Physics 221 – Spring 2007 – Final Exam
PHYSICS 221
Spring 2007
FINAL EXAM: May 1st 2007 4:30pm—6:30pm
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 sections 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 28 but score will be out of 27 (so one
question is “extra credit”). Questions are numbered 56-83.
Best of luck, David Atwood and Paula Herrera-Siklody
Physics 221 – Spring 2007 – Final Exam
Neglect air resistance in all problems.
56. The acceleration of a particle constrained to move along the x-axis
is ax = 4.0 m/s 4 t 2 . At t = 0, the particle is at x = 0 and its velocity is −3.0 m/s.
(
)
Where is the particle at t = 3.0 s?
(A)
(B)
(C)
(D)
(E)
x = 18 m
x = 30 m
x = 96 m
x = 150 m
x = 320 m
57. You want to kick a ball into your neighbor’s yard, over the 2.0-m high fence. The
ball leaves the ground at 8.0 m/s and just barely clears the fence when it is at the
top of its trajectory. At what angle was the ball moving relative to the horizontal
right after the kick?
(A)
(B)
(C)
(D)
(E)
22°
38°
44°
52°
63°
Physics 221 – Spring 2007 – Final Exam
58. A coin is placed near the edge of a turntable with radius 30 cm. The turntable
makes 20 turns in one minute. What is the minimum coefficient of static friction
needed to ensure that the coin moves along with the turntable?
(A)
(B)
(C)
(D)
(E)
0.13
0.42
0.51
0.70
0.82
59. Two blocks 1 and 2 (m1 = 4m2) on an incline are connected through an ideal,
massless string that goes through an ideal, massless pulley as shown in the figure.
The incline makes an angle of 30° with the horizontal. The blocks are released
from rest and there is no friction between the blocks or between block 1 and the
incline.
2
1
30°
Find the acceleration of block 1 right after it is released.
(A)
(B)
(C)
(D)
(E)
0
2.9 m/s2
5.9 m/s2
7.4 m/s2
9.8 m/s2
Physics 221 – Spring 2007 – Final Exam
60. A 100g ball is launched vertically using a spring as shown below. The spring is
compressed by 10cm from its relaxed length so that the ball is at ground level.
The ball rises to a maximum height of 1m. What is the force constant, k, of the
spring?
1m
100g
(A) 49 N/m
(B) 98N/m
(C) 196 N/m
(D) 392 N/m
(E) 588 N/m
10 cm
Physics 221 – Spring 2007 – Final Exam
61. Consider the two situations depicted below where a block is attached to an ideal
string which winds around the given pulley without slipping. In both cases the
mass of the pulley is m, but the blocks have different masses m and M (see
figure). The blocks accelerate downwards at the same rate in both cases. What is
the ratio M:m?
Solid uniform disk of
Hoop of mass m (all mass
mass m
concentrated on rim)
(A) 3:1
(B) 2:1
(C) 1:1
(D) 1:2
(E) 1:3
m
M
62. Two particles of masses m1 and m2 = 4m1 head toward each other along the x axis
with velocities v1x = 30 m/s and v2x = –10 m/s. The particles collide elastically.
What is the speed of particle 1 right after the collision?
(A) 0
(B) 6.0 m/s
(C) 10 m/s
(D) 25 m/s
(E) 34 m/s
Physics 221 – Spring 2007 – Final Exam
63. John wants to ride a jet ski across a river that is 1.0-km wide and flows from north
to south at a rate of 5.0 km/h. Starting at point A on the west bank he would like
to drive his jet ski in a straight line to point B due east of point A. If the jet ski can
move at a speed of 10 km/h with respect to the water, how long does it take to
cross the river?
(A)
(B)
(C)
(D)
(E)
0.013 hours
0.089 hours
0.10 hours
0.12 hours
0.20 hours
5.0 km/h
A
John's
trajectory
B
64. A uniform sphere of mass 5M and radius R is glued to a uniform rod of mass 3M
and length 2R. The rod is perpendicular to the surface of the sphere. The system
rotates about axis P, which is perpendicular to the page through a point in the
surface of the sphere (see figure). What is the moment of inertia of this rigid body
for this axis?
(A) 3MR 2
(B) 6MR 2
(C) 8MR 2
(D) 11MR 2
(E) 35MR 2
P
R
5M
2R
3M
Physics 221 – Spring 2007 – Final Exam
65. The graph below shows a position-dependent net force acting on a 1.0-kg block
moving along the x-axis. Initially the block is at x = 0 m, moving in the +x
direction. When it reaches 8.0 m, it has a kinetic energy of 30 J. What was the
initial kinetic energy of the block?
