on this metal, electrons are
ejected from the surface of the metal. If we measure the kinetic energy of these ejected
electrons, what maximum value will we find?
29-4. Consider the compton effect. We direct an x-ray beam into some material. The
wavelength of the x rays is [04]
nm. (a) Find the wavelength of the x rays
which are scattered back towards the source (θ = 180◦ ). (b) Find the kinetic energy of
the electrons which these photons knock out of the material. Consider the work function
of the material to be insignificantly small.
30-1. Find the kinetic energy of an electron which has a de Broglie wavelength equal to
[01]
nm.
30-2. De Broglie postulated that the relationship λ = h/p is valid for relativistic particles.
What is the de Broglie wavelength for a (relativistic) electron whose kinetic energy is
[02]
MeV?
30-3. Helium forms a solid at low temperatures and high pressures. To maintain the order
present in a solid, each atom must remain at its assigned position. Suppose that this
restricts the uncertainty in the position to [03]
nm. (a) Find the uncertainty
in momentum of the helium atom. Use ∆x∆px ≥ h̄/2 for the uncertainty principle.
(b) Find the uncertainty in the kinetic energy of the helium atom. At low pressures, the
bonds between helium atoms are not very strong. They cannot hold together atoms with
this amount of kinetic energy. The zero point motion produced by the confinement of the
helium atom is great enough to break the bonds. For this reason helium does not form a
solid at low pressures, even at absolute zero temperature. Helium forms a solid only if
high pressure on its surface assists the bonds in holding together the atoms.
30-4. Four possible transitions for a hydrogen atom are listed below:
I. ni = 2; nf = 5
II. ni = 5;
nf = 3
III. ni = 7;
nf = 4
IV. ni = 4;
nf = 7
(a) Which transition will emit the shortest-wavelength photon? (b) For which transition
will the atom gain the most energy? (c) For which transition(s) does the atom lose
energy?
30-5. Suppose we somehow knock out an electron from an atom. The energy level of the
electron is [04]
keV. Another electron in that atom makes a transition from
its level at −1.8 keV to that empty level and emits a photon. (a) Find the energy of the
emitted photon. (b) Find the wavelength of the photon. This is how x rays are produced
in commercial instruments. A beam of high-energy electrons is directed at a target where
they knock electrons out of atoms. Other electrons in the atoms make transitions to
these empty levels, emitting photons.
31-1.
140
55 Cs
undergoes beta decay, emitting an electron. Its half-life is 66 s. At a given time,
0.0127% of the Cs atoms in a [01]
-kg sample of CsCl are
140
55 Cs
atoms.
(a) Identify the product of the decay. Type the chemical symbol followed by the mass
number (no spaces). For example Na23, not Na 23 or na23 or NA23. (b) How many
millimoles of
140
55 Cs
does the sample contain? Use the atomic masses of Cs and Cl as
given in Appendix A of the textbook. 1 millimole = 0.001 mole. (c) How many atoms
does the sample contain?
31-2.
140
55 Cs
undergoes beta decay, emitting an electron. Its half-life is 66 s. A sample contains
2.56 × 1020 atoms of
123
53 I
140
55 Cs
atoms are in the sample after
is radioactive with a half-life of 13.3 h. How long do we need to wait until
[03]
31-4.
(a) How many
s? (b) How many electrons were emitted during that time interval?
[02]
31-3.
140
55 Cs.
147
62 Sm
147
62 Sm
147
62 Sm
% of the
123
53 I
atoms in a sample have decayed?
undergoes alpha decay with a half-life of 1.06 × 1011 y. The natural abundance of
is 14.97%. This means that a sample of Sm as found in nature contains 14.97%
by weight. If we have a [04]
-g sample of Sm, how many alpha particles
does it emit per second? (Assume that the mass of a
147
62 Sm
31-5. All living things are radioactive due to the presence of
emitting an electron. The half-life of
14
6 C
14
6 C
atom is 147 u.)
which undergoes beta decay,
14
6 C
14
6 C
is 5730 y. In live specimens, the level of
present is constant. After death, the decay of
14
6 C
slowly reduces the amount of
present. Each gram of a live specimen emits 15.3 electrons per minute. An animal bone
found at an archaeological site emits [05]
electrons per minute. Its mass is
13.2 g. How old is the bone? (How long ago did the animal die?)
