Download The situation described below pertains to the next two questions:

PHYSICS 221
SPRING 2009
EXAM 2: April 2, 2009 8:00pm—10:00pm
Name (printed): ______________________________________________
Recitation Instructor: _________________________
Section #_______
INSTRUCTIONS:
This exam contains 25 multiple-choice questions plus 2 extra credit questions, each worth 3
points. 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 and 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, is permitted.
Electronic devices that can store large amounts of text, data or equations (like laptops, palmtops,
pocket computers, PDA or e-book readers) are NOT permitted. If you are unsure whether or not
your calculator is allowed for the exam, ask your TA.
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. Always use two digits (e.g. 01, 09,
11, 13). Honors sections: H1 → 02; H2 → 13; H3 → 25.
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. 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, Soeren Prell and Paula Herrera.
28. The potential energy function for a particle is given by
U(x) = 2/3 [J m–3] x3 – [J m–2] x2 + 1 J
The particle is originally at rest at x = 1m. When released, the particle ______.
a.
b.
c.
d.
e.
will accelerate in positive x direction.
will accelerate in negative x direction.
is in a stable equilibrium.
is in a neutral equilibrium.
is in an unstable equilibrium.
29. A child fires a marble of mass m with a spring-loaded toy cannon vertically
up. The child stretches the spring with spring constant k by a distance Δx and
the marble reaches a height h (h >> Δx) after the spring is released. For a
second shot with the same cannon the child stretches the spring twice as far
and uses a marble with twice the mass of the first marble. The second marble
reaches a height of _____.
a.
b.
c.
d.
e.
h/4
h/2
h
2h
4h
30. A particle with mass m = 1.0 kg is subjected to a force associated with the
potential U shown in the figure. No other forces act on the particle. At
position x = −2.0 m, the particle has a velocity vx. For the particle to go past
the potential maximum at x =1m, the velocity must exceed _____m/s.
a.
b.
c.
d.
e.
0.25
0.5
1.0
2.0
4.0
U[J]
3
2
1
0
-1
-2
-3
−2
−1
0
1
2
3
4
x [m]
31. A student of mass m = 80 kg is standing on a cart that has a mass of
M = 200 kg and goes with a speed of 6.0 m/s in positive x-direction. The
student jumps off the cart to the back with a speed of 6.0 m/s relative to the
initial velocity of the cart. The velocity of the cart after the student jumped off
is _____ m/s.
a.
b.
c.
d.
e.
−2.8
0.0
4.6
8.4
12.0
32. The cross section of a piece of metal of uniform density is shown in the figure
below. The y-position of the center of mass of the piece is at ______ .
a.
b.
c.
d.
e.
0.0 m
0.25 m
0.5 m
0.75 m
1.5 m
33. The planet Mars has a mass of 0.107 ME and a radius of 0.53 RE, where ME
and RE are the earth’s mass and radius, respectively. If a person weighs
150 lbs on earth, how much does the same person weigh on Mars?
a. 16 lbs
b. 30 lbs
c. 57 lbs
d. 150 lbs
e. 534 lbs
34. A box with mass m = 3 kg is released on a frictionless incline at height
h = 2.4 m over the ground as shown in the figure below. The incline has an
angle of 30o with the horizontal. The horizontal is a rough surface and has a
coefficient of kinetic friction of μk = 0.2. What distance d does the box slide
on the horizontal before it comes to a stop?
a.
b.
c.
d.
e.
