Final_Exam_2112_Sp22
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Louisiana State University *
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Course
2112
Subject
Mechanical Engineering
Date
Dec 6, 2023
Type
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9
Uploaded by BarristerHawkMaster195
1
PHYS 2112
Spring 2022
Final Exam
May 9, 2022
Last Name
(print)_________________________
First Name
(print)_________________________
Signature ________________________________
LSUID No. ______________________________
TURN OFF AND PUT AWAY ANY AND ALL
NONAPPROVED ELECTRONIC DEVICES.
Have your LSU ID ready when you turn in your paper.
You may only use an ordinary scientific or graphing
calculator.
You may not use a cell phone, smart phone, or
tablet application as your calculator.
Examine your paper to be sure it is complete and legible.
There should be 20 multiple-choice questions and 4 free-
response problems points. There are 9 pages, including the
cover sheet.
For the multiple choice questions
, bubble in the correct answer on your ScanTron for each question.
There is room on the exam for scratch work or calculations, but that work will not be checked or graded.
Partial credit may be awarded on multiple-choice questions, but this partial credit will be based on the
answers that you have bubbled in on the ScanTron and NOT on your scratch work on the exam itself.
For the free-response problems, show all relevant work in the space provided.
Without supporting
work, even a correct answer will receive little or no credit. Partial credit will be awarded as warranted.
If your work for a problem is somewhere other than the space provided for that part of the problem, you
must indicate where your work is located.
For example, if you need more room for your solution, then
you may write on the back of the page. Be sure to add a note to this effect; otherwise, anything on the
back of the paper will be regarded as scratch work and will not be checked or graded.
Be sure that numerical answers appear with appropriate
SI units
. Points will be deducted for missing,
incorrect, or "silly" units. In addition, you must carry the units through each calculation – it is not
enough to just stick the correct units onto your final answer. If the final answer is, in fact, a
dimensionless quantity, please write the numerical result followed by the word dimensionless.
You will have 120 minutes to complete this examination.
°
Your free response will be graded for consistency.
That is, if you need a
quantity from a previous part and didn’t get it right or could not complete
it, you will be graded on your work for the part you are working on.
Circle one:
MWF 11:30 am (M. Gaarde)
MWF 1:30 pm (M. Tzanov)
TTh 9:00 am (S. Marley)
2
Question #1 (no points)
Bubble in the answer choice corresponding to your class section number.
A.
Sec. 1; MWF 11:30 am (M. Gaarde)
B.
Sec. 2; MWF 1:30 pm (M. Tzanov)
C.
Sec. 3; TuTh
9:00 am
(S. Marley)
Question #2 (no points)
Your version of the test is
A
. Bubble in answer
A
on your ScanTron.
Question #3 (5 points)
1.2-kg lead ball is heated to 75.0 °C and dropped into an ideal calorimeter
containing 0.7 kg of water initially at 10.0 °C. What is the final equilibrium temperature of the lead ball?
The specific heat capacity of lead is 128 J/(kg · C°); and the specific heat of water is 4186 J/(kg · C°).
A.
19.7 °C
B.
13.2 °C
C.
66.4 °C
D.
20.8 °C
E.
42.1 °C
Question #4 (5 points)
A Carnot engine operates between hot and cold reservoirs with temperatures
710 °C and 46 °C, respectively. If the engine performs 3700 J of work per cycle, how much heat is
extracted per cycle from the hot reservoir?
A.
6441 J
B.
2001 J
C.
1669 J
D.
5478 J
E.
1120 J
Question #5 (5 points)
One mole of an ideal gas expands reversibly and isothermally at temperature T
until its volume has tripled. The change of entropy of this gas for this process is:
A.
17.3 J/K
B.
9.1 J/K
C.
11.5 J/K
D.
18 J/K
E.
26.9 J/K
Question #6 (5 points)
A transverse periodic wave on a string with a linear density of 0.10 kg/m is
described by the following equation:
y
= 0.1 sin(16
x
-181
t
), where
x
and
y
are in meters and
t
is in
seconds. What is the tension in the string?
A.
6.6 N
B.
21.0 N
C.
43.1 N
D.
10.2 N
E.
12.8 N
3
Question #7 (5 points)
Two sinusoidal waves have the same angular frequency, the same amplitude
y
m
,
and travel in the same direction in the same medium. If they differ in phase by 32°, the amplitude of the
resultant wave is given by:
A.
