Re: pool table physics (long)

[brian whatcott <inet@INTELLISYS.NET>]

At 12:37 4/21/01 -0700, Ben Crowell wrote:
> ... an old CalTech entrance exam. A pool ball is rolling
> without slipping, and collides perpendicularly with the cushion. The
> cushions on a pool table are built so that their point of contact with
> a ball is above the ball's center by a certain height b. Assume that
> the cushion's force on the ball is horizontal, and determine the
> optimal value of b if the ball is to be rolling without slipping again
> when it rebounds....


I finally took care to reread this initial note carefully.
 Physics problems of this kind are not meant to represent the real world,
it seems to me. A numerical approach to modelling a plausible mechanism
is all that is desired.
  And it seems to me you succeeded in this.

But if you notice a discrepancy with the real behavior of the modelled
objects,it would be reasonable to look at the model assumptions again.
As John Denker immediately pointed out, the horizontal force assumption
as given is suspect.

I now suppose that the downward cushion deflection which acts to reverse
the direction of the ball's angular momentum is the crucial component.
 I suppose that the area of contact varies through the interaction time,
dipping with increased deflection. If I recall, cushions are wedge shaped,
 with a horizontal top.
It is almost inevitable that the spin reverse lifts some force from the
 ball's weight. The builder's job is simply to ensure that the lift does
not greatly exceeed the weight in the worst case.




brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!