A 100gram steel marble traveling at 5 m/s [Right] collides with a target
sphere at rest. The magnitude of the force between the marble and the sphere
is given by
2
2
max
2
F
kF
t
k t
where F
max
= 10.0 N and the constant
k
= 500
N/s. The force is graphed vs. time at right. The curve forms a semicircle.
1.
The collision begins at time
t
= 0 when the force between the marble on the sphere
increases from zero. The collision ends when the force decreases to zero again.
How long does the collision last?
2.
The impulse imparted to the target sphere is given by the area under the force vs.
time curve. What impulse is imparted to the target sphere?
(Hints:
The horizontal radius of the circle is half of the elapsed time. The vertical
radius of the circle is the maximum force. The area of the semicircle could be
stated as
A = ½
R
h
R
v
instead of
A = ½
R
2
.)
3.
What impulse is imparted to the marble?
4.
What is the momentum of the marble before the collision?
5.
What is the momentum of the marble after the collision?
6.
What is the velocity of the marble after the collision?
7.
If the collision is elastic, what is the “shortcut” equation tha
t links the final velocity of the sphere with the final velocity of
the marble?
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 Spring '10
 Phys123
 Energy, Kinetic Energy, Mass, Momentum, Velocity

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