# mgh mv kx + = ```1 of 8
Don't forget to review the old stuff.
RIII-1. A mass m is moving east at with constant velocity, coasting under its own inertia. Then a
constant force of magnitude F is applied in the northern direction. What
happens to the speed of the mass?
F
A) speed increases
B) decreases C) remains constant
v
m
Answer: speed increases. This is different than circular motion with constant speed. With circular
motion, the force changes direction to always be perpendicular to the velocity. That is not the case
here.
RIII-2. A mass m is dropped from rest from a height hi above a table top on which sits a spring with
spring constant k. The mass compresses the spring by a maximum amount x and stops for an instant at
a height hf . There is no friction in this problem. Which of the following equations correctly expresses
conservation of energy and allows one to solve for the compression x of the spring?
A)
mgh i  12 mv 2  12 kx 2
B)
mgh i  12 kx 2  mgh f
C)
mgh i  12 kx 2  mgh f
D)
mg h f  h i   12 kx 2  12 mv 2
E) None of these equations is correct.
Answer: mgh i  12 kx 2  mgh f
m
hi
k
x
hf
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RIII-3. Ball 1 of mass m moving right with speed v bounces off ball 2 with mass M (M &gt; m), and then
moves left with speed 2v.
What is the magnitude of the impulse I = p of ball 1?
M
m
M
m
v
2v
A) mv
B) 2mv
E) None of these
C) 3mv
D) (1/2)mv
By how much did the momentum of ball 2 decrease?
A) Mv
B) 2Mv
C) 3mv
D) (1/2)mv
E) zero
Answer: 3mv (by Conservation of Momentum)
RIII-4. A bullet of mass m traveling horizontally with initial speed v strikes a wooden block of mass
M resting on a frictionless table. The bullet buries itself in the block, and the block+bullet have a final
speed vf.
Fill in the blank: The total kinetic energy of the bullet+block after the collision is ___________ the
total KE before the collision.
m
M+m
v
M
vf
Before
A) greater than
B) less than
After
C) equal to
Answer: less than There is friction between the bullet and the block, which generates thermal energy.
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RIII-5. Two balls, labeled 1 and 2, collide. Their initial momenta and
the final momentum of ball 1 is shown in the figure. +x to right, +y up
in diagram.
p1f
What is the x-component of the final momentum of ball 2?
A) –2 B) –1 C) 0
D) +1 E) +2
What is the y-component of the final momentum of ball 2?
A) –4 B) –3 C) –1 D) 0
E) +4
p2i
p1i
Answer: p2f_x = +2, p2f_y = 0.
RIII-6.
What is the magnitude of the torque about the origin?
A) r F sin
B) r F cos

F
r
axis
Try again. What is the torque about the origin?
A) r F sin
B) r F cos
F

r

axis
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RIII-7. An irregularly-shaped object of total mass M is free to rotate
The object, initially at rest, is acted on by a torque of constant
magnitude  for some time t and it reaches a final angular velocity of
 . There are no other torques acting. What is the time t required to
achieve the final angular velocity  of the bar?

A)
I
B)
I

C)

M
axis
M, I
M, I
D) 0
E) None of these.
I

RIII-8.
A disk of mass M and area A and radius R is reshaped into a uniform square of the same area A (and
the same mass M). The edge length L of the square is related to the radius R of the disk by L2 = R2
(same areas).
The moment of inertia I of the square is ..
A) larger
B) smaller
C) the same as
that of disk.
RIII-9.Which has larger moment of inertia, axis through C.M. or axis
to one side of C.M.?
A) Axis through C.M.
B) Axis to one side of C.M.
C) Depends on shape of object
Answer: Axis to one side of C.M. See Parallel Axis Theorem.
A
B
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RIII-10. A very light rod of length L has a mass M at the top end.
The bottom end is placed on the ground and the rod is released from
rest at an angle . It falls over, rotating about the fixed bottom end.
Instantaneously after the rod is released (t=0+, in the limit that t
approaches 0 from the + side), the upper end….
(Hint: net = I 
has initial angular velocity 
zero.
A) zero
B) not
has initial angular acceleration 
A) zero
B) not zero.
has initial tangential acceleration atan
A) zero
B) not zero.
A)zero B) not zero.
M
L

Answers: Initially,  is zero,  is not zero, atan is not zero, ar is zero.
As the rod falls over (as  decreases to zero), the angular acceleration 
A) increases
B) decreases
C) remains constant.
Answer: increases (since the torque increases)
RIII-11. A frictionless sliding hockey puck and a rolling hoop each have the same mass m and the
same initial speed v. Each has enough initial KE to travels up an inclined plane a height h as shown.
m
h
v
m
v
Which object has more total KE at the top of the hill?
A) Hoop
B) puck
C) Same KE at the top.
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RIII-12. Two forces are applied to a bar as shown in the diagram. Force F is applied at a 45o angle at
the center of the bar; force 4F is applied at a 90o angle at the right end of the bar. Is it possible to
maintain the bar in static equilibrium by applying an appropriate third force at the left end of the bar?
4F
?
F
A) No
B) Yes
Answer: No. You can't have both Fnet and net be zero. The net torque about the left end of the rod is
non-zero, no matter what force you apply there.
RIII-13. Two people pull on a door which is in static equilibrium. Seen from above the people pulls
are ....
hinge
force?
2F
30o
2F
The force on the door from the hinge can be completely determined by using only the equation(s)…
A)
Fx = 0 , Fy = 0
B)
 = 0 with origin about right end
C)
 = 0 with origin about center of door
Answer: Fx = 0 , Fy = 0
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RIII-14. A cylinder with moment of interia IB = 10 kg m2 is rotating on a frictionless platform with
initial angular velocity of magnitude i = 4 rad/s. A second non-rotating cylinder with IT = 5 kg m2 is
dropped onto the first as shown, and the two cylinders then rotate together. We seek the final angular
velocity of the cylinders f .
IT
f
i
IB
Before
After
Does Conservation of Angular Momentum apply in this problem?
A) Yes
B) No
C) Depends on how much friction there is between the cylinders
Is the following equation true?
A) Yes
B) No
IB i  IT f
Answers: Conservation of Angular Momentum does apply. The correct equation is
IB i  (IT  IB ) f
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RIII-15. A mass on a spring is oscillating and the position x(t) is shown as the solid curve.
x
t
The dotted curve could be …
A) the velocity v
B) the acceleration a
C) both of these
D) neither of these