32-1.
228
90 Th
undergoes alpha decay. Identify the product of the decay. Type the chemical
symbol followed by the mass number (no spaces). For example Na23, not Na 23 or na23
or NA23.
32-2. (a)
(b)
234
90 Th undergoes beta decay, emitting an electron. Identify
8
5 B undergoes beta decay, emitting a positron. Identify the
the product of the decay.
product of the decay.
(c) A certain nuclide undergoes beta decay by electron capture, resulting in the product
7
3 Li.
Identify the nuclide undergoing the decay. For each answer above, type the chemical
symbol followed by the mass number (no spaces). For example Na23, not Na 23 or na23
or NA23.
32-3. Identify X (chemical symbol and mass number) in each of the following decays:
(a)
212
83 Bi
→ X + 42 He
(b)
95
36 Kr
→ X + e− + ν̄
(c)
X → 42 He + 140
58 Ce
Type the chemical symbol followed by the mass number (no spaces). For example Na23,
not Na 23 or na23 or NA23.
32-4. Identify X (chemical symbol and mass number) in each of the following reactions:
(a)
1
X + 42 He → 24
12 Mg + 0 n
(b)
235
92 U
1
+ 10 n → 90
38 Sr + X + 20 n
Type the chemical symbol followed by the mass number (no spaces). For example Na23,
not Na 23 or na23 or NA23.
33-1. Consider the following nuclear fission reaction:
235
92 U + n
142
→ 91
37 Rb + 55 Cs + xn, where x is
the number of neutrons emitted in the reaction. Find the value of x.
33-2. Identify the nuclide X in the following fission events.
(a)
235
92 U
+ n → 140
54 Xe + X + n.
(b)
235
92 U
+ n → 100
40 Zr + X + 2n.
For each answer above, type the chemical symbol followed by the mass number (no
spaces). For example Na23, not Na 23 or na23 or NA23.
33-3. What mass of
235
92 U
must undergo fission to operate a 1000-MW power plant for one day
if the conversion efficiency is [01]
event.)
%? (Assume 208 MeV released per fission
33-4. When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At
temperatures above 1.0 × 108 K, helium fusion can occur, as described in the following.
(a) Two alpha particles fuse to produce a nucleus A and a gamma ray. What is
nucleus A? (b) Nucleus A absorbs an alpha particle to produce a nucleus B and a gamma
ray. What is nucleus B? For each answer, type the chemical symbol followed by the mass
number (no spaces). For example Na23, not Na 23 or na23 or NA23.
Answers to Homework Problems, Physics 123, Spring Term, 2011
