Phys123_2021-22_Q2_Final
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University of Washington *
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Subject
Mathematics
Date
Jan 9, 2024
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Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 1 I. Lecture Multiple choice (70 points –
21 questions) Use the following scenario for the next two questions. Suppose a block on a frictionless surface is attached to a massless horizontal spring with a spring constant of 150 N/m. The block is displaced by 𝐴 = 0.20
m from the equilibrium position, as shown. Then the block is let go, causing it to oscillate. 1)
(3 pts) As the block reached the left most extent for the first time, which of the following statements are correct? i.
The magnitude of acceleration of the block is maximum. ii.
The speed of the block is maximum. iii.
There is a force on the block directed to the right. A.
i. only B.
ii. only C.
iii. only D.
i. and iii. E.
None of these statements are correct. 2)
(3 pts) When the block is 0.10 m from the equilibrium position (half of the initial displacement), what is kinetic energy of the block? A.
0.75 J B.
1.50 J C.
2.12 J D.
2.25 J E.
3.00 J 3)
(3 pts) One end of a horizontal string is attached to a vibrator, and the other end is fixed in place. The string has a length of ? = 3.0
m and a mass per unit length of 7.8 × 10
−4
kg/m. When the vibrator oscillates with a frequency of 30.0 Hz the standing wave shown in the figure is produced. What is the tension in the string? A.
0.047 N B.
0.70 N C.
1.6 N D.
2.8 N E.
6.3 N
2 4)
(3 pts) A wave machine is 1.0 m long (like those used in the demos for transverse waves), and transverse waves propagate along the wave machine at 0.25 m/s. The end at 𝑥 = 0.0
m is free
and the end at 𝑥 = 1.0
m is fixed
. A wave pulse is generated at 𝑥 = 0.0
m, and the displacement curve at 𝑥 =
0.0
m before any reflections is shown at right. Which of the following shows the wavefunction at 𝑡 = 8.0
s? 5)
(3 pts) Two coherent sources S
1
and S
2
emit waves with frequency 𝑓 = 150
Hz in a medium with wave speed ? = 3.0
m/s. In the configuration shown at right, point P is on a nodal
line, 15 cm away from S
2
. Now suppose that source S
2
is moved along the dashed diagonal line, for what positions of S
2
will P
now be on an antinodal
line? i.
3.0 cm further away from P. ii.
2.0 cm closer to P. iii.
1.0 cm further away from P A.
i. only B.
ii. only C.
iii. only D.
i. and ii. E.
i. and iii.
Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 3 6)
(4 pts) A construction worker is using a jack hammer to break concrete. The sound intensity is 2.4 W/m
2
at a distance of 1.8 m from the jack hammer. What is the sound intensity level at a distance of 45 m from the jack hammer? A.
70 dB B.
84 dB C.
96 dB D.
110 dB E.
124 dB 7)
(3 pts) A light ray travels from air into a long cylindrical pipe of acrylic of length ? = 20
m. The light enters the pipe at the center of its circular face at one end. The angle the light ray makes with the normal after it enters the pipe is 𝜃 = 30
°, as shown. The indices of refraction of air and acrylic are ?
1
= 1.0
and ?
2
= 1.5
, respectively. What is the distance travelled by the light ray when it exits the pipe at the other end? A.
The light ray does not exit the other end of the pipe. B.
10 m C.
17 m D.
23 m E.
40 m 8)
(4 pts) You make an image of an object with a pinhole camera shown at right. The distance between the object and the pinhole is 1.5 m. At what distance from the pinhole do you have to place the screen to obtain a magnification of ? = −5
? A.
0.10 m B.
0.30 m C.
0.50 m D.
5.0 m E.
7.5 m
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4 9)
(3 pts) An object is placed at ? = 30
cm in front of a mirror. If the mirror forms a real image with magnification |?| = 0.1
, what is the type and radius of curvature ?
of the mirror? A.
