PHYSICS 221
Fall 2007
FINAL EXAM: December 10, 2007 7:00-9:00 pm
Name (printed): ______________________________________________
Recitation Instructor: _________________________
Section #_______
INSTRUCTIONS:
This exam contains 25 multiple-choice questions plus 2 extra credit questions, each worth 4
points. Choose one answer only for each question. Choose the best answer to each question.
Answer all questions.
Allowed material: Before turning over this page, put away all materials except for pens, pencils,
erasers, rulers and your calculator. There is a formula sheet attached at the end of the exam.
Other copies of the formula sheet are not allowed.
Calculator: In general, any calculator, including calculators that perform graphing, is permitted.
Electronic devices that can store large amounts of text, data or equations (like laptops, palmtops,
pocket computers, PDA or e-book readers) are NOT permitted. If you are unsure whether or not
your calculator is allowed for the exam, ask your TA.
How to fill in the bubble sheet:
Use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one.
Write and fill in the bubbles corresponding to:
Your last name, middle initial, and first name.
  Your ID number (the middle 9 digits on your ISU card)  
Special codes K to L are your recitation section. (Honors section, please enter 24). Always use
two digits (e.g. 01, 09, 11, 13)
Please turn over your bubble sheet when you are not writing on it.
If you need to change any entry, you must completely erase your previous entry. Also, circle
your answers on this exam. Before handing in your exam, be sure that your answers on your
bubble sheet are what you intend them to be. You may also copy down your answers on a piece
of paper to take with you and compare with the posted answers. You may use the table at the
end of the exam for this.
When you are finished with the exam, place all exam materials, including the bubble sheet, and
the exam itself, in your folder and return the folder to your recitation instructor.
No cell phone calls allowed. Either turn off your cell phone or leave it at home. Anyone
answering a cell phone must hand in their work; their exam is over.
Best of luck, Paul Canfield and Paula Herrera
55. Three capacitors and a battery are connected as shown below. The capacitors are fully
charged. The charge in capacitor #3 is 20 nC. What is the emf of the battery?
C1
C3
C1 = 1.0 nF
C2 = 2.0 nF
C3 = 3.0 nF
C2
V0
A)
B)
C)
D)
E)
10 V
13 V
20 V
27 V
30 V
56. A parallel plate capacitor with charge Q is filled and surrounded by vacuum. Let E
and V be the magnitude of the electric field and the magnitude of the potential
difference between the plates, respectively. If the space between the plates is filled
with a dielectric with κ > 1, which of the following comparisons to the unfilled
capacitor is true?
A)
B)
C)
D)
E)
E increases, V remains the same
E decreases, V decreases
E remains the same, V remains the same
E increases, V decreases
E decreases, V remains the same
57. The circuit below consists of three resistors and three ideal batteries. Find the current
through the 2.0 Ω resistance.
A)
B)
C)
D)
E)
5.0 Ω
1.4 A
2.2 A
4.3 A
5.0 A
10 A
2.0 Ω
20 V
5.0 Ω
10 V
58. A brick-shaped object with dimensions 1.0 cm × 0.1 cm × 0.1 cm is made of some
ohmic material with resistivity 1.0 × 10–7 Ω m. What is the resistance to an electric
current flowing along the long side?
A. 10−1 Ω
B. 10−3 Ω
C. 10−5 Ω
D. 10−9 Ω
E. 10−11 Ω
10 V
59. A positive point charge is placed near a solid conducting sphere. Consider points X,
Y on the surface of the sphere, and point O, the center of the sphere. Rank the electric
potential at these points:
A. VX < VO < VY
B. VX = VO = VY
C. VX > VO > VY
D. VX = VY > V0
E. VX = VY < V0
X●
+
O●
Y●
60. Two point charges are fixed as shown. Find the electric potential at point P, assuming
the potential is zero at infinity.
y
9
A. −4.5 × 10 V
B. −2.3 × 109 V
C. −1.9 × 109 V
D. 0
a
Q1 = 1.0 C
E. 1.1 × 1010 V
Q2 = −2.0 C
Q2
Q1
x
a = 2.0 m
a
●
P
61. Four identical bulbs are connected to an ideal battery as shown below. Rank the
brightness of the bulbs, from brightest to dimmest.
A. B1 = B4 > B2 = B3
B. B1 > B4 > B2 = B3
C. B1 > B4 > B2 > B3
D. B4 > B1 > B2 = B3
E. B4 = B1 > B2 > B3
1
2
4
3
62. A parallel plate capacitor, filled with air, is charged by a battery through copper wires
with length L and cross-sectional area A. For some applications, the charging of the
capacitor (e.g., to reach 95% of the applied potential difference) needs to be done as
fast as possible. Which of the following is the most efficient way to speed up such a
charging process?
A.
B.
C.
D.
