PHYSICS 221
Fall 2006
FINAL EXAM: December 12 2006 7:00pm—9:00pm
Name (printed): ______________________________________________
ID Number: _________________________________________________
Recitation Instructor: _________________________
Section #_______
INSTRUCTIONS:
This exam contains 28 equally weighted multiple-choice questions (24 regular questions + 4
lab questions). 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, 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 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.
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)
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 booklet. 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, Paula Herrera and Anatoli Frishman
NOTE! The questions in this exam are numbered 59 through 86
59. The position of an object is given by the equation x = A + Bt +Ct2, where t refers
to time. What are the dimensions of A, B, and C?
a. distance, distance, distance
b. distance, time, time2
c distance, distance/time, distance/ time2
d. distance/time, distance/ time2, distance/ time3
e. None of the above.
60. A ball is thrown horizontally with an initial speed of 5.0 m/s from a window
located 10 m above the street. At what angle with the horizontal does the ball hit
the ground?
a.
b.
c.
d.
e.
32°
54°
62°
70°
79°
61. A body that is suspended by a massless rope has a weight of 75 N. The rope is
pulling the body up at decreasing speed. The tension in the rope is
__________________ and the net work on the body is _______________.
a.
b.
c.
d.
e.
equal to 75 N, zero
greater than 75 N, negative
greater than 75 N, positive
less than 75 N, positive
less than 75 N, negative
62. A block of mass m moves at constant speed along on a rough horizontal table
pulled by a force F that makes an angle θ ≠ 0 with the horizontal (see figure). Let
N be the normal force and f the kinetic friction exerted by the table on the block.
Which of the following relations is true?
F
θ
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
63. Two boxes of masses m and 3m are stacked as shown in the figure. They are
pulled by a horizontal force F on a horizontal, frictionless surface. If the boxes
move together, what is the magnitude of the static friction force on the less
massive box?
a.
b.
c.
d.
e.
3F
F
F/2
F/3
F/4
m
3m
F
64. A 2.0-kg rock is tied to the end of a 1.2-m long string that moves in a vertical
circle. At the bottom of the trajectory, the rock has a speed of 3.5 m/s. What is the
magnitude of the tension in the rope?
a.
b.
c.
d.
e.
10 N
20 N
30 N
40 N
50 N
65. A uniform solid sphere with mass m = 1.5 kg and radius R = 5.0 cm is released at
rest from the top of an incline of height h. The sphere rolls without slipping down
the incline. At the bottom of the incline, it is moving at 2.5 m/s.
m, R
h
30°
Find the height of the incline, h.
a.
b.
c.
d.
e.
0.13 m
0.22 m
0.32 m
0.45 m
0.58 m
66. Puck 1 (mass m), moving at 2.5 m/s on a horizontal, frictionless surface, collides
elastically and head-on with puck 2, of mass 2m, that is initially at rest. What is
the speed of puck 2 right after the collision?
a.
b.
c.
d.
e.
1.0 m/s
1.7 m/s
2.5 m/s
3.2 m/s
3.8 m/s
67. A block of mass m is attached to a massless rope that is wrapped around a
uniform cylinder of mass 4m and radius R (see figure). When the system is
released, the block falls and the rope does not slip on the cylinder. The net torque
on the cylinder is:
4m, R
a. mgR
b. 2mgR
c. 3mgR
d. 5mgR
e. None of the above
m
68. A dog naps on a 10-kg plank that rests on two scales placed 2.0-m apart (see
figure). The right scale reads 20 kg and the left scale reads 10 kg. How far from
the right scale is the dog’s center of mass?
a.
b.
c.
d.
e.
0.30 m
0.45 m
0.50 m
0.67 m
0.72 m
2.0 m
69. Satellite A has twice the mass of satellite B, and rotates in the same circular orbit.
The speed of B is _______________ the speed of A.
a.
b.
c.
d.
e.
four times
twice
equal to
one half
one fourth
70. Consider two point charges Q1 and Q2 = 2Q1. Which of the following figures best
represents the electrostatic forces exerted by these charges on one another?
a.
b.
c.
d.
e.
Q1
Q2
Q1
Q2
Q1
Q2
Q1
Q2
Q1
Q2
71. An infinite line of charge with uniform charge per unit length λ is set along the x
axis. What is the electric flux through an imaginary sphere of radius R and center
at the origin?
a.
b.
c.
d.
e.
λR
ε0
2λ R
ε0
λR
2ε 0
2πλ R
ε0
4πλ R
ε0
72. Two 3.00-µC charges are fixed at the ends of an insulating meter stick. Find the
electrical potential at the center of the meter stick.
a.
b.
c.
d.
e.
0
120 V
4
2.70 × 10 V
4
5.40 × 10 V
5
1.08 × 10 V
73. A conducting sphere of radius 2.0 cm has a net charge of 2.0 nC. Find the
potential difference between the center of the sphere and a point located 9.0 cm
from the center of the sphere.
a.
b.
c.
d.
e.
100 V
200 V
700 V
900 V
Infinity
74. A point charge Q is placed at distance R from the surface of a conducting thin
spherical shell of radius R with charge Q (see figure). Find the magnitude of the
electric field at the center of the shell.
