PHYSICS 221
Fall 2006
EXAM 2: November 15 2006 8:00pm—10:00pm
Name (printed): ______________________________________________
ID Number: _________________________________________________
Recitation Instructor: _________________________
Section #_______
INSTRUCTIONS:
This exam contains 28 equally weighted multiple-choice questions, numbered 31 through
58. 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
1
NOTICE!!! QUESTIONS ARE NUMBERED 31 THROUGH 58
31. Find the magnitude of the force exerted at point P (0,1,2) m if the potential energy
associated with the force is U = 12 x 2 + 12 y 2 + 12 z 2 + 2 xy , where U is in Joules if x , y,
z are in meters.
A. 1 N
B. 2 N
C. 3 N
D. 4 N
E. 5 N
32. A 75 kg man is riding on a 50 kg cart, traveling at a speed of 2 m/s. He jumps off
with zero horizontal speed relative to the ground. What is the resulting change in
the speed of the cart?
A.
B.
C.
D.
E.
It decreases by 5 m/s
It increases by 5 m/s
It increases by 3 m/s
It decreases by 3 m/s
It remains the same
2
33. Two identical 1500-kg cars are moving perpendicular to each other. One moves
with a speed of 25 m/s due north and the other moves at 15 m/s due east. What is the
total momentum of the system?
A.
B.
C.
D.
E.
4
4.4 × 10 kg·m/s at 31° N of E
4
4.4 × 10 kg·m/s at 59° N of E
4
6.0 × 10 kg·m/s at 31° N of E
4
6.0 × 10 kg·m/s at 59° N of E
None of the above.
34. Two particles of masses m and 2m move directly towards each other with speeds v
and 2v, respectively. They collide head-on and elastically. Find the speed of the
heavier particle after the collision.
v
2v
2m
m
A.
B.
C.
D.
E.
0
v
2v
2v/3
4v/3
3
35. A 1.0-kg block of mass m1 = 1.0 kg moves to the right on a horizontal, frictionless
surface at 1.0 m/s. It collides head-on with another block of mass m2 = 5.0 kg, that is
initially at rest and is in contact with a relaxed spring with spring constant k = 50
N/m (see figure). After the collision, both blocks stick together and compress the
spring. How much will the spring be compressed before it pushes the blocks back to
the left?
m2
m1
A.
B.
C.
D.
E.
3.2 cm
5.8 cm
8.4 cm
14 cm
20 cm
36. Two equal-mass particles (A and B) are located at some distance from each other.
Particle A is held stationary while B is moved away at speed v. What happens to the
center of mass of the two-particle system?
A.
B.
C.
D.
E.
it does not move
it moves away from A with speed v
it moves toward A with speed v
it moves away from A with speed 1/2 v
it moves toward A with speed 1/2 v
4
37. Pete (80 kg) stands on one end of a 5.0 m long cart (40 kg) that can roll perfectly on
a horizontal surface. The cart and Pete are initially at rest. After Pete runs to the
opposite end, the cart moves to the left. How much does the center of mass of the
Pete+cart system move?
80 kg
5.0 m
A.
B.
C.
D.
E.
4.0 m to the left
2.5 m to the left
0
2.5 m to the right
4.0 m to the right
38. A uniform hoop, a disk and a solid sphere, all with the same mass M and the same
radius R, are released simultaneously from rest at the top of a ramp. In which order
do they reach the bottom (first to last)?
A.
B.
C.
D.
E.
Hoop, disk, sphere
Disk, sphere, hoop
Sphere, disk, hoop
Sphere, hoop, disk
The all reach the bottom at the same time.
5
39. Two forces are applied as shown on two uniform disks that can rotate without
friction about axles through their centers. Both disks have each a mass of 1.0 kg. In
order to impart identical angular accelerations to both disks, how large must F2 be?
F2 ?
F1 = 1.0 N
Axis
Axis
M = 1.0 kg
R = 0.50 m
M = 1.0 kg
R = 1.0 m
A. 0.25 N
B. 0.50 N
C. 1.0 N
D. 2.0 N
E. 4.0 N
40. A 4.00-m long uniform rod is hinged at one end. The rod is initially held in the
horizontal position, and then released as the free end is allowed to fall. What is the
angular acceleration right after it is released?
A.
B.
C.
D.
E.
2
2.45 rad/s
2
3.68 rad/s
2
4.90 rad/s
2
6.75 rad/s
9.81 rad/s2
6
The following two questions refer to the situation below:
A box of mass m = 3.00 kg is suspended from a light rope that passes over a pulley
(uniform disk of mass M = 2.00 kg and radius R = 20.0 cm) and is wrapped around a
solid, uniform cylinder of mass 2M and radius 2R. Both the cylinder and the pulley
rotated without friction about the axles through their centers. The rope does not slip on
either the cylinder or the pulley. The box is released from rest.
M
2R
2M
pulley
R
m
cylinder
box
41. After the system is released, the net torque on the cylinder is:
A.
B.
C.
D.
E.
2mgR, into the page
Larger than 2mgR, into the page
2mgR, out of the page
Larger than 2mgR, out of the page
None of the above.
42. Determine the speed of the box when it has fallen 1.50 m
A.
B.
C.
D.
E.
3.2 m/s
3.8 m/s
4.5 m/s
5.4 m/s
6.1 m/s
7
43. A figure skater rotates with arms extended. When the arms are pulled in, the moment
of inertia decreases to 75% of the original value. What is the ratio between the final
and the initial angular speed?