(A) 12 J
(B) 18 J
(C) 24 J
(D) 36 J
(E) 48 J
Net Force
3N
2N
1N
1m
2m
3m
4m
5m
6m
7m
8m
x
Physics 221 – Spring 2007 – Final Exam
66. A uniform plank of length 4.0 m and mass 4.0 kg is placed on the edge of a table
with 75% of its length on the table. We want to place a 6.0 kg cube of side 1.0 m
on the free end of the plank without tipping over the system. What is the
maximum allowed value of d?
1.0 m
d?
6.0 kg
4.0 kg
4.0 m
(A)
(B)
(C)
(D)
(E)
1.0 m
0.052 m
0.17
0.33
0.67
The system tips over for any (positive) value of d.
67. A 1.0-kg particle attached to a spring with k = 400 N/m oscillates with simple
harmonic motion along the x axis. As it passes the equilibrium position, the
velocity of the particle is vx = 2.0 m/s. What is the position of the particle 2.0 s
after?
(A)
(B)
(C)
(D)
(E)
x = –6.7 cm
x = –3.2 cm
x = +1.2 cm
x = +7.5 cm
x = +10 cm
Physics 221 – Spring 2007 – Final Exam
68. The solar system of the Ugly Star (mass 1030 kg) has two planets, 1 and 2, that
have circular orbits of radii r1 = 1011 m and r2 = 2 r1. A 1000-kg spacecraft is to
be sent from planet 1 to planet 2. The spacecraft leaves planet 1 when this is in the
position shown in the figure, and reaches planet 2 on the other side of the star,
traveling along the trajectory shown in the figure below. Note that the velocity
vector of the spacecraft is parallel to the velocity vector of planet 1 at launch and
parallel to the velocity vector of planet 2 on arrival.
Planet 1 (position upon
launching)
Ugly Star
spacecraft
How long will the spacecraft trip take?
(A)
(B)
(C)
(D)
(E)
700 hours
2650 hours
6200 hours
11200 hours
23900 hours
Planet 2 (position upon
spacecraft arrival)
Physics 221 – Spring 2007 – Final Exam
The situation below refers to the next two questions:
Two charges are fixed at the positions shown below.
y
Q1 = 3.0μC
Q2 = −3.0μC
Q1
Q2
x
x = 3.0 cm
69. Find the force on Q1 by Q2.
(A)
(B)
(C)
(D)
(E)
3.0 ×107 i N
−3.0 × 107 i N
90i N
−90i N
None of the above
70. Determine the y-component of the total electric field at point (x, y) = (0, 3.0 cm).
(A)
(B)
(C)
(D)
(E)
Ey = 0
Ey = 1.2 × 107 N/C
Ey = 1.5 × 107 N/C
Ey = 1.7 × 107 N/C
Ey = 1.9 × 107 N/C
Physics 221 – Spring 2007 – Final Exam
71. Shown below are four conducting spheres, each with a total charge Q. Point P is
in each case at the same distance from the center of the sphere. In cases 1 and 2,
point P is outside the spheres. In cases 3 and 4, it is inside the spheres. (Each
sphere is to be considered an isolated system, very far from any other charged
object)
4
3
2
1
P
P
P
P
Rank the magnitude of the electric field at point P in each case.
(A)
(B)
(C)
(D)
(E)
E1 = E2 = E3 = E4
E1 < E2 = E3 = E4
E1 < E2 < E3 < E4
E1 = E2 > E4 > E3
E1 = E2 > E3 = E4
72. A sphere of radius R has a charge Q uniformly distributed throughout its volume.
Consider an imaginary sphere of radius R/2 with center located at distance R/2
from the real sphere (see figure). What is the electric flux through the imaginary
sphere?
(A) 0
Q
(B)
ε0
Q
2ε 0
Q
(D)
4ε 0
Q
(E)
8ε 0
(C)
R/2
R
R/2
Physics 221 – Spring 2007 – Final Exam
73. Two very thin surfaces with equal uniform charge density σ = +8.85 nC/m2 are
placed parallel to the yz axes, at x1 = 0 and at x2 = 2.0 cm, respectively. If we take
the electric potential to be zero at x = 0, what is the electric potential at x = 6.0
cm?
(A)
(B)
(C)
(D)
(E)
0V
−60 V
60 V
−40 V
40 V
74. The figure below shows the electric field lines produced by an electric dipole.
Compare the electric potential at points A, B and C.