7.2 m
12.0 m
18.0 m
24.0 m
32.4 m
35. A particle with mass m = 1 kg is subjected to a force associated with the
potential U as shown in the figure. No other forces act on the particle. The
particle is released from rest at position x = 2.5 m. The particle has maximum
speed at _______.
a.
b.
c.
d.
e.
x1 = −2.4 m
x2 = −1.6 m
x3 = 0.0 m
x4 = 0.8 m
x5 = 1.6 m
36. Two blocks slide on a frictionless surface in the positive x direction. Block 1
has mass m1 and block 2 has mass m2 = 2m1. Before the two blocks collide,
block 1 has velocity v1 = 6 m/s and block 2 has velocity v2 = v1/2. After the
collision, which is elastic, the velocity of block 1 is _____.
v1
a. −2 m/s
b. 0 m/s
c. 2 m/s
d. 3 m/s
e. 5 m/s
m1
v2
m2
37. A box of mass m = 500 kg has dimensions 3m × 3m × 6m. Originally it lies on
one of its large sides as shown in the figure below. How much work is needed
to stand the box on one of its small sides?
before
a.
0 kJ
b. 7.4 kJ
c. 14.8 kJ
d. 26.5 kJ
e. 29.6 kJ
after
3m
6m
6m
3m
38. An object with mass m sits between two very heavy spheres of mass 2M and
M, respectively, as shown in the figure below. The object is 2r away from the
center of the heavier sphere and r away from the center of the lighter sphere.
The net force on the object is _______, where G is the gravitational constant.
a.
b.
c.
d.
e.
G mM/ r2 to the left
G mM/ (2r2) to the left
0
G mM/ (2r2) to the right
G mM/ r2 to the right
2M
2r
m
r
39. Which of the statements below about conservative forces is false?
a.
b.
c.
d.
e.
A conservative force can be derived from a potential energy function.
The work done by a conservative force along a closed path is zero.
If only a conservative force acts, total mechanical energy is conserved.
Gravity is a conservative force.
The work done by a conservative force is always positive.
M
40. A red car of mass mr = 800 kg is moving with a velocity of vr = 30 m/s in
positive x direction and a blue car of mass mb = 600 kg is moving with a
velocity of vb = 40 m/s in positive y direction. What is the speed of the center
of mass of the two car system?
a.
b.
c.
d.
e.
24 m/s
34 m/s
40 m/s
50 m/s
70 m/s
41. A solid, uniform sphere of mass M and radius R is glued to the tip of a thin
rod of length 2R and mass M. Find the moment of inertia of the system for
rotations about an axis through the free end of the rod.
a.
b.
c.
d.
e.
0.7MR2
1.7MR2
3.7MR2
9.7MR2
10.7MR2
2R
axis
R
42. A solid cylinder (S) and a hollow cylinder (H), both with mass M, radius R
and length L, are released at the top of an incline. The cylinders roll without
slipping down the incline. Compare their speeds and rotational kinetic
energies at the bottom of the incline.
a.
b.
c.
d.
e.
vS < vH
vS < vH
vS = vH
vS > vH
vS > vH
;
;
;
;
;
KErot S <
KErot S >
KErot S =
KErot S <
KErot S >
KErot H
KErot H
KErot H
KErot H
KErot H
43. A toy truck of mass 250 g moves to the right on top of a meter stick that rests
on two fulcrums. The mass of the meter stick is 300 g. The left fulcrum is at
the 0 mark. The right fulcrum is at the 65 cm mark. The system will tip over
when the center of mass of the truck goes beyond the ________ mark.
a.
b.
c.
d.
e.
.
74 cm
78 cm
83 cm
89 cm
92 cm.
The situation described below pertains to the next two questions:
A uniform rod of mass 10 kg and length 5.0 m is hinged to the ceiling at one end. The
other end is supported by a 5.0 m massless cable attached to the ceiling (see figure).
44. What is the tension in the cable?
a.
b.
c.
d.
e.
14 N
36 N
49 N
72 N
98 N
hinge
20°
45. The string suddenly snaps. What is the angular acceleration of the rod right
after this?
a.
b.
c.
d.
e.
1.0 rad/s2
1.8 rad/s2
2.8 rad/s2
3.0 rad/s2
3.4 rad/s2
46. Three forces of equal magnitude 10 N are applied on a uniform rod of length
1.0 m as shown. What is the net torque about the center of mass of the rod?
