The Wham-o theory
According to researcher Margaret D. Campbell, ". . . when two superballs of different masses are dropped with the larger on the bottom, the smaller one has its velocity increased by a factor of three and reaches a final height of nine times its original height."
"The first collision will have only the effect of reversing the large ball's velocity. For the second collision, involving both balls, we use the fact that the total momentum and the total kinetic energy of the two balls is the same before and after the collision, and, solving for the final velocities, obtain the equations (where Mr = M1/M2 is the mass ratio):
V1f = [(Mr - 1) / (Mr + 1)]V1i + [2 / (Mr + 1)]V2i
V2f = [2Mr / (Mr + 1)]V1i + [(1 - Mr) / (Mr + 1)]V2i
or, if V1i = V2i = Vi
V1f = [(-Mr + 3) / (Mr + 1)] Vi
V2f = [(1 - Mr) / (Mr + 1)] Vi
and Mr -->0,
V1f = 3Vi . . . [and thus,] the smaller ball will gain three times the velocity it started with . . . ."
Source: http://members.aol.com/doder1/super1.htm
The "Not - So - Wham-o" theory
Description:
(the above formula is given as a
non-variable, and the following theory was tested on a visual
basis)
To prove that these balls are not the same as the Wham-o balls, and have a much less recovery rate, the mass ratio from the above formula was substituted with the mass ratio of the "not - so - Wham-o" balls, the larger of the masses on the bottom.
Hypothesis:
The "not - so - Wham-o" balls will have a lower recovery rate in comparison to the Wham-o balls, and the above formula will prove incorrect.
Results:
The "not - so - Wham-o" balls had approximately (estimated) recovery rate of 40%, and the smaller ball will not gain three times the velocity it started with. The smaller ball had an increased velocity (not measured here). Thus, the above formula of Margaret D. Campbell is not correct for the "not - so - Wham-o" balls.