1-1. 100, 300 N
1-2a. 4.00, 9.99 m
1-2b. 1.00, 3.00 mm
1-3. 0.600, 0.700
1-4. 2.00, 5.00 N
2-1a. 5.00, 5.20 N
2-1b. 1.70, 2.70 N
2-2. 1.40, 2.30 cm
2-3. 110, 180 g
2-4a. 2.40, 3.00 m
2-4b. 12.0, 20.0 lb
3-1. 10, 40 m/s
3-2a. 1.10, 2.30 liters/s
3-2b. 2.00, 4.00 m/s
3-2c. 70.0, 100.0 psi
3-3a. 1000, 1900 ± 10 Pa
3-3b. 100, 300 lb
3-4. 90, 120 m/s
4-1. 60.0, 90.0 cm
4-2a. 4.00 × 1014 , 8.00 × 1014 Hz
4-2b. 1.00 × 10−15 , 3.00 × 10−15 s
4-3a. 5.0, 15.0 cm
4-3b. 300, 600 cm
4-3c. 10.0, 16.0 s
4-3d. 20.0, 60.0 cm/s
4-4a. 210, 340 m
4-4b. 2.80, 3.60 m
4-5. 50.0, 80.0 m/s
5-1a. 10, 30 cm
5-1b. 1.0, 3.0 s−1
5-1c. 0.010, 0.025 cm−1
5-1d. 3.0, 4.0 rad
5-2a. 80.0, 90.0 dB
5-2b. 3.0 × 10−5 , 9.0 × 10−5 W/m2
5-3. 0.20, 0.80 m
5-4. 0.10, 0.60 W/m2
6-1a. 124.00, 140.00 Hz
6-1b. 100.00, 124.00 Hz
6-2. 20.0, 35.0 m/s
6-3b. 1.00 × 108 , 2.00 × 108 m/s
6-4. 250.0, 280.0 Hz
7-1. 1.20, 2.00 s
7-2. 3.00, 6.00 cm
7-3. 20.0, 50.0 cm
7-4. 3.00, 4.30 Hz
7-5. 4.00, 8.00 N
8-1. 1200, 2500 ± 10 Hz
8-2. 1.0, 4.0 cm
8-3. 441.0, 444.0 Hz
8-4. 1.0, 8.0 mm
9-1. 60.0, 90.0 Hz
9-2a. 100, 200 lb
9-2b. 10.0, 20.0 tons
9-3. 3.0, 9.0 cm
9-4a. 23.00, 25.00 cm
9-4b. 0.30, 0.70 cm
9-4c. 365.0, 371.0 Hz
9-5a. 250.0, 280.0 Hz
9-5b. 5.0, 40.0 Hz
10-1. 0.2508, 0.2520 inch
10-2. 9.9920, 9.9970 cm
10-3. 36.0, 39.0 psi
10-4. 130, 190◦C
11-1. 400, 950 cal
11-2. 20.50, 21.00◦C
11-3. 2.0, 9.0◦C
11-4a. 0◦C
11-4b. 10.0, 50.0 g
12-1a. 1.00 × 105 , 1.30 × 105 Pa
12-1b. −17.0, −21.0 J
12-2a. −100, −140 J
12-2b. 0 J
12-2c. 100, 140 J
12-3. 1.5, 3.6 cm/h
12-4. 103.0, 110.0◦ C
12-5. 300, 400 K
13-1a. 3.00 × 104 , 6.00 × 104 Pa
13-1b. 1000, 2000 ± 10 J
13-1c. −1000, −2000 ± 10 J
13-2. 85.0, 95.0◦C
13-3a. 7.0 × 10−3 , 9.0 × 10−3 mol
13-3b. 100, 500◦C
13-3c. 10, 90 J
13-4a. 30.0, 50.0 J/mol · K
13-4b. 10000, 30000 ± 100 J
13-4c. −2000, −6000 ± 100 J
13-4d. 10000, 30000 ± 100 J
14-1a. 300, 400 K
14-1b. 100, 990 ± 10 J
14-1c. 100, 990 ± 10 J
14-1d. 1.00 × 105 , 4.00 × 105 Pa
14-1e. 1.00 × 105 , 4.00 × 105 Pa
14-2a. 2.20, 3.00 liters
14-2b. −30, −60◦C
14-2c. −100, −300 J
14-2d. 100, 300 J
14-3a. 7.00, 9.99 cm
14-3b. 7.00, 9.99 cm
14-40. 1.5 × 1012 , 3.5 × 1012
15-1a. 10.0, 20.0 J
15-1b. 100.0, 130.0 J
15-2a. 1.00, 2.00 MW
15-2b. 1.00, 2.00 MW
15-3. 1900, 2900 ± 10 J
15-4. 2000, 3000 ± 10 W
16-1a. 40.0, 70.0%
16-1b. 160, 210 J
