PHYSICS 221
Spring 2006
FINAL EXAM: May 2 2006 2:15pm—4:15pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice. Choose
the best answer to each question.
Before turning over this page, put away all materials except for pens, pencils, erasers, rulers, your
calculator and “aid sheet”. An “aid sheet” is one two sided 8½×11 page of notes prepared by the
student. There is also a list of possibly useful equations at the end of the exam.
"In general, any calculator, including calculators that perform graphing numerical analysis
functions, is permitted. Electronic devices that can store large amounts of text, data or equations
are NOT permitted." If you are unsure whether or not your calculator is allowed for the exam ask
your TA.
Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+
Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C.
Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket computer,
PDA or e-book reader.
In marking the multiple choice bubble sheet use a number 2 pencil. Do NOT use ink. If
you did not bring a pencil, ask for one. Fill in your last name, middle initial, and first
name. Your ID is the middle 9 digits on your ISU card. Special codes K to L are your
recitation section, for the Honors section please encode your section number as follows:
H1⇒02; H2⇒13 and H3⇒25.
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.
It is strongly suggested that you circle your choices on the question sheet. 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.
Total number of questions is 30 (59 through 88). Question 83 is for extra credit.
Best of luck, David Atwood and Paula Herrera-Siklody
Final Exam – Physics 221 – Spring 2006
The situation below refers to the next two questions:
A bob of mass m = 1.0 kg is attached at the bottom of a massless, ideal string of
length 80 cm to make a pendulum. When the string makes an angle of 15º with the
vertical, the speed of the bob is 1.2 m/s.
59. What is the tension on the string at the position described?
A.
B.
C.
D.
E.
1.8 N
4.6 N
7.7 N
9.5 N
11 N
60. How long does the bob take to go through a complete oscillation cycle?
A.
B.
C.
D.
E.
0.6 s
0.9 s
1.2 s
1.8 s
2.2 s
61. A block of mass m is being pulled at an angle by a force F on a horizontal
surface as shown in the figure. The block moves to the right at constant speed.
Let f be the friction between the block and the surface and N be the normal
force on the block by the surface.
F
Which of the following relations between magnitudes is true?
A.
B.
C.
D.
E.
f =F
f =F
f <F
f <F
f <F
;
;
;
;
;
N = mg
N < mg
N < mg
N = mg
N > mg
2
Final Exam – Physics 221 – Spring 2006
62. A 2.0-kg block is pressed against an ideal spring so it compresses the spring
4.5 cm from its relaxed length. When released, the block slides on a rough,
horizontal surface with µk = 0.2 and comes to a stop due to friction 85 cm from
its initial position. Determine the spring constant.
A.
B.
C.
D.
E.
9.2 N/m
87 N/m
174 N/m
1450 N/m
3290 N/m
The situation below refers to the next two questions:
Two identical capacitors C1 = C2 = 3.0 µF are connected as shown to a battery that
provides a potential difference V0 = 10 V
63. What is the total electric energy stored by the circuit?
A.
B.
C.
D.
E.
75 µJ
150 µJ
300 µJ
450 µJ
500 µJ
C1
C2
V0
64. If a dielectric is inserted between the plates of C1, what happens to the charges
on each capacitor (as compared to before the dielectric was inserted)?
A.
B.
C.
D.
E.
Both charges increase.
Both charges decrease.
Q1 increases, Q2 decreases
Q1 increases, Q2 remains the same
Q1 decreases, Q2 remains the same
3
Final Exam – Physics 221 – Spring 2006
65. When a resistor R = 90 Ω is connected to a given battery, a current of 1.0 A
runs through the wires. The resistor is then placed over a flame so its
temperature increases by 50ºC. If the temperature coefficient of resistivity α of
the resistor is 0.005 (ºC)−1, what is the current through the circuit after the
heating?
A.
B.
C.
D.
E.
1.3 A
1.0 A
0.9 A
0.8 A
0.6 A
66. Four identical bulbs are connected in a circuit with an ideal battery as shown
below.
1
3
2
4
Rank the brightness B of bulbs 1, 2 and 3:
A.
B.
C.
D.
E.
B1 > B2 > B3
B1 > B2 = B3
B1 > B3 > B2
B1 = B2 > B3
B1 = B2 < B3
4
Final Exam – Physics 221 – Spring 2006
67. A neutron star has a radius of 10 km and a mass of 2.8×1030 kg (about 1.4
times that of the Sun). If you (somehow!) dropped a coin 1 m above the surface
of such a star, how fast would it be moving by the time it hits the surface?
A.
B.
C.
D.
E.
280 km/s
1400 km/s
1900 km/s
8500 km/s
13000 km/s
68. A charge Q1 = 4.0 µC is kept fixed at the origin. Another charge Q2 = −2.0 µC
is fixed on the x-axis, at x1 = 3.0 m. What is y-component of the electric field at
(x, y) = (0, 3.0) m ?
A.
B.
C.
D.
E.