E.
Double the emf of the battery
Double the resistance of the wire, R.
Insert a dielectric with κ = 2 between the plates.
Double the length of the wires (keeping the cross-sectional area the same).
Double the cross-sectional area of the wires (keeping their length the same).
63. A non-ideal battery with emf 12 V is connected to points A and B in the circuit
below. An ideal voltmeter connected to points A and B reads 9.0 V. What is the
internal resistance of the battery?
A.
B.
C.
D.
E.
1.8 Ω
2.2 Ω
2.8 Ω
4.2 Ω
6.7 Ω
20 Ω
A●
●B
10 Ω
64. Which of the following diagrams shows the equipotential surfaces produced by two
infinite sheets with identical, uniform charge density σ?
B)
A)
C)
D)
E) None of the above.
65. A book is at rest on a desk top. Which of the following forces forms a Newton’s third
law pair with the book’s weight?
A) The normal force of the table on the book
B) The force of the book on the table
C) The gravitational force of the earth on the book
D) The gravitational force of the book on the table
E) None of the above
66. The sketch below shows the x-dependence of a force. Which point (or points) is a
stable equilibrium point(s)?
A) A
B) B
C) C
D) D
E) both A and C are stable equilibrium points.
67. The graph below shows the potential energy of a force as a function of x.
Potential energy
1 square = 1 J × 1 m
x
Rank the x component of the force (including signs!) associated with this potential at
points x = –2 m, x = –1 m and x = 5 m
A)
B)
C)
D)
E)
Fx(–2 m) < Fx(–1 m) < Fx(5 m)
Fx(–1 m) < Fx(–2 m) < Fx(5 m)
Fx(–1 m) < Fx(5 m) < Fx(–2 m)
Fx(5 m) < Fx(–2 m) < Fx(–1 m)
Fx(5 m) < Fx(–1 m) < Fx(–2 m)
68. Two blocks of masses m and 3m are connected through a massless, ideal string that
runs over an ideal, massless pulley in the arrangement shown below. There is no
friction between the blocks and the surfaces. Determine the magnitude of the
acceleration of the upper block.
A) 1/8 g
B) 1/4 g
C) 3/8 g
D) 1/2 g
E) g
3m
m
30°
69. A 100 g mass is attached to a spring (k = 30 N/m) that is compressed 10 cm from its
equilibrium position. If the coefficient of friction between the mass and the table is
μK = 0.50, what is the velocity of the mass when the spring has expanded by 5.0 cm
(i.e. when the spring is only compressed by 5.0 cm)?
k
μK
m
x = −10 cm x = −5.0 cm
A) 0.61 m/s
B) 0.80 m/s
C) 1.1 m/s
D) 1.2 m/s
E) 1.3 m/s
x=0
70. An insulating rod is balanced at its center of mass and is allowed to rotate about the
origin of the horizontal xy plane. The rod has a positive charge on one end of the rod
and an equally sized, negative charge on the other end of the rod. If an electric field,
E = 1000 N/C j, is applied, how should the rod be oriented so as to have the lowest
potential energy?
A)
B)
C)
D)
E)
Along the x axis, with the positive charge on the positive x side
Along the x axis, with the positive charge on the negative x side
Along the y axis, with the positive charge on the positive y side
Along the y axis, with the positive charge on the negative y side
None of the above
71. A non-uniform rod of mass 1.00 kg and length 2.00 m can rotate freely about an axis
through a point P that is 1.20 m away from the center of mass of the rod. The rod is
released from the horizontal position. When the rod is vertical, the angular speed of
the rod is 4.30 rad/s. What is the moment of inertia of the rod about point P?
A)
B)
C)
D)
E)
1.12 kg m2
1.27 kg m2
1.33 kg m2
1.44 kg m2
1.67 kg m2
P
×
CM
×
CM
72. A playground merry-go-round has a radius of 2.00 m and a mass of 150 kg and can be
treated as a uniform disk. It is spinning with an angular velocity, ω0 = 0.45 s-1. If a
50 kg child, with a velocity of 0.90 m/s runs onto the merry go round as shown
(tangentially, a distance of 2.00 m from the center), what is the new angular velocity
of the combined child /
merry go round system?
A) 1/4 ω0
B) 3/4 ω0
C) ω0
D) 4/3 ω0
E) 4 ω0
73. Treat the orbits of Earth and Mars as essentially circular. A spacecraft is in an orbit
about the Sun with the perihelion point at the orbit of Earth and the aphelion point at
the orbit of Mars. Calculate the flight time for the spacecraft to travel from Earth
orbit to Mars. (The radius of Mars’s orbit is 2.3 × 1011 m and the radius of Earth’s
orbit is 1.5 × 1011 m. The masses of Mars, Earth and the Sun are 6.42 × 1023 kg,
5.97 × 1024 kg, and 1.99 × 1030 kg respectively.)