0.85
y
m
B.
1.70
y
m
C.
0.96
y
m
D.
1.92
y
m
E.
0.42
y
m
Question #8 (5 points)
A stationary source S generates circular outgoing waves on a lake. The wave
speed is 6.0 m/s and the crest-to-crest distance is 1.8 m. A person in a motor boat heads directly toward
S at 2.1 m/s. To this person, the frequency of these waves is:
A.
1.4 Hz
B.
2.2 Hz
C.
2.5 Hz
D.
4.5 Hz
E.
5.1 Hz
Question #9 (5 points)
A point source emits electromagnetic energy at a rate of 100 W. The intensity
10 m from the source is:
A.
10 W/m
2
B.
1.6 W/m
2
C.
1.0 W/m
2
D.
0.080 W/m
2
E.
0.024W/m
2
Question #10 (5 points)
The diagram shows the passage of a ray of light from
air into a substance X. The index of refraction of X is:
A.
0.53
B.
0.82
C.
1.2
D.
1.9
E.
3.0
Question #11 (5 points)
A converging lens has a focal length of 12 cm. If an object is placed 6 cm
from the lens, the image is:
A.
4 cm from the lens on the side of the object
B.
4 cm from the lens on the opposite side of the object
C.
12 cm from the lens on the side of the object
D.
12 cm from the lens on the opposite side of the object
E.
at infinity
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4
Question #12 (5 points)
In the figure, three pulses of light—
a
,
b
, and
c
—of the same wavelength are
sent through layers of plastic having the given indexes of refraction and along the paths indicated. Rank
the pulses according to their travel time through the plastic layers, greatest first.
a)
a>b>c
b)
b>c>a
c)
c>a>b
d)
a=b=c
e)
a>c>b
f)
c>b>a
Question #13 (5 points)
In a Young's double-slit experiment, light of wavelength 500 nm illuminates
two slits which are separated by 1 mm. The separation between adjacent bright fringes on a screen 5 m
from the slits is:
A.
0.10 cm
B.
0.25 cm
C.
0.50 cm
D.
1.0 cm
E.
none of the above
Question #14 (5 points)
The Hubble space telescope is in orbit around the earth.
The aperture diameter
of the telescope is 2.6 m.
You are using the telescope to look at the cover of your physics textbook
sitting on the surface of the earth.
In green light (550 nm) Hubble can resolve the letters “P” and “y” in
the word “Physics” on the cover.
These two letters are separated by a distance of 7.5 cm.
What is the
height of Hubble’s orbit?
(Neglect the effects of earth’s atmosphere.)
A.
355 km
B.
319 km
C.
499 km
D.
112 km
E.
291 km
Question #15 (5 points)
In a Compton-shift experiment, light of wavelength 0.1 nm is scattered in the
forward direction, at
ϕ
= 45° in the figure after transferring energy to an electron.
What is the Compton
shift, Δλ, of the photon?
A.
0.100 nm
B.
0.107 nm
C.
0.710 pm
D.
0.099 nm
E.
1.150 pm
5
Question #16 (5 points)
Consider the following three particles:
Rank them according to the de Broglie
wavelengths, from least to greatest
1.
a free electron with speed
v
0
2.
a free proton with speed
v
0
3.
a free proton with speed 2
v
0
A.
1 < 2 < 3
B.
3 < 2 < 1
C.
2 < 3 < 1
D.
2 = 3 <
1
E.
1 < 2 = 3
Question #17 (5 points)
A proton is confined to a nucleus that has a diameter of 4.5×10
-15
m.
If this
distance is considered to be the uncertainty in the position of the proton, what is the minimum
uncertainty in its velocity?
A.
1.4 ×10
7
m/s
B.
4.4 ×10
7
m/s
C.
1.3 ×10
10
m/s
D.
8.2 ×10
5
m/s
E.
3.9 ×10
6
m/s
Question #18 (5 points)
In the figure, objects A, B, and C have the same
volume.
Rank, in order, the sizes of the magnitude of the buoyant
forces F
A
, F
B
, and F
C
on A, B, and C:
A.
F
C
= F
B
= F
A
B.
F
C
> F
B
> F
A
C.
F
c
> F
B
= F
A
D.
