Physics 221 2007S
Exam 2
PHYSICS 221
Spring 2007
EXAM 2: March 29 2007 8:00pm—10:00pm
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 28. Questions are numbered 28-55.
Question 55 is “extra credit”
Page 1 of 20
Physics 221 2007S
Exam 2
[28] Assume that the moon can be modeled as a solid sphere of uniform density. The
mass of the moon is 7.4 ×1022 kg and the radius of the moon is 1800 km. Which is the
best estimate of the moment of inertia of the moon about an axis through the moon’s
center of mass?
(A) 2.4 × 1035 kg m 2
(D) 9.6 ×1034 kg m 2
(B) 1.6 × 1035 kg m 2
(E) 4.8 × 1034 kg m 2
(C) 1.2 × 1035 kg m 2
[29] Three objects of mass m are dropped from a height h. One falls straight down, one
slides down a frictionless incline and one swings at the end of a pendulum. What is the
relationship between their speeds when they reach the ground? Neglect air resistance.
(A) vF > vI > vP
(D) vF < vI < vP
Fall
(B) vF > vP > vI
(E) vF < vP < vI
(C) vF = vI = vP
Incline
Pendulum
h
vF
vI
Page 2 of 20
vP
Physics 221 2007S
Exam 2
[30] A truck with mass 2000kg is driving along a road. It collides with a stationary car
with mass 1000kg. The two vehicles fuse together and the moment after the collision, the
fused wreckage of the two vehicles is moving at a speed of 10m/s. What was the initial
speed of the truck?
(A) 10m/s
(B) 15 m/s
(E) None of the above.
(C) 17 m/s
(D) 25 m/s
[31] Particle B has twice the mass of particle A and particle B is moving with linear
momentum twice as big as particle A. What is the ratio:
Kinetic energy of B : Kinetic energy of A?
(A) 4:1
(B) 2:1
(C) 1:1
(D) 1:2
(E) 1:4
Page 3 of 20
Physics 221 2007S
Exam 2
[32] Consider the assembly depicted below of nine 1m×1m tiles. Six of the tiles have
mass 1kg while the other three have mass 2kg as shown. Using the axes in the figure,
what is the location of the center of mass for the system?
(A) (2.2m , 1.5m)
(B) (1,5m , 2.2m)
(C) (1.5m , 1.5m)
(D) (1.5m , 1.7m)
(E) (1.7m , 1.5m)
y-axis
1kg
2kg
1kg
1kg
1kg
2kg
1kg
1kg
2kg
x-axis
Page 4 of 20
Physics 221 2007S
Exam 2
[33] Horizontal disk 1 of radius R and mass M rotates with an angular speed ω.
Horizontal disk 2 with the same axis, same radius, mass M/3 and no initial angular speed
is dropped on top of disk 1. What is the final angular velocity, ωf , of the two disk system
when the disks stop rubbing and rotate as a single unit? Assume that there is no friction
on the axle or other external torques.
(A) ωf =4ω
(B) ωf =4ω/3
(C) ωf =ω
(D) ωf =3ω/4
(E) ωf =ω/4
Disk 2
ω
Disk 1
[34] A particle with mass m=5.0kg resting on a frictionless horizontal surface is
connected to an ideal spring with force constant k=100N/m. If the amplitude of the
oscillations is 10cm, what is the mechanical energy of the system? Take the zero for the
spring potential energy at the point where the spring is in equilibrium.
k=100 N/m
5kg
(A) 50 J
(B) 10 J
(C) 5.0 J
(D) 1.0 J
Page 5 of 20
(E) 0.50 J
Physics 221 2007S
Exam 2
[35] The graph below represents the position of a block attached to a spring. If the force
constant of the spring is k=10N/m, what is the kinetic energy of the system at time t=0s?
(A) 10J
(B) 15J
(C) 20J
(D) 30J
(E) 40J
[36] If a collision is elastic then which of the following must be true?
(A) The total kinetic energy is conserved
(B) The total linear momentum is not conserved
(C) The total kinetic energy is not conserved
(D) The velocity of the center of mass of the system changes.
(E) The relative speed of the two particles is reduced after the collision
Page 6 of 20
Physics 221 2007S
Exam 2
[37] A bullet of mass 1g with velocity of 200m/s collides with an iron block of mass 1kg
resting on a frictionless ice surface. After the collision, the bullet bounces off and is
moving at 150m/s in the +y direction. What is the final speed of the block after the
collision with the bullet?