Ey = 2000 N/C
Ey = 2600 N/C
Ey = 3000 N/C
Ey = 3300 N/C
Ey = 4700 N/C
5
Final Exam – Physics 221 – Spring 2006
69. A 150-g toy car rolling on a horizontal table at 0.80 m/s comes to the edge of
the table and lands on the floor 40 cm away from the edge of the table in the
horizontal direction. At what angle with the horizontal does it strike the floor?
A.
B.
C.
D.
E.
16º
24º
62º
72º
81º
70. Consider the system depicted below. A block of mass m = 1.0 kg is resting on a
wedge of mass M =10 kg and angle θ =30°. The wedge is in turn resting on an
incline of angle θ as shown so that the surface on which the block rests is level.
Initially the block and wedge are at rest. Assume that there is no friction
between the block and wedge and likewise no friction between the wedge and
incline. If the block and wedge are released, which of the arrows most correctly
indicates the direction of the acceleration of the block?
m
A
θ
E
M
D
B
C
θ
6
Final Exam – Physics 221 – Spring 2006
71. Rigid bodies P, Q, R and S are each rotating about an axle parallel to the z-axis.
The angular momenta and rotational kinetic energies of these rigid bodies are
given in the table below. Which is the correct ranking of the z-components of
the angular velocities of these rigid bodies?
Rigid Body
Rotational KE
Angular
Momentum
P
Q
R
K0
2K 0
K0
L0 k̂
L0 k̂
2L0 k̂
S
2K 0
2L0 k̂
A. ωR > ωS > ωP > ωQ
B. ωR > ωP > ωS > ωQ
C. ωQ > ωS > ωP > ωR
D. ωQ > ωP = ωS > ωR
E. None of the above
72. As shown below, a 13-m beam with a mass of 10 kg where the mass is
distributed uniformly is attached to the ceiling with a hinge on one end and a
5m massless string at the other. What is the tension in the string if the system is
in equilibrium?
Ceiling
90º
Hinge
A.
B.
C.
D.
E.
10-kg beam
Length=13 m
Massless
string
5m
49 N
82 N
196 N
470 N
510 N
7
Final Exam – Physics 221 – Spring 2006
73. In the three systems below, the inclines have the same angle with the
horizontal and the objects are released from the same height h.
1. A solid sphere of uniform
density, mass M and radius R
rolling down without slipping.
h
θ
2. Hollow cylinder of mass
M and radius R rolling
down without slipping.
h
θ
3. Hollow cylinder of mass
M and radius 2R rolling
down without slipping.
h
θ
How do their speeds at the bottom of the incline compare?
A.
B.
C.
D.
E.
v1 < v2 = v3
v1 < v2 < v3
v1 > v2 > v3
v1 > v3 > v2
v1 > v2 = v3
8
Final Exam – Physics 221 – Spring 2006
74. A projectile is fired from the Moon’s surface at exactly the escape velocity in a
horizontal direction as shown. It passes points P and Q where RP and RQ are
the distances between each point and the center of the Moon. Likewise, vP and
vQ are the velocities of the projectile as it passes points P and Q respectively.
If RQ = 2 RP , what is the ratio vQ : vP ?
A.
B.
C.
D.
E.
1:1
1: 2
1: 2
1: 2 2
1:4
RQ = 2 RP
vQ : vP =?
•P
Moon
•Q
75. Which of the following statements about equipotential surfaces (EPS) is false?
A.
B.
C.
D.
E.
The electric field is always perpendicular to the EPSs.
The electric field lines are always perpendicular to the EPSs.
The electric flux through an EPS is always zero.
The surface of a conductor in equilibrium is an EPS
The EPSs of a point charge are concentric spheres.
9
Final Exam – Physics 221 – Spring 2006
The situation below refers to the next two questions:
Four point charges of charge Q are arranged in a square of side length L as shown.
76. What is the magnitude of the electrostatic force on one of the charges due to
the other three?
A.
5kQ 2
2 L2
kQ 2 
B.
2 + 2 
L2 
C.
kQ 2
L2
D.
3kQ 2
2 L2
E.
3kQ 2
L2
1

2 + 2


+Q
L
L
L
+Q
+Q
L
+Q
77. Find the electric potential at the center of the square if V(∞) = 0.
A.
B.
C.
D.
E.
4kQ
L
4kQ
2
L
2kQ
2
L
2kQ
L
0
10
Final Exam – Physics 221 – Spring 2006
78. A point charge Q is at the center of a hollow symmetric spherical shell made
out of an insulating material with inner radius 2R and outer radius 4R as
shown. The material has a uniform charge density and a total charge Q. What
is the magnitude of the electric field at a point at distance R from the center of
the shell?
2R
kQ
R2
2kQ
E= 2
R
kQ
E=
2R2
kQ
E=
4R2
None of the above.
A. E =
B.
C.
D.
E.
Q
Q
4R
79. Each of the five capacitors in the circuit below has a capacitance of 1.0 pF.
What is the equivalent capacitance of this circuit?
1pF
A.
B.
C.
D.
E.
0.25 pF
0.50 pF
1.0 pF
2.0 pF
4.0 pF
1pF
1pF
1pF
1pF
11
Final Exam – Physics 221 – Spring 2006
80. A rock is thrown straight downwards at a speed of 29.4 m/s from a bridge over
a river of height 78.4 m. What is the speed of the rock the instant before the
rock strikes the river? Neglect air resistance.
