Part 2: coefficient of restitution – PASCO PS-2141 Force Platform User Manual

Page 7

M o d e l N o . P S - 2 1 4 1

E x p e r i m e n t : B o u n c i n g B a l l

Set the sample rate of the platform to 5 Hz. Press the tare button. Place the ball on
the platform and collect data for a few second. Use the measured force to calcu-
late the mass of the ball (m).

Calculate the change in momentum of the ball:

If the ball left the platform slower than it hit, why is

∆P positive?

On the graph of force versus time, zoom in on the second bounce. Measure the
area under the curve over the time interval starting when the ball touches the plat-
form and ending when it leaves the platform; this is the impulse. Compare this
value to your answer from step 6.

Part 2: Coefficient of Restitution

Procedure

Repeat the procedure from Part 1, but this time drop the ball from a lower height and
allow it to continue bouncing until is comes to rest on the platform. You will probably
have to try several times.

Analysis

What is the maximum force measured during the first bounce? How does it com-
pare to the weight of the ball? What is the force measured between bounces when
the ball is in the air?

Notice that the maximum force of each bounce is less than the preceding bounce.
Find an simple equation that approximately models this decrease over the entire
series of bounces.

At some point on the graph, the ball stops bouncing off the platform but contin-
ues to oscillate while remaining in contact with the platform. How can you iden-
tify this point?

Zoom in on the area of the graph where the ball is oscillating but not bouncing.
Describe what happens to the minimum force measured for each cycle of oscilla-
tion as the ball comes to rest.

What is the final force measured after the ball has come to rest on the platform?
How is this force related to the ball’s mass?

Further Study

Measure the hang times between several successive bounces and record them in a
table. Use Equation 3 to calculate the launch speed of the ball after every bounce.
(Assume that the launch speed after a bounce is equal to the impact speed before
the next bounce.) Make a graph of these speeds and use an exponential curve fit
to find the coefficient of restitution.

Measure the impulses of two or more bounces. Can you find the coefficient of
restitution using only the impulse data? (Hint: for any single bounce, show that
∆P is proportional to the impact speed.)

∆P

down

–

(

)