Diverging mirror with ? = 3.3
cm B.
Converging mirror with ? = 3.3
cm C.
Converging mirror with ? = 5.5
cm D.
Diverging mirror with ? = 5.5
cm E.
Diverging mirror with ? = 6.7
cm Use the following scenario for the next two questions. A beam of x-rays with a wavelength of 2.6 × 10
−10
m is fired at a crystal. The crystal has a flat surface and the distance between layers in the crystal is 4.0 × 10
−10
m. 10)
(3 pts) What is the maximum Bragg angle at which you observe a diffraction maximum? A.
13
°
B.
19
°
C.
41
°
D.
71
°
E.
77
°
11)
(4 pts) Now instead of x-rays, you fire electrons. If you observe diffraction maximum at the same angles as with the x-rays, what is the speed of the electrons? Note that the mass of an electron is ?
𝑒
= 9.1 × 10
−31
kg. A.
1.8 × 10
6
m/s B.
2.1 × 10
6
m/s C.
2.8 × 10
6
m/s D.
4.3 × 10
6
m/s E.
There is no electron speed that could produce a diffraction maximum 12)
(3 pts) Consider a thin film of oil on the surface of flat acrylic. The index of refraction of oil is ?
𝑜
= 1.40
, and the index of refraction of acrylic is ?
𝑎
= 1.50
. Light with wavelength 580 nm in air is incident very close to normal to the surface of the oil, and you observe that the reflected light has minimum intensity. What is the minimum increase
in the thickness of the oil so that the reflected light would again have minimum intensity? A.
104 nm B.
145 nm C.
193 nm D.
207 nm E.
290 nm
Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 5 Use the following scenario for the next two questions. A U tube is initially filled with mercury (
𝜌 = 13.5 × 10
3
kg
·
m
-3
) to the same height on both sides of the tube. A stopper with a pressure gauge is then inserted on the right-hand side of the tube. Mercury is slowly removed from the left-hand side of the tube until the level on the right-
hand side drops by 𝛥ℎ
2
= 0.10
cm and the pressure gauge reads ?
gauge
= −1500
Pa. The removal of the mercury is a quasistatic process and the system is in excellent thermal contact with its environment. 13)
(4 pts) By how much does the mercury level drop on the left-hand side of the tube 𝛥ℎ
1
? A.
0.11 cm B.
1.2 cm C.
7.4 cm D.
11 cm E.
76 cm 14)
(3 pts) What is the distance between the bottom of the stopper to the mercury level on the right-hand side of the tube in the final state? A.
0.11 cm B.
2.0 cm C.
6.8 cm D.
10 cm E.
Not enough information to answer the problem. 15)
(3 pts) A syringe with a barrel of cross-sectional area of 𝐴
1
= 1.0 × 10
−4
m
2
and a spout of cross-sectional area 𝐴
2
= 1.0 × 10
−6
m
2
is filled with water (
𝜌 = 1.0 × 10
3
kg
·
m
-3
). A force is applied to the syringe such that the difference in pressure between the back of the syringe, P
1
, and the spout, P
2
, is 5.0 × 10
3
Pa. At what speed does water flow out of the spout?
A.
2.8 m
·
s
-1
B.
3.2 m
·
s
-1
C.
4.5 m
·
s
-1
D.
28 m
·
s
-1
E.
32 m
·
s
-1
6 16)
(3 pts) A thermally insulated box is separated by a partition that is free to move and transfer thermal energy between sides of the partition. ?
?
= 1.0 × 10
24
particles of monatomic (
? = 3
) ideal gas A are placed on one side of the partition, and ?
?
= 6.0 × 10
23
particles of diatomic (
? = 5
) ideal gas B are places on the other side of the partition. The system of the two gases is in equilibrium. Which of the following macroscopic variables ?
𝑡ℎ
, 𝑇
, ?
, and 𝑉
are equal for both gases? A.
All: ?
𝑡ℎ
, 𝑇
, ?