16-2. 10.0, 20.0 J
16-3a. 3.00, 7.00 J/K
16-3b. 3.00, 7.00 J/K
16-4. 1.5, 3.5 J/K
16-5a. 100, 999 kPa
16-5b. 100, 999 K
16-5c. 100, 999 kPa
16-5d. 100, 999 K
16-5e. 10.0, 99.9 L
16-6. 4.0, 12.0 J/K
17-1a. 34.0, 38.0◦
17-1b. 60.0, 70.0◦
17-2a. 49.00, 50.00◦
17-2b. 49.00, 51.00◦
17-2c. 48.00, 50.00◦
17-3. 1.10, 2.30 m
17-4. 55.0, 75.0◦
18-1a. 3.70, 4.30 cm
18-1b. −0.20, −0.50
18-1c. −0.50, −0.90 cm
18-2a. −2.0, −9.9 cm
18-2b. 1.0, 5.0
18-2c. 1.0, 5.0 cm
18-3a. −1.50, −1.80 cm
18-3b. 0.140, 0.200
18-3c. 0.50, 0.99 cm
18-4. 150, 200 cm
19-1a. 4.00, 9.50 cm
19-1b. −1.00, −4.00
19-1c. −1.00, −4.00 cm
19-2a. −3.0, −9.0 cm
19-2b. 1.5, 2.5
19-2c. 1.5, 2.5 cm
19-3a. −2.50, −3.50 cm
19-3b. 0.30, 0.50
19-3c. 1.50, 2.50 cm
19-4a. 3.30, 4.80 cm
20-1. 10.0, 13.0 cm
20-2a. 40.0, 70.0 mm
20-2b. 0.10, 0.70 mm
20-2c. 0.040, 0.099 mm
20-2d. 0.010, 0.040 mm
20-3. −40, −60 cm
20-4. 10, 90 cm
21-1a. 0.100, 0.150◦
21-1b. 0.150, 0.200◦
21-1c. 1.30, 1.60
21-2. 1.2, 2.5 cm
21-3. 5.0, 9.9 mm
21-4a. 0.150, 0.250 mm
21-4b. 1.00, 1.60◦
21-4c. 30.0, 60.0 cm
22-1. 160, 300 Hz
22-2. 1.9, 3.7 mm
22-3. 400, 800 ± 10 nm
23-1. 100, 150 nm
23-2. 480, 660 nm
23-3. 200, 400 nm
23-4a. 10, 40 m
23-4b. 10, 40 m
24-1. 0.20, 0.60 mm
24-2. 0.50, 0.99 mm
24-3. 1.0, 9.0 km
24-4a. 0.80, 1.30 D
24-4b. 1.00, 1.60 λ
24-5a. 1.00, 1.50 m
24-5b. 2.00, 4.00 m
25-1. 30, 50◦
25-2. 60.0, 70.0◦
26-1. 0.999900, 0.999990c
26-2. 6.0 × 10−12 , 9.9 × 10−12 m
26-3. 0.999880, 0.999950c
26-4a. 5.0, 8.0 years
26-4b. 10.0, 12.0 years
27-1a. 40.0, 70.0 years
27-1b. 0.060, 0.099 years
27-1c. 40.0, 70.0 years
27-2. 0.65, 0.95c
27-3. 0.950, 0.990c
27-4. 0.100, 0.400c
28-1. 0.850, 0.950c
28-2a. 0.50, 0.99 keV
28-2b. 50, 99 keV
28-3a. 200, 950 ± 10 keV
28-3b. 0.700, 0.950c
28-4a. 0.960, 0.990c
28-4b. 1.00 × 10−21 , 1.60 × 10−21 kg · m/s
28-4c. 3.00, 5.00 ns
29-1. 1.70, 2.50 eV
29-2. 3.0 × 10−13 , 7.0 × 10−13 m
29-3. 0.40, 0.99 eV
29-4a. 0.1540, 0.1650 nm
29-4b. 220, 270 eV
30-1. 4.90 × 10−25 , 9.70 × 10−25 J
30-2. 2.00 × 10−13 , 6.00 × 10−13 m
30-3a. 1.0 × 10−25 , 5.0 × 10−25 kg · m/s
30-3b. 3.0 × 10−24 , 9.0 × 10−24 J
30-5a. 7.00, 9.50 keV
30-5b. 0.130, 0.180 nm
31-1b. 0.300, 0.800 millimoles
31-1c. 2.00 × 1020 , 5.00 × 1020
31-2a. 5.0 × 1019 , 9.0 × 1019
31-2b. 1.60 × 1020 , 2.10 × 1020
31-3.
31-4.
31-5.
33-3.
80.0, 99.0 h
190, 260/s
6000, 9900 ± 100 years
2.0, 5.0 kg