30°
50 cm
a.
b.
c.
d.
e.
0.67 N m
2.5 N m
7.5 N m
9.3 N m
18 N m
47. Three identical solid cylinders of mass M and radius R are used in the system
shown below. Two of them (1 and 3) are attached to a massless, ideal string
that goes through their center of mass, and roll without slipping on either side
of a double incline. The last cylinder (2) can only rotate about its axis and is
used as a pulley. The string does not slip on the pulley. If cylinder #1 rolls up
the incline with speed v, what is the total kinetic energy of the system?
a.
b.
c.
d.
e.
3
Mv 2
2
5
Mv 2
2
3
Mv 2
4
5
Mv 2
4
7
Mv 2
4
1
30°
2
3
45°
48. A 5.0 kg block hangs at the end of a massless, ideal rope wound around a
solid, uniform cylinder with mass 6.0 kg and radius 20 cm. The cylinder can
only rotate about its axis. What is the tension in the cable when the system is
released?
a.
b.
c.
d.
e.
13 N
18 N
25 N
32 N
49 N
6.0 kg
5.0 kg
49. A rough model of a star is a rotating uniform sphere. If the star was to shrink
due to its own gravitational pull to another uniform sphere with one tenth of
its original radius but without any mass loss, what would be the ratio between
the final and the initial rotational kinetic energy, KEfinal/KEinitial?
a.
b.
c.
d.
e.
10–4
10–2
1
102
104
50. A rod is attached to the ceiling through a hinge, so it can rotate about that
point. A ball of putty with an initial speed v strikes the rod near its bottom and
sticks to the rod. Which of the following quantities is conserved during the
collision for the rod+ball system?
a. Total linear momentum
b. Total angular momentum about the center
of mass of the rod
c. Total angular momentum about the hinge
d. Mechanical energy
e. All of the above.
m
v
51. A child of mass m rides on a merry-go-round. The child can be assumed to be
a point-like particle, and the merry-go-round is a uniform disk of mass
M = 50 kg and radius R = 1.0 m with negligible friction at the axle. The child
is initially at the edge of the merry-go-round, which rotates with an angular
speed ω0 = π rad/s. When the child jumps in the direction of motion with
speed v = 5.0 m/s relative to the ground, the merry-go-round stops. What is
the mass of the child?
a.
b.
c.
d.
e.
30 kg
37 kg
42 kg
48 kg
52 kg
m
Child
m
v
At rest
M
M
R
Before jump
ω0
R
After jump
52. Seven point-like identical particles are held together in a two-dimensional
rigid structure with massless rods (symbolized by dashed lines). Three
possible axes of rotation (symbolized by the bold lines) are given. The
particles, rods and axes are in the plane of the paper. Rank the resulting
moments of inertia of the system.
2
1
3
a.
b.
c.
d.
e.
I1 < I2 < I3
I1 < I3 < I2
I2 < I3 < I1
I2 < I1 < I3
I3 < I2 < I1
53. A tow truck is pulling a car out of a ditch by means of a steel cable that is
9.1 m long and has a radius of 0.50 cm. When the car just begins to move, the
tension in the cable is 890 N. How much has the cable stretched?
a.
b.
c.
d.
e.
0.1 mm
0.5 mm
0.9 mm
1.2 mm
1.5 mm
54. A piece of aluminum is surrounded by air at normal atmospheric pressure.
The aluminum is then placed at the bottom of the Mariana Trench (the deepest
point of the ocean), where the pressure is approximately 1000 atm. Determine
the change in the volume of the aluminum.
a.
b.
c.
d.
e.
0.001%
0.01%
0.1%
1%
10%
You may record your answers on this page and take it with you after the exam to
compare to the posted solutions.
28
38
48
29
39
49
30
40
50
31
41
51
32
42
52
33
43
53
34
44
54
35
45
36
46
37
47