A)
B)
C)
D)
E)
522 days
261 days
179 days
104 days
88.0 days
74. A proton with speed of 5.00 × 108 cm/s enters an electric field of magnitude
1.00 ×107 N/C, traveling along the field lines, as shown below. If the region with the
electric field is 1.50 cm long, what is the proton’s speed when it emerges from this
region?
A)
B)
C)
D)
E)
1.93 × 108 cm/s
4.44 × 108 cm/s
5.00 × 108 cm/s
5.36 × 108 cm/s
7.33 × 108 cm/s
●
p
plastic
75. An uncharged metal rod is resting on a small stand
rod
uncharged
that is free to rotate. When a negatively charged
plastic rod is brought close to one end (A) of the metal metal rod
rod, the metal rod is attracted toward the plastic rod.
Assume now that the negative rod is removed, and that
instead a positively charged plastic rod is brought in
A
B
turn close to each of the ends of the metal rod.
Which of the following best describes the behavior of
rotating stand
the rod?
A) There will be neither attraction nor repulsion of the metal rod (it is uncharged).
B) The metal rod will be repelled when the plastic rod is near end A, and attracted when
the plastic rod is near end B.
C) The metal rod will be attracted when the plastic rod is near end A, and repelled when
the plastic rod is near end B.
D) The metal rod will be repelled, whichever end is close to the plastic rod.
E) The metal rod will be attracted, whichever end is close to the plastic rod
76. A 300 g mass, shaped like a cube, is attached to a string that is wrapped around a
pulley. The pulley is a uniform disk with a mass of 100 g and a radius of 20 cm and
the string unwinds from the pulley without slipping. What is the acceleration of the
cubic mass as the string unwinds?
A)
B)
C)
D)
E)
6.67 m/s2
7.36 m/s2
7.77 m/s2
8.41 m/s2
9.81 m/s2
77. The graph below shows the time dependent force that a 3.00 kg mass, with an initial
(t = 0 s) velocity of 2.00 m/s in the positive x direction, experiences. If the force is in
the positive x direction, what is the mass’s velocity at t = 1.00 s?
A)
B)
C)
D)
E)
8.33 m/s
10.3 m/s
13.3 m/s
18.7 m/s
None of the above
100
F (N)
200
700
t (ms)
Laboratory Final
Consider a cart whose position is measured with an ultrasonic
transducer (a “motion detector”), as you did in lab. (Assume the
sensor gives positions relative to the X axis illustrated in the figure).
78. From the graphs below, pick one graph that definitely indicates
that the cart has reversed direction. Note the labels on the graph axes!
X
A
X
B
t
Vx
C
t
Vx
D
t
E) None of the above graphs.
79. As in the Collision in Two Dimensions lab, consider
two air pucks sliding with little friction on a smooth,
level surface. Assume they each are moving with
some velocity, collide, and then one subsequently
rebounds from the edge of the table.
Consider the total vector momentum, P, of the two
pucks (only). Let P1 be its value before the collision of
the pucks, P2 its value after collision, and P3 its value
after one of the pucks hits the edge of the table.
Which of the following most accurately describes the
relationship between these quantities?
A)
B)
C)
D)
E)
X
0
P1 = P2 ≠ P3
P1 = P2 = P3
P1 ≠ P2 = P3
P1 ≠ P2 ≠ P3
Without knowing whether the collisions are elastic, one cannot say.
t
rod
force
probe
spring
X
lab
table
plate
135 cm
80. In the experiment in which the free oscillation of a plate hung from a
spring was studied, the position of the plate was measured repeatedly
by an ultrasonic "motion" detector. Using position data from this
system, the computer calculated the velocity of the plate.
Such velocity data is represented in the graph below. Assuming that
the coordinate system shown in the figure was used (increasing x
representing an increasing distance between the force probe and the
plate), what point on the graph corresponds to the plate being nearest
to the floor?
Vx
B
motion
detector
A
C
time
D
E) For an object executing simple harmonic motion, it is not possible to say where the
object is from such velocity information.
mesh
81. In the rotational motion experiment, the following graph was obtained when the wheel of
the apparatus which you used was rotated by hand. Provide the most likely explanation
for this particular graph.
A) The wheel was rotated rapidly then stopped for a second or two, then rotated rapidly,
then stopped again, and so on.
B) The wheel was rotated at different velocities, increasing in steps as time went on.
C) The wheel was rotated slowly, and the angular encoder on the wheel axis has a
resolution of 1/20 of a revolution.
D) The wheel was rotated slowly, and the angular encoder on the wheel axis has a
resolution of 1/200 of a revolution.
E) The apparatus likely was malfunctioning.
You may record your answers on this page and take it with you after the exam to
compare to the posted solutions.
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