B
A
(A)
(B)
(C)
(D)
(E)
VB < VA < VC
VA = VB < VC
VB < VC < VA
VA > VB = VC
VA < VB = VC
C
Physics 221 – Spring 2007 – Final Exam
75. Three capacitors are connected to an ideal battery as shown below. When the
capacitors are all fully charged, a dielectric with κ > 1 is inserted between the
plates of capacitor C2. Due to this, and compared with the values before the
dielectric was inserted, the charge in C1 __________________ and the charge in
C3 __________________
.
C2
V0
C1
C3
(A) decreases, decreases
(B) decreases, remains the same
(C) increases, remains the same
(D) remains the same, increases
(E) remains the same, decreases
76. An electric dipole made of two charges ± 3.0 ×10−18 C separated a distance
1.0 ×10−6 m is placed between the plates of a parallel plate capacitor that is
connected to a 9.0-V battery. The plates of the capacitor have an area of 400 m2
and are separated by an air-filled gap 0.10 mm wide. The dipole moment makes
an angle of 60° with the plates of the capacitor. Determine the magnitude of the
torque on the dipole.
(A) 0
(B) 4.1×10−20 Nm
(C) 8.2×10−20 Nm
(D) 1.4×10−19 Nm
(E) 2.7×10−19 Nm
Physics 221 – Spring 2007 – Final Exam
The situation below refers to the next two questions:
An ideal battery and four resistors are connected as shown below. All wires are ideal.
The ideal ammeter reads 0.40 A.
R1 = 10 Ω
R2 = 20 Ω
R3 = 30 Ω
R4 = 40 Ω
R2
R1
R3
A
R4
V0
77. Find the equivalent resistance of the circuit.
(A)
(B)
(C)
(D)
(E)
6.7 Ω
17 Ω
26 Ω
55 Ω
100 Ω
78. Determine the power dissipated in resistor R3.
(A)
(B)
(C)
(D)
(E)
1.2 W
3.1 W
4.8 W
8.8 W
16 W
Physics 221 – Spring 2007 – Final Exam
79. In the circuit below, all resistors are 10 Ω and all batteries are 10 V. The wires
and the battery are ideal. Determine the current through the central wire.
(A)
(B)
(C)
(D)
(E)
0.33 A
0.67 A
1.0 A
1.3 A
2.0 A
Physics 221 – Spring 2007 – Final Exam
Laboratory Final
80. 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, versus time of the cart
during the same time interval?
ax
ax
ax
t
0
A
ax
t
B
ax
t
C
t
D
81. Consider a hollow metal sphere mounted on a thin insulating rod. Using
standard apparatus (e.g., an electrophorus), the largest possible electric
charge is placed on the sphere.
Where is the electric field largest, and for a sphere of a given size, what
factor determines the magnitude of the maximum charge?
location where electric
field is largest
A
B
C
D
E
center of sphere
surface of sphere
surface of sphere
center of sphere
none of the above
factor that determines the
magnitude of the maximum
charge
dielectric strength of air
type of metal
dielectric strength of air
type of metal
t
E
Physics 221 – Spring 2007 – Final Exam
82. Using the rotating wheel apparatus such as you used in lab, a disk (which is not
spinning) is dropped concentrically upon the wheel as it is rotating freely. Assume
that the disk has a moment of inertia of 0.5I0 , where I0 is the moment of inertia of
the rotating wheel. Which of the following graphs best represents the angular
velocity, ω, as a function of time before, during, and after the disk is dropped?
ω
A
ω
t
B
ω
C
t
ω
D
t
ω
E
t
83. Consider two air pucks (made of some unknown
material) which can slide upon a smooth
horizontal surface with little friction, leaving
trails of spark marks, with marks produced at a
fixed frequency. The pucks are of equal mass,
and are pushed (and released) toward one
another, and then collide. Assume that the pucks
rotate little before and after the collision.
For the record shown above, select the comment listed below which is most
appropriate.
(A) The data looks O.K., although the collision clearly is not elastic.
(B) The data must be invalid since clearly momentum is not conserved.
(C) The data must be invalid since the collision clearly is not elastic.
(D) The data looks O.K.; both momentum and mechanical energy appear to be
conserved.
(E) One must know the time between sparks to make a definitive statement.
NOTE: By the data being invalid is meant that, for the situation described, such
data is impossible. To obtain such data, then some large extraneous factor must be
at work (such as hidden magnets, angels, etc.)
t
Physics 221 – Spring 2007 – Final Exam
You may record your answers on this page and take it with you after the exam to
compare to the posted solutions. Solutions posted on WebCT about one hour after exam.
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