Re: [Phys-L] Tennis Ball on Basketball

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> Philip at N. Salinas High uses a coin on the ball.  Works well.  No separation
> there.
>
>
> A reasonable height is one meter.  So speed ~ 4.4 m/s  (E principle easier
> than kinematics)   Re then ~  69k,   therefore, Cd ~ 0.5
>
> Drag then  v. ~  0.55N    Mass of basket ball ~ 0.625   force then v. ~  6N  so
> ignorable (treat as free fall)  E at impact v. ~ 6 J.
>
> If coefficient of restitution v. ~ 0.85  then initial speed after impact is ~ 3.74
> m/s
>
> mass one cent  2.5 g     momentum principle  > 900 m/s
>
>
> bc amateur physicist and thinks something wrong there.
>
> done v. hurriedly
>
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Bernard,

If there is separation, an upper limit on the speed of the coin just after its collision with the basketball would be 3 times the speed of the basketball at the last instant before it hits the floor, so 13.2 m/s.

I think the assumption of separation (as suggested by John D.) is a good one.  If, upon release, the object on top of the basketball is resting on the basketball there is a normal force equal to the weight of the upper object acting upward on the upper object.  So, upon release, the upper object is experiencing an acceleration, relative to the basketball, of 9.8 m/s^2 away from the basketball.  That relative acceleration quickly drops off to zero but the decompression of the basketball results in a significant separation by the time the basketball hits the floor.

I find the separation to be about s = sqrt(m/k)gt (treating the object on top of the basketball as a rigid body having mass very small compared to that of the basketball)
where:
m is the mass of the object on top of the basketball
k is the spring constant of the basketball
g is 9.8 m/s^2
t is the time it takes for the basketball to make contact with the floor starting upon release from rest

For the case you discuss, the penny on the basketball, using the spring constant of 20 000 N/m from
<http://robbophysics.wikispaces.com/file/view/Part+D(92-95)+Revision.doc >
I get a separation of about 1.5 cm when the basketball hits the floor, and using the spring constant of 5 000 N/m from
<https://stanford.edu/~ddshin/ME331A_MIPSI_Report> 
I get a separation of about 3 cm.