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Physics 221 2007S Exam 2 SOLUTIONS
Page 1 of 24
[28] Assume that the moon can be modeled as a solid sphere of uniform density. The
mass of the moon is
22
7.4 10 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)
35
2
2.4 10 kg m
×
(B)
35
2
1.6 10 kg m
×
(C)
35
2
1.2 10 kg m
×
(D)
34
2
9.6 10 kg m
×
(E)
34
2
4.8 10 kg m
×
Answer [D]: For a solid sphere of uniform density,
2
2
5
I
MR
=
, so plugging in the
numbers from the problem:
22
2
2
3
4
2
2
5
0.4(7.4 10 kg)(1800000m)
9.6 10 kg m
IM
R
==
×
=
×
[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)
FIP
vvv
>>
(B)
FPI
(C)
=
=
(D)
<<
(E)
<
<
Answer: [C]
because the only force which does work is the conservative
force of gravity. Thus the net work done on the object, hence the increase in kinetic
energy, is the same in all cases. Since all of the objects have the same mass, it follows
that the final velocity is the same.
h
v
F
v
I
v
P
Fall
Incline
Pendulum
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Page 2 of 24
[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) 6.7m/s
(B) 15 m/s
(C) 13 m/s
(D) 25 m/s
(E) None of the above.
Answer [B]: Using conservation of momentum, if
i
v
is the initial velocity and
f
v
is the
final velocity, then
()
2000 kg+1000 kg
10
2000 kg
m
15
s
it
r
u
c
k
i
f
truck
car
f
truck
car
if
truck
pmv
pm
m
v
mm
vv
m
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
Answer [B] : The kinetic energy is given in terms of momentum and mass by
2
2
p
K
m
=
Thus
22
::
:
(2
) :
)
4:2
2:1
BA
B
AA
B
A
pp
KK
p
mp
m
m
=
=
=
Physics 221 2007S Exam 2 SOLUTIONS
Page 3 of 24
[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)
Answer [E]: The total mass of the system is 12 kg. The simplest way to approach the
problem is do divide it up into three pieces where the CM is obvious and then combine
those results into a grand center of mass. The division is shown
in red. The grand center
of mass for the whole system is thus
ˆˆ
(4kg)(1.5m
2.5m )
(4kg)(1.0m
1.0m )
(4kg)(2.5m
1.0m )
(4kg) (4kg) (4kg)
(1.7m
1.5m )
AA
BB
CC
cm
ABC
mr mr mr
r
mmm
ij
++
=
+
=
=+
GGG
G
Another way of simplifying the problem is by noting that the y component of the CM has
to be in the middle (
y
CM
=1.5 m) because the system is made of three horizontal slices of
4 kg each.
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This note was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrerasiklody during the Spring '08 term at Iowa State.
 Spring '08
 HerreraSiklody
 Inertia, Mass

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