(A) 0.05 m/s
(B) 0.10 m/s
(C) 0.15 m/s
(D) 0.20 m/s
(E) 0.25 m/s
Top View
150 m/s
200 m/s
1kg
iron
block
[38] A uniform pole is 4.00m long with negligible diameter. It has a mass of 200kg and it
is stuck in the ground tilted at an angle 30º from the vertical. What is the magnitude of
the torque due to the weight of the pole about the point at the bottom of the pole?
(A) 1960 Nm
Pole
Mass=200kg
(B) 3395 Nm
(C) 3920 Nm
(D) 6790 Nm
30°
Length=4m
Torque by
weight=?
Page 7 of 20
(E) 7840 Nm
Physics 221 2007S
[39]
In the figure at right, a horizontal massless
rod of length 2m is attached to a wall with a
frictionless ideal hinge. An ideal massless
string connects the end of the rod to the wall
at a point 2m above the hinge. A box with
weight 20N is hung from the end of the rod
with an ideal massless string. If the system is
in equilibrium, what is the magnitude of the
net force exerted on the hinge by the rod?
Exam 2
2m
2m
Hinge
20N
Wall
(A) 0N
(B) 20N
(C) 28N
(D) 40N
(E) 57N
[40] A 250-g particle attached to a spring with k = 150 N/m is also subject to a damping
force F = − bv, where v is the velocity of the particle and b = 1.5 kg/s. Which of the
graphs shown below best represents the mechanical energy of the particle as a function of
time?
Page 8 of 20
Physics 221 2007S
Exam 2
[41] Several forces F are applied to the 2D objects depicted below. All forces have equal
magnitude. All the objects have the same mass, uniformly distributed. Which of the
following statements about the magnitude of the angular acceleration about the center of
mass of each system is true?
(A) α P < α Q < α R
(B) α P < α R < α Q
(D) α Q < α R < α P
(E) α R < α Q < α P
(C) α Q < α P < α R
P
F
Q
F
Rod
Rod
60°
F
F
F
2R
2R
Solid Disk
F
2R
R
F
Page 9 of 20
F
60°
Physics 221 2007S
Exam 2
[42] 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 speed of the particle at
x1 and x2.
U
E
x
x1
A.
B.
C.
D.
E.
x2
| v1 |<| v2 |
|F1| > |F2|
|F1| > |F2|
| v1 |>| v2 |
|F1| < |F2|
| v1 |<| v2 |
|F1| < |F2|
| v1 |>| v2 |
It is not possible to answer the question without knowing the initial position
and velocity of the particle.
Page 10 of 20
Physics 221 2007S
Exam 2
[43] The figure below shows blocks of mass m attached to pulleys of mass m with an
ideal string which pulls without slipping. Which is the correct ranking for the
acceleration of the blocks?
(A) aP < aQ < aR
(B) aQ < aP < aR
(D) aP = aQ > aR
(E) aP = aQ = aR
Solid uniform disk of mass m,
radius R/2.
(C) aP = aQ < aR
Solid uniform disk of mass m,
radius R
m
m
P
Q
Page 11 of 20
Hoop of mass m; radius R: all
mass concentrated on rim.
m
R
Physics 221 2007S
Exam 2
[44] Consider the two situations depicted. In each a block of mass M=1kg is suspended
from the ceiling by a spring with force constant k=10 N/m. In case 1 the block is pulled
down a distance of 10cm from equilibrium and then released. In case 2 the block is pulled
down a distance of 20cm from equilibrium and then released. If T1 is the period of
oscillation in case 1 and T2 the period in case 2, what is the ratio T1:T2?
Case 1
Case 2
k
k
M
M
20 cm
10 cm
(A) 4:1
(B) 2:1
(C) 1:1
(D) 1:2
(E) 1:4
[45] Which of the following statements is true about a conservative force?
(A) The force does a positive amount of work when a particle moves around a closed
loop.
(B) The work done by the force as a particle moves from point A to point B depends
on the path of the motion.
(C) Kinetic friction is a conservative force.
(D) When a conservative force does work on an object, its temperature will change.
(E) None of the above.
Page 12 of 20
Physics 221 2007S
[46] A 1.00m long rod of uniform mass
distribution weighing 200N is supported at its
ends by wires A and B. A 100N weight is attached
to the rod 20cm from wire A. What is the tension
in wire A if the system is in equilibrium?
