PHYSICS 126 – Final Exam Total 121

PHYSICS 126 – Final Exam
Name:
Student ID:
Answer the questions in spaces provided on each sheet. If you run out of
room for an answer, continue on the back.
One Sheet of Notes may be used.
Exam Time: 2 hours
Question Points Score
1 11
2 8
3 19
4 29
5 24
6 30
Total 121
Page 1 of 8

1. An object is placed 6 cm from a lens with a focal length of 3 cm.
3 (a) Ray trace the object to find the location of the image. Label your diagram with
the object distance and the image distance.
F
F
3 (b) Is the image real or virtual? Explain.
5 (c) Using the lens equation, find the image distance.
Page 2 of 8

2. An object is placed 2 cm from a mirror with a focal length of 4 cm.
3 (a) Ray trace the object to find the location of the image. Label your diagram with
the object distance and the image distance.
C
F
5 (b) Using the mirror equation, find the image distance.
Page 3 of 8

3. A 1 cm radius pipe connects a 3 m tall water tower to a faucet.
7 (a) What is the gauge pressure at the faucet when the faucet is closed?
12 (b) What is the gauge pressure at the faucet if the faucet is opened so that there is a
flow of 0.2 l/s? Assume that the water flow is laminar.
Page 4 of 8

4. A violin has four strings that are 32 cm long and are typically tuned to concert G, D,
A, and E (196 Hz, 294 Hz, 440 Hz, and 660 Hz).
7 (a) What is the wavelength of the fundamental mode of oscillation on the A string?
Sketch the waveform.
7 (b) What is the wavelength of the sound in air when the D string is played (at 294 Hz)?
Assume that the velocity of sound in air is 343 m/s.
15 (c) Calculate the frequency of the third harmonic (second overtone) on the D string
and the second harmonic (first overtone) on the A string. You will find that the
harmonics have similar frequencies. What is the beat frequency between the two
harmonics?
Page 5 of 8

5. The Pacific Crest Trail stretches from Mexico to Canada through the mountains of
California, Oregon and Washington. Hikers on this trail must carefully estimate the
amount of fuel they will need. They will typically carry a small camp stove which
produces 700 J/s of heat (this is heat added to the food, extra heat is needed to heat the
pan, stove, air, and ground, but we will ignore that) and which burns 0.15 l/h of fuel.
5 (a) If the initial water temperature is 10 ◦ C, how much time is required to bring 5 l of
water to boiling temperature?
9 (b) How much time will be required to melt 5 kg of ice which has an initial temperature
of -5 ◦ C? The final temperature will be 0 ◦ C.
10 (c) Water found in mountain streams is often boiled for 10 min to make sure that it is
safe to drink. If the camp stove is used to boil 5 l of water for 10 min, how much
water is vaporized?
Page 6 of 8

6. A heat engine containing an ideal gas has a reversible cycle which consists of 2 constant
volume segments with V = 1 l and V = 3 l and two constant pressure segments
with P = 1 atm and P = 2 atm (see figure below). The temperature at point “c” is
T c = 273 K.
5 (a) Is the path of the cycle clockwise or counter-clockwise? Explain.
10 (b) How much work is done by the engine in one cycle?
15 (c) What is the efficiency of the engine? Notice that this is a reversible engine, so recall
the efficiency of a Carnot engine and use the ideal gas law.
Page 7 of 8

Physical Constants
2 Speed of light in vacuum
3.00×10 8 m/s
Average acceleration due to gravity on earth 9.8 m/s 2
Avogadro’s number
6.02×10 23 mol −1
Boltzman’s constant
1.38×10 −23 J/K
Universal gas constant
8.315 J/molK
Absolute Zero
-273 ◦ C
Standard temperature 273 K (0 ◦ C)
Density of air 1.29 kg/m 3
Density of water 1000 kg/m 3
Specific heat of water
4186 J/kg ◦ C
Specific heat of ice
2100 J/kg ◦ C
Latent heat of fusion for water
3.33×10 5 J/kg
Latent heat of vaporization for water 22.6×10 5 J/kg
Index of refraction for water 1.3
Index of refraction for glass 1.5
1 l = 1×10 −3 m 3
1 atm = 1×10 5 N/m
Page 8 of 8