A.
B.
C.
D.
E.
83.7 m/s
49.0 m/s
40.4 m/s
25.9 m/s
Cannot be determined without knowing the mass of the rock.
81. The figure below is the energy diagram for a particle that can move along the x
axis. Compare the magnitude of the force acting on the particle and the kinetic
energy of the particle at x1 and x2.
U
E
x1
A.
B.
C.
D.
E.
x
x2
|F1| > |F2|
KE1 > KE2
KE1 < KE2
|F1| > |F2|
KE1 > KE2
|F1| < |F2|
KE1 < KE2
|F1| < |F2|
It is not possible to answer the question without knowing the initial position
and velocity of the particle.
12
Final Exam – Physics 221 – Spring 2006
82. A 1.5 kg rock at rest undergoes an explosion into three fragments of mass 0.5
kg each. Fragment #1 has a kinetic energy of 100 J; Fragment #2 has a kinetic
energy of 36 J and fragment #3 has a kinetic energy of 25 J. What is the angle
between the velocity vectors of fragment #1 and fragment #2?
A.
B.
C.
D.
E.
71°
138°
158°
There is not enough information given to determine this angle
The scenario described is not physically possible.
83. (Extra credit) In the circuit below, each of the capacitors has a capacitance of
2.0 F and the resistor has a resistance of 4.0 Ω. Initially, at t = 0, capacitor C1
has charge of 2.0 C while capacitor C2 has no charge. Which of the following
is the best estimate of the total amount of energy dissipated by the resistor
during the subsequent 60 s?
A.
B.
C.
D.
E.
1/16 J
1/8 J
1/4 J
1/2 J
1J
R=4Ω
C1 = 2.0 F
Q1(t = 0) = 2.0 C
C2 = 2.0 F
Q2(t = 0) = 0
13
Final Exam – Physics 221 – Spring 2006
PHYSICS 221 - Spring, 2006
Laboratory Final
84. As you did in lab, consider the motion of a cart which is given
an initial velocity up an inclined track toward a "motion
detector". Assume the cart goes part of the way up, and then
returns back down the track. (As was done in lab, assume the
sensor gives positions relative to the X axis illustrated above).
X
0
Which of the following best graphs illustrates the velocity, VX , of the cart (after leaving
your hand) versus time?
Vx
Vx
t
0
A
Vx
Vx
t
Vx
t
B
t
C
t
D
E
85. The reading of the left load cell and left protractor used in the Forces and Vectors lab
are given in the table below.
LEFT
Cell reading
Protractor reading
Y
125.0 LB
60
55°
X
30
Using the coordinate system shown, what is the
X component of the force exerted by the left
load cell ON the suspended system (student,
seat, etc.) (in lb.)?
0
You, chair,
etc.
(Note: cos (55°) = sin (35°) and sin (55°) = cos (35°) )
A. 125 cos (55°)
B. −125 sin (55°)
C. 125 sin (55°)
D. −125 cos (55°)
E. 0 (The total force must be zero, since nothing is accelerating.)
14
Final Exam – Physics 221 – Spring 2006
86. As in the Collision in Two Dimensions lab,
consider two air pucks sliding with little friction
on a smooth, level surface. Assume they are each
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.
P1 = P2 = P3
P1 = P2 ≠ P3
P1 ≠ P2 = P3
P1 ≠ P2 ≠ P3
Without knowing whether the collisions are elastic, one cannot say.
87. Using the rotating wheel apparatus such as you used in lab, a second disk is dropped
concentrically upon the wheel as it is rotating freely. Which of the following graphs
best represents the total angular momentum, L, (wheel plus disk) versus time before,
during, and after the disk is dropped?
L
A
L
t
B
L
t
C
L
t
D
L
E
t
t
15
Final Exam – Physics 221 – Spring 2006
+
+ +
+ +
+
+
C. Move the ball about so that it repeatedly touches the outside of the right can
and then the inside of the left can.
D. Move the ball about so that it repeatedly touches the outside of the right can
and then the outside of the left can.
None of the above since the best one can do by simple mechanical means is
to equalize the charge on the cans (it’s like trying to remove wallpaper paste
by simply touching or rubbing it; eventually everything gets covered equally
with paste.)
16
+
B. Place the ball so that it touches one can, then move the
other electroscope so that the second can touches the ball.
+
+
+
A. Move one electroscope so that one can touches the other
can.
E.
+ + + +
+ + + +
88. Consider two metal cans, each perched atop an
electroscope. Assume that the right one is charged, and that
the left one is not. By what procedure, say by moving an
electroscope, or by using a conducting ball mounted on an
insulated rod, can one move essentially the entire net
charge from the can on the right to the one on the left?
Final Exam – Physics 221 – Spring 2006
You may record your answers here and take this page with you to compare with the
posted answers.
59
69
79
60
70
80
61
71
81
62
72
82
63
73
83
64
74
84
65
75
85
66
76
86
67
77
87
68
78
88
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