Exam 2
1.00m
A
200N
(A) 300N
(B) 180N
(C) 150N
(D) 130N
(E) 75N
100N
[47] Romeo (100 kg) sits in the left end of a 4.0 m-long symmetric boat (100 kg) that
floats still at some distance from the shore and plays a romantic song with his guitar to
Juliet (50 kg), who sits in the right end. After the serenade, Juliet carefully moves to
Romeo’s side to plant a kiss on his cheek. How far to the right does Romeo move during
this process? Assume negligible friction between the boat and the water.
(A) 0.0m
(B) 0.8m
(C) 1.0m
4.0 m
Page 13 of 20
(D) 2m
(E) 3.2m
B
Physics 221 2007S
Exam 2
[48] Cylinder 1 is released on an incline and rolls down (without slipping).
Cylinder 2 has an initial angular speed at the bottom of the ramp and thus starts rolling up
(again without slipping).
What is the direction of the static friction force in each case as they roll along the ramp?
Cylinder 1
Cylinder 2
Page 14 of 20
Physics 221 2007S
Exam 2
[49] A system consists of two identical solid disks of mass M and radius R attached
together as shown below. What is the moment of inertia of the system about an axis
perpendicular to the page at point P?
(A) 7MR²
(B) 6MR²
(C) 5MR²
P
●
R
90°
R
Solid disk
Mass M
Radius R
R
Solid disk
Mass M
Radius R
Page 15 of 20
(D) 4MR²
(E) 3MR²
Physics 221 2007S
Exam 2
[50] Consider the three forces of magnitude 1.00N exerted on an equilateral triangle of
uniform density depicted below with side length 2.00m. What is the magnitude of the
torque about the center of mass of the system?
(A) 1.30 Nm
(B) 2.25 Nm
(C) 2.60 Nm
(D) 3.00 Nm
1N
90°
2m
2m
90°
2m
90°
1N
Page 16 of 20
1N
(E) 5.20 Nm
Physics 221 2007S
Exam 2
[51] A particle of mass 5kg is located at the point (1m, 2m, 3m) and has a velocity of
m
G
v = (3iˆ + 2 ˆj + 1kˆ) . What is the y-component of the angular momentum vector of the
s
particle about the origin?
(A) Ly = −50 Js
(B) Ly = +50 Js
(D) Ly = −40 Js
(E) Ly = +40 Js
(C) Ly = +130 Js
[52] A 20-g rubber ball bounces on a table as shown in the figure below. The ball and the
table are in contact for 15 ms. What is the magnitude of the average force exerted on the
ball by the table?
Ball
60 m/s
60 m/s
60°
(A) 0 N
(B) 30 N
(C) 80 N
60°
(D) 140 N
Page 17 of 20
(E) 160 N
Physics 221 2007S
Exam 2
[53] A particle is released from rest at x = x0 in the presence of a conservative force with
the potential energy shown below. No other forces are present. Which of the following
best describes the subsequent motion of the particle?
U
x
x0
(A) The particle oscillates about the first minimum.
(B) The particle oscillates about the second minimum.
(C) The particle has a complex oscillation that includes both minima.
(D) The particle moves in the positive x direction all the time.
(E) None of the above.
[54] A 1.0-kg block is pressed against a horizontal ideal spring with spring constant k =
400 N/m. The spring is compressed 10 cm from its relaxed position. When released, the
block slides on a horizontal surface for 50 cm and then up an incline, where it reaches a
maximum height of 15 cm vertically above the initial level. What is the magnitude of the
work done by the friction forces?
(A) 0.5 J
(B) 1.0 J
(C) 1.5 J
(D) 2.0 J
Page 18 of 20
(E) 2.5 J
Physics 221 2007S
Exam 2
[55 Extra Credit] An 18g bullet is shot vertically upwards into a 10kg block and quickly
becomes imbedded in the block. If the block lifts upwards 9.0mm, what is the initial
kinetic energy of the bullet?
(A) 0.0016 J
(B) 0.88 J
(C) 49 J
(D) 330 J
(E) 490 J
End of Exam
Best of luck
David Atwood
Paula Herrera-Siklody
Page 19 of 20
Physics 221 2007S
Exam 2
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 1 hour after exam;
Grades posted: Friday afternoon after the exam.
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