, and 𝑉
B.
?
𝑡ℎ
, 𝑇
, and ?
only C.
𝑇
, ?
, and 𝑉
only D.
?
𝑡ℎ
, and 𝑉
only E.
𝑇
, and 𝑉
only 17)
(3 pts) A box contains ? = 1.0 × 10
24
monoatomic gas molecules. If the temperature of the gas is 𝑇 = −23
°C
, what is the average kinetic energy per particle, ?
𝑎𝑣
? A.
1.7×10
-21
J B.
5.2×10
-21
J C.
8.6×10
-21
J D.
1.7×10
-20
J E.
5.2×10
-20
J 18)
(4 pts) In an isochoric process, energy ?
is transferred thermally into a container filled with 1.5 × 10
23
helium atoms. If the temperature of the helium increases by 0.3 K, what is ?
? Helium is a monatomic gas with ? = 3
and its heat capacity per particle at constant pressure is ?
𝑃
= 3.46 × 10
−23
J K
-1
. A.
0.94 J B.
1.3 J C.
1.6 J D.
2.3 J E.
3.3 J
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Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 7 19)
(4 pts) Consider the process shown in the PV diagram at right for an ideal gas. The process is isothermal. What is the work done on or by the gas in the process 1
→
2? A.
11.5 J done by
the gas B.
16.6 J done by the gas C.
21.5 J done on the gas D.
31.5 J done by the gas E.
31.5 J done on
the gas 20)
(3 pts) Gas in a heat engine undergoes the Carnot cycle shown in the PV diagram at right. Which of the following statements are correct? i.
The change in entropy ΔS of the gas after one complete cycle is zero. ii.
The change in entropy ΔS of the gas during process 2 to 3 is positive. iii.
The change in entropy ΔS of the gas during process 1 to 2 is zero. A.
i. only. B.
i. and ii. C.
i. and iii. D.
ii. and iii. E.
All of the statements are correct. 21)
(4 pts) A Carnot engine operates with energy transferred thermally into the engine at 355 K and energy transferred thermally out of the engine at 300 K. If the energy transferred thermally out of the gas in a single cycle of the engine is 710 J, what is the work done by the gas in a single cycle? A.
130 J B.
840 J C.
3872 J D.
4582 J E.
6000 J
8
Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 9 II. Lab multiple choice (15 points –
4 questions) 22)
(3 pts) In lab A1 you used Excel to make a simulation of a ball of mass ?
hanging from a vertical spring with spring constant 𝑘
. Let y
0
, v
0
, and a
0
, respectively, represent the position, velocity, and acceleration of the ball at time t
0
. You calculated the position and
velocity a short time, d
t
, later using the equations: v
1
= v
0
+ a
0
*d
t
and y
1
= y
0
+ v
1
*dt
, respectively. Why is this only valid for a short time interval? A.
Computer simulations store numbers with limited precision, so if you use long time intervals, the precision of the numbers causes large errors. B.
These equations assume constant acceleration and velocity, respectively, and if the time interval is too long, then this assumption causes large errors. C.
We only considered short time intervals so that we could plot an animation of the ball position. 23)
(4 pts) In lab A3 you were asked to modify the simulation in some way and explore how the modification affected the behavior of a wave propagating down a string. For each non end ball in the original simulation there is a force due to the spring on the left, F_left
, and right, F_right
. Your group decided to add an additional force on the ball due to friction given by the equation F_fric
= -f*ball.v
, where ball.v
is the current velocity of the ball and f
is a constant that was varied as the independent variable. Which of the following would make good possible dependent variables? i.
The height of the pulse after 1 second. ii.
The width of the pulse when the pulse has travelled halfway down the string. iii.
The initial amplitude of the pulse. A.
i. only B.
ii. only C.
i. and ii. D.
i. and iii. E.