Q
a. 0
Q
4R2
Q
c. k
2R2
Q
d. k 2
R
2Q
e. k 2
R
b. k
Q
R
R
75. Which of the following statements is wrong?
a. The work done by the electric field is zero for any motion along an equipotential
surface.
b. The electric field is always parallel to equipotential surfaces.
c. The electric field points in the direction of decreasing potential.
d. The surface of a conductor in equilibrium is always an equipotential.
e. All points of a conductor in equilibrium have the same potential.
76. Two copper wires have lengths L1 = 2L2 and radii r1 = 2r2. What is the ratio of
their resistances R1/R2?
a.
b.
c.
d.
e.
4
2
1
½
¼
The following two questions refer to the situation below:
Three capacitors are connected to an ideal battery as shown below. The capacitors are
fully charged.
C1
C2
C3
C1 = 20 µF
C2 = 20 µF
C3 = 10 µF
V0 = 10 V
V0
77. Find the total charge stored in the system.
a.
b.
c.
d.
e.
80 µC
100 µC
200 µC
260 µC
300 µC
78. A dielectric with κ > 1 is inserted between the plates of capacitor C1. Compared to
before the dielectric was inserted, now the total energy stored by the system is
_________ and the charge in capacitor C3 is __________________.
a.
b.
c.
d.
e.
larger, smaller
larger, larger
larger, the same
smaller, larger
smaller, smaller
The following two questions refer to the situation below:
Three identical bulbs with resistance R = 40 Ω are connected to a 120-V ideal battery as
shown below. The switch is initially open
1
120 V
2
3
79. When the switch is closed, bulb 1 is _____________ and bulb 2 is
_____________ than when the switch was open.
a.
b.
c.
d.
e.
dimmer, dimmer
the same, dimmer
brighter, dimmer
dimmer, brighter
brighter, the same
80. With the switch closed, what is the current through bulb 2?
a.
b.
c.
d.
e.
1.0 A
2.0 A
2.6 A
3.0 A
3.5 A
81. A battery with an emf of 12 V and an internal resistance of 2.0 Ω is connected to a
resistance of 22 Ω. What is the voltage at the terminals of the battery?
a.
b.
c.
d.
e.
12 V
11 V
10 V
9V
3V
6
82. A 2.0-µF capacitor is charged to 12 V and then discharged through a 2.0 × 10 Ω
resistor. How long will it take for the voltage across the capacitor to drop to 3.0
V?
a.
b.
c.
d.
e.
3.2 s
4.0 s
5.5 s
6.4 s
8.0 s
Laboratory Final
83. Consider the motion of a cart like the one you used in lab,
and which is adjusted to have significant frictional drag.
Assume that the friction is well described by the "laws" of
(dry) friction that you studied this semester. Also assume
that the cart is given an initial velocity toward the left on
the horizontal track and then released. (Assume the sensor
gives positions relative to the X axis illustrated in the figure).
X
0
Which of the following best illustrates the acceleration, aX, of the cart versus time
after it leaves your hand?
ax
ax
ax
t
0
A
ax
t
ax
t
B
C
t
D
t
E
84. As done in lab, a student, seat, chain, and two load cells are at rest and supported
by cables attached to the upper (sensitive) fittings of the two load cells. The cell
readings and those of the large protractors are given in the table below.
protractors
LEFT
RIGHT
Cell reading
531 N
600 N
Protractor
reading
60°
50°
load cells
0
Y
Use this information to estimate the total force
in the Y direction exerted by the two cables
together on the student, seat, chain and cells.
A) 919 N
0
chain
B) 265 N
seat
C) 386 N
E) 0 (The total force must be zero, since nothing is accelerating.)
X
D) 651 N
85. In a collision of two pucks, #1 and #2, on an air table
such as you used in lab, the spark system failed for
puck #2 after the collision, so that is no record of its
trajectory after the collision.
Using the principle of conservation of momentum and
the data for the other trajectories, it is determined that
the momentum components of puck #2 after the
collision are:
+Y
?
#1
#2
#1
+X
P2X = −20 kg • cm/s;
P2Y = +20 kg • cm/s;
From this information, determine if you can the direction of travel (with respect to
the +X axis) of puck #2 after the collision.
B) 90°
C) 45°
D) 30°
A) 135°
E) Cannot be determined from the information given, since the mass of the puck
is not given.
86. Consider two conducting spheres mounted on insulating
rods and located (with the relative positions shown) in a
region of large electric field, near a negatively charged
rod as shown.
#1
#2
Assume that both of the spheres are initially uncharged.
Then one of the two spheres is displaced slightly so that
the two spheres touch each other briefly and are separated
again. Assume that neither touches the rod, and that their
relative positions are as shown.
Which of following are possible values for the resulting charge on each sphere, #1
and #2, respectively, after the sequence of events described?
A
B
C
D
E
#1
+3.0 nC
−3.0 nC
−3.0 nC
+3.0 nC
0 nC
#2
−3.0 nC
+3.0 nC
−3.0 nC
+3.0 nC
0 nC
Here you can write down your answers and keep this page to compare with the posted
solutions.
59
73
60
74
61
75
62
76
63
77
64
78
65
79
66
80
67
81
68
82
69
83 (lab)
70
84 (lab)
71
85 (lab)
72
86 (lab)