PASCO PS-2141 Force Platform - Manual (Page 5)

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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
5
Experiment: Bouncing Ball
In this experiment you will drop a ball on the Force Platform and allow it to bounce.
In Part 1 you will examine the relationship between the impulse of a single bounce
and the time between bounces. In Part 2, you will observe what happens as the ball
undergoes a series of decreasing bounces and comes to rest on the platform.
Theory
As a ball undergoes a series of bounces on the platform, there are two alternating
phases.
Phase 1: ball in contact with platform
This phase starts when the descending ball makes contact with the platform and ends
when the ball leaves the platform. During this time, the platform applies force (mea-
sured by the platform) which causes a change in velocity (
V up
−
V down
) of the ball,
where V down
(a negative value) is the velocity of the ball as it hits the platform and V up
(positive) is the velocity as it leaves the platform. The change in momentum (
∆P) of
the ball is given by
(eq. 1)
where m is the mass of the ball. By Newton’s Second Law, , the change
in momentum is equal to the impulse of the collision.
Thus
∆P is also equal to the area under a force versus time plot.
Phase 2: ball in free fall
The free-fall phase occurs between bounces, when the ball is not in contact with the
platform. (Though it is said to be in free “fall,” the ball travels upwards during the
first half of this phase.) If the ball’s maximum height is less than about a meter, the
frictional air drag is small, and we can assume that the ball undergoes constant accel-
eration while in free fall.
If the ball leaves the platform at time t
0
= 0, traveling (upwards) with a velocity of
V 0
,
we can write
(eq. 2)
where
V
is the velocity at some later time t and g = 9.8 m/s 2
. If t is equal to time that
the ball spends in the air between bounces (the “hang time”), then V =
−
V 0
. In other
words, the ball hits the platform at the same speed that it previously left the platform.
Thus,
Required Equipment Part Number
Force Platform PS-2141
PASPORT Interface See PASCO catalog or www.pasco.com
Inflated Rubber Ball
∆P
m V
up
V
down
–
( )
=
F dP dt
⁄
=
∆P
impulse F t d
∫
= =
V V
0
gt – =