All of these would make good dependent variables. 24)
(4 pts) Coherent monochromatic light is incident on a mask with 3 evenly spaced identical slits. The resulting pattern observed on a screen placed some distance from the mask is shown at top right. Point C represents the center of the screen. Which point on the screen corresponds to a point with the phasor diagram at bottom right? A.
Point X B.
Point Y C.
Point Z D.
Both points Y and Z
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10 25)
(4 pts) In lab B2 you shone a laser with a wavelength of 650 nm through a mask with two slits separated by a center-to-center spacing ?
. You observed the diffraction pattern on a screen placed 1.5 m from the mask and measured the distance between the central bright spot and the bright spot to the right of it, ?
. You performed these measurements with the following mask parameters: ? = 0.125
mm and slit widths of 0.04 mm. ? = 0.250
mm and slit widths of 0.04 mm. You then simulated the same setup, but obtained measurements with many values of ?
. You made the following plot from your measurements of the physical setup and your simulation. From your measurements, what can you conclude about the relationship between ?
and ?
? i.
The simulation measurements are consistent with 1/?
being proportional to ?
. ii.
The physical setup measurements are consistent with 1/?
being proportional to ?
. iii.
Increasing the wavelength of light used would increase ?
. A.
i. only B.
iii. only C.
i. and ii. D.
i. and iii. E.
We can conclude all of the statements.
Name ___________________________________________UW net ID ____________________ last first Phys 123A Final exam 11 III. Tutorial multiple choice (15 points –
5 questions) 26)
(3 pts) Students 1 and 2 each generate a single transverse pulse by moving the ends of a spring at unknown times. Originally, there was a line of cups, numbered 1 to 6, below the spring, as shown below. The diagram shows the pulses before any cups are knocked over. After the pulses have reached the opposite ends, which of the cups are knocked over? A.
Cups 5 and 6. B.
Cup 4 only. C.
All cups except cup 4. D.
All the cups. E.
None of the cups. 27)
(3 pts) Two point sources (
S
1
and S
2
) separated by a distance ?
generate periodic waves by tapping the surface of the water with the frequency 𝑓
. The sources produce waves with wavelength 𝜆
. The following diagram shows the interference created: antinodal lines
are represented by solid lines
and nodal lines
are represented by dashed lines.
A.
Between 1.5λ and 2λ
B.
2λ
C.
Between 2λ and 2.5λ
D.
2.5λ
E.
Betwe
en 2.5λ and 3λ
12 28)
(3 pts) A U tube is partially filled with water as shown. The left side of the tube is open to the atmosphere. The right side is sealed so there is no air between the stopper and the water. How does the pressure at point P, ?
𝑃
, compare to atmospheric pressure, ?
𝑎𝑡𝑚
? A.
?
𝑃
= 0
B.
0 < ?
𝑃
< ?
𝑎𝑡𝑚
C.
?
𝑃
= ?
𝑎𝑡𝑚
D.
?
𝑃
> ?
𝑎𝑡𝑚
29)
(3 pts) An ideal gas is confined to a cylindrical chamber with a moveable piston. The PV
diagram at right shows a sequence of two thermodynamic processes on the gas. The solid lines represent one process and the dashed lines represent the second, distinct process. The units of P
and V in the diagram are arbitrary. Is the absolute value of the change in internal energy during process X→1→Z
greater than, less than,
or equal to
the absolute value of the change in internal energy during process X→2→Z
. A.
equal to B.
greater than C.
less than D.
Not enough information to answer. 30)
(3 pts) The device shown at right represents a heat engine operating between thermal reservoirs at T
=300 K and T
=800 K. The numbers and arrows indicate either energy transferred thermally or work done during each cycle. Which of the following statements are correct? i.
This heat engine violates the 1
st
law of thermodynamics (conservation of energy). ii.
This heat engine violates the 2
nd
law of thermodynamics. iii.
This heat engine represents a Carnot cycle. A.
i. only B.
ii. only C.
iii. only D.
i. and ii. E.
None of these statements are correct.
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