A.
B.
C.
D.
E.
2
4/3
4
2/3
9/4
44. A child (40 kg) stands on the edge of a stationary merry-go-round (uniform disk of
radius 1.2 m and mass 50 kg). The child jumps off at 1.0 m/s with respect to the
ground in the direction tangential to the edge. Find the angular speed of the merrygo-round after the jump. Assume the friction on the axle of the merry-go-round is
very small.
A.
B.
C.
D.
E.
0.67 rad/s
0.75 rad/s
0.83 rad/s
1.1 rad/s
1.3 rad/s
8
45. A uniform beam of mass M = 10 kg and length L = 4.0 m leans against a smooth
wall. (We can neglect the friction between the wall and the beam.) The frictional
force between the floor and the beam keeps it from slipping. The angle between the
beam and the wall is φ = 20°. Determine the magnitude of the frictional force
between the beam and the floor.
A.
B.
C.
D.
E.
18 N
24 N
29 N
36 N
42 N
46. A uniform board of mass 2.0 kg pivoted on its center serves as a seesaw for two
children. One child has s mass of 30 kg and sits 2.5 m from the pivot point. At what
distance from the pivot must another child of mass 25 kg place himself to balance the
seesaw?
A.
B.
C.
D.
E.
4.0 m
3.5 m
3.0 m
2.5 m
2.0 m
9
The following two questions refer to the situation below:
A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal,
frictionless surface. The object oscillates in simple harmonic motion. At t = 0, the mass
is at the equilibrium position (x = 0) and is moving in the positive x direction at 1.5 m/s.
47. At what distance from the equilibrium position are the kinetic energy and the
potential energy the same?
A.
B.
C.
D.
E.
0.068 m
0.12 m
0.17 m
0.29 m
0.33 m
48. We can describe the position of the mass as a function of time with
x(t ) = A cos (ωt + ϕ ) . Determine the phase angle in radians.
A.
B.
C.
D.
E.
0
π/4
π/2
π
3π/2
10
49. When the mass of a simple pendulum is tripled, the time required for one complete
oscillation changes by a factor of:
A.
B.
C.
D.
E.
9
3
1 (does not change)
1/3
1/9
50. Shown below are a simple pendulum made with a massless string of length L and a
bob of mass M, and a physical pendulum made with uniform rod of length L and
mass M suspended from its upper end. Find the ratio of their angular frequencies for
small oscillations , ωsimple / ωphysical.
A.
1
3
B.
2
3
C.
1
2
D.
1
6
E.
1
12
L
M
11
L, M
51. The mass of the Sun is about 3×105 times the mass of the Earth. The magnitude of
the gravitational force exerted by the Sun on the Earth is _________________ the
magnitude of the gravitational force exerted by the Earth on the Sun.
A.
B.
C.
D.
E.
about 9×1010 times larger than
about 3×105 times larger than
the same as
about 3×105 times smaller than
about 9×105 times smaller than
52. A spherically symmetric planet has four times the Earth's mass and twice its radius.
If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it
weigh on the surface of this planet?
A.
B.
C.
D.
E.
6.0 N
12 N
24 N
36 N
42 N
12
53. A comet passes near the Sun (2.0×1030 kg) as shown below. At its perihelion P (point
where it is closest to the Sun), its distance to the Sun is rP = 8.0×1010 m. What is the
minimum speed of the comet at this point for the orbit to be open?
A.
B.
C.
D.
E.
34 km/s
58 km/s
87 km/s
98 km/s
120 km/s
P
•
rP
Sun
54. A 2000 kg satellite moves in a circular orbit 400 km above the Earth’s surface. How
long will it take for the satellite to go around the Earth once?
A.
B.
C.
D.
E.
83 min
93 min
103 min
166 min
186 min
13
55. A negatively charged rod is brought near one end of an uncharged metal bar. The
opposite end of the metal bar (furthest from the charged rod) will be ___________
and the net force between the rod and the metal bar will be __________
A.
B.
C.
D.
E.
positive, attractive
negative, attractive
positive, repulsive
negative, repulsive
None of the above
56. Three identical charges of 3.0 µC are placed at the vertices of an equilateral triangle
which measures 30 cm on a side. What is the magnitude of the electrostatic force on
any one of the charges?
A.
B.
C.
D.
E.
1.6 N
1.8 N
2.0 N
2.2 N
2.4 N
14
57. A solid metal sphere of radius 2.0 cm carries a total charge of −1.0 µC. What is the
electric field at a point located 1.0 cm away from the center of the sphere?
A.
B.
C.
D.
E.
0.9 ×106 N/C, direction radially out
9.0 ×106 N/C, direction radially out
0.9 ×106 N/C, direction radially in
9.0 ×106 N/C, direction radially in
0
58. Which of the following statements about the charges whose electric fields are shown
below is correct?
Q1
A.
B.
C.
D.
E.
Q2
Q1 > 0, |Q1| > |Q2|
Q1 > 0, |Q1| < |Q2|
Q1 < 0, |Q1| > |Q2|
Q2 > 0, |Q1| < |Q2|
Q2 < 0, |Q1| < |Q2|
15
Here you can write down your answers and keep this page to compare with the posted
solutions.
31
46
32
47
33
48
34
49
35
50
36
51
37
52
38
53
39
54
40
55
41
56
42
57
43
58
44
45
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