F
A
= F
C
> F
B
E.
F
A
> F
B
> F
C
Question #19 (5 points)
A hydraulic press has one piston of diameter 2.0 cm and the other
piston of diameter 8.0 cm. What force must be applied to the smaller piston to
obtain a force of 1600 N at the larger piston:
A.
1600 N
B.
400 N
C.
100 N
D.
6400 N
E.
200 N
Question #20 (5 points)
A helium blimp is cruising slowly at low, constant altitude wherein the density
of air is 1.21 kg/m
3
.
The volume of the helium-filled interior space is 5,500 m
3
and the density of
helium gas is 0.16 kg/m
3
.
What is the total weight of the crew and cargo?
A.
65.2 kN
B.
56.6 kN
C.
48.3 kN
D.
36.4 kN
E.
8.6 kN
6
Problem #1 (27 points) – SHOW YOUR WORK!!!
The figure shows a reversible cycle where 1.25 moles of a
diatomic ideal gas is taken, where,
P
a
= 6×10
5
Pa, P
b
= 2×10
5
Pa , V
a
= V
c
= 3.5×10
-3
m
3
. As shown, process
ab
is an
isothermal expansion, process
bc
is isobaric compression, and
process
ca
is an isochoric expansion.
a) (6 points)
Determine the volume at point b (V
b
)
b) (9 points)
Determine the amount of heat transferred during each process (a→b, b→c, c→a).
Specify
whether heat is added or removed.
c) (6 points)
What is the net work done over one cycle?
d) (6 points)
What is the efficiency of this cycle?
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7
Problem #2 (22 points) – SHOW YOUR WORK!!!
In the figure,
S
is a small loudspeaker driven by an audio oscillator and
amplifier, adjustable in frequency from 1000 to 2900 Hz only. Tube
D
is a
piece of cylindrical sheet-metal pipe 50.9 cm long and
open at both ends.
(a)
If the speed of sound in air is 344 m/s at the existing temperature, at
how many frequencies will a resonance occur in the pipe when the
frequency emitted by the speaker is varied from 1000 Hz to 2900 Hz?
(b)
What is the lowest resonant frequency in the given interval?
(c)
What is the lowest resonant frequency of the pipe?
8
Problem #3 ( 22 points) -
SHOW YOUR WORK!!!
A sodium vapor lamp is placed at the center of a large hollow sphere made of LiH (Φ
LiH
= 1.85 eV) that
absorbs all of the light reaching it.
The rate at which the lamp emits energy is 100 W; assume that the
emission from the sodium lamp is entirely at a wavelength of 589 nm.
a) (5 points)
What is the energy of a photon emitted by the sodium vapor lamp, in units of eV?
b) (6 points)
At what rate are the photons absorbed by the LiH sphere?
c)
(5 points)
What is the maximum kinetic energy of photoemitted electrons from the LiH?
d) (6 points)
What is the de Broglie wavelength of the photemitted electrons from part c) ?
9
Problem #4 (24 points)
-
SHOW YOUR WORK!!!
In the figure, the fresh water behind a
reservoir dam has depth
D
=
16.5 m. A horizontal pipe passes through the dam at depth
h
=
7.40 m. The pipe at point
1
has an area of
a
1
= 75.0 cm
2
and then
narrows to an area of
a
2
= 25.0 cm
2
as it exits the dam at point
2
.
Originally, a plug (shown black in the figure) secures the pipe
opening at point
2
.
[
The area of the reservoir is VERY large compared with
the cross-sectional area of the pipe]
a) (5 points)
With the plug in place (no flow through pipe), what
is the
gauge
pressure
(difference between absolute pressure
and atmospheric pressure)
at point
1
?
b) (8 points )
The plug is now removed.
What is the velocity of the water exiting the dam through the
pipe at point
2
?
[hint: only consider the opening in the dam at point
2
; forget about point
1
]
c) (6 points)
With the plug removed, what is volume flow rate (
R
V
) at point
2
(hint: = point
1
)
?
d) (5 points)
With the plug removed, what is the velocity of the water flowing through the pipe at point
1
?
1
!
!
2
h
a
1
=75 cm
2
a
2
= 25
cm
2
=7.40 m
=16.5 m
p
0
=1 atm
p
0
=1 atm
Water
Dam
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