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Physics: Year 1
PX132 Assignment 4 (NOT assessed)
Due at 5:00pm on Friday, December 7, 2007
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A Superball Collides Inelastically with a Table
Description:
A ball is dropped onto a table from a given height and rebounds to another (smaller) height. Find the average
force and impulse exerted by the table on the ball, momentum before and after the collision, and change in kinetic energy.
All numerical.
As shown in the figure , a superball with mass
equal to 50 grams is dropped from a height of
. It collides with a
table, then bounces up to a height of
. The duration of the
collision (the time during which the superball is in contact with the table) is
. In this problem, take the positive
y
direction to be upward, and
use
for the magnitude of the acceleration due to gravity.
Neglect air resistance.
Part A
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Find the
y
component of the momentum,
, of the ball immediately before the collision.
Hint A.1
How to approach the problem
To find the superball's
speed
immediately before the collision, use the fact that energy is conserved as the ball descends.
Apply conservation of energy by setting the initial (potential) energy of the ball equal to its final (kinetic) energy at the
moment it hits the table. Determine the velocity of the ball when it hits the table and use that velocity to compute the ball's
momentum.
Part A.2
Find the speed of the ball
Find the speed
of the ball just before it hits the table.
Hint A.2.a The speed of the ball
Using conservation of energy, you can show that the speed of the ball just before it hits the the table is
, where
is
the height it falls through, and
is the magnitude of the acceleration due to gravity.
Express your answer numerically in meters per second.
ANSWER:
=
Now find the momentum (mass times velocity). Remember to use the correct direction.
Express your answer numerically, to two significant figures.
ANSWER:
=
Part B
Find the
y
component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table.
Hint B.1
How to approach the problem
Recall that the ball reaches a height of only
on the rebound. To find the ball's velocity immediately after the
collision (that is, just as it is leaving the table), use the fact that energy is conserved as the ball ascends. (Note: Energy is
not
conserved during the collision!) Apply conservation of energy by setting the initial (kinetic) energy of the ball when it
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 Fall '07
 Hamilton
 Calculus

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