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1
1. (15 points)
A solid cylinder
⎟
⎠
⎞
⎜
⎝
⎛
=
2
2
1
MR
I
with mass 30.0 kg and
radius 0.200 m rolls without slipping up a hill, as shown in
the figure to the right.
It has an initial velocity to the right,
0
v
, of 10.0 m/s.
a)
What is the initial angular velocity of the cylinder? (2 pts.)
b)
Find the initial total kinetic energy of the rolling disk. (4 pts.)
c)
How far up the hill (i.e. the maximum height,
h
) does the ball roll before it stops? (6 pts.)
d)
In the diagram below, draw a free body (force) diagram of the cylinder as it rolls up the hill.
Be sure to draw the force vectors starting exactly where each force acts on the object.
(3 pts.)
15
v
0
h
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View Full Document2
2. (18 points)
A massless spring with spring constant
k
= 200. N/m is attached
to a block of mass
m
= 1.25 kg and stretched from its
equilibrium position by amount
x
0
= 0.0500 m and released.
Take the time
t
= 0 as the time when it is first released.
Assume
the mass is moving on a frictionless surface.
a)
Find the period of the resulting simple harmonic motion. (2 pts.)
b)
Find the velocity of the mass at the point where the potential and kinetic energy is
equal. (4 pts.)
c)
Find the two locations (i.e. x positions) where the potential and kinetic energy are
equal.
(4 pts.)
d)
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 Spring '08
 all
 mechanics, Mass

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