Part 1: impulse and momentum – PASCO PS-2141 Force Platform User Manual
Page 6
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F o r c e P l a t f o r m
E x p e r i m e n t : B o u n c i n g B a l l
6
(eq. 3)
By measuring the hang times before and after a collision, we can calculate the speeds
of the ball just before and just after the collision. (Note that we do not assume these
speeds to be equal.) Using these speeds, we can calculate the change in momentum.
The change in momentum can be compared to the impulse calculated using the area
under the force versus time graph.
Coefficient of Restitution
The coefficient of restitution is the ratio of the ball’s speeds just before and just after a
single bounce (both speeds are measured as positive values). This ratio is the same for
every bounce. You can see the effect of this speed reduction by observing that the
maximum height after each successive bounce decreases. With the Force Platform
you can also observe that the maximum force of each bounce decreases and the time
between bounces decreases.
An ideal ball on an ideal surface would continue bouncing indefinitely, with the max-
imum height after each bounce approaching zero asymptotically. A real ball eventu-
ally stops bouncing, but continues to oscillate for some time while remaining in
contact with the platform before finally coming to rest.
Part 1: Impulse and Momentum
Procedure
1.
Set the sample rate of the Force Platform as high as possible (either
1000 Hz or 2000 Hz).
2.
Press the tare button.
3.
Hold the ball about 0.5 m above the platform. Start data collection and
drop the ball. Allow the ball to bounce three times. Stop data collec-
tion.
The ball should hit the platform close to the center at every bounce. If it
does not, delete the data and try again.
Analysis
1.
Measure the hang time between the first and second bounces (t
before
).
2.
Calculate the velocity of the ball just before the second bounce.
3.
Measure the hang time between the second and third bounces (t
after
).
4.
Calculate the velocity of the ball just after the second bounce.
V
0
1
2
--- gt
=
V
down
1
2
---gt
before
–
=
V
up
1
2
--- gt
after
=