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Re: Pool Ball Physics



The use of a virtual reflection line inside the bumper may be obvious, but I
have not seen it mentioned anywhere. Your second reference does not mention
this, and merely talks about reflections at the bumper. I suspect that
adept pool players automatically compensate for this particular problem.
Some web simulations programmed by physicists imply that you put a mirror at
the bumper instead of inside it to visualize a shot.

The article was published in a refereed math journal, so apparently the
result was not known to mathematicians. I really think that it is a
suitable topic for math as students need to get applications in their math
classes. This is the vital end to a complete learning cycle. Math classes
do very little to prepare students for math intensive courses like physics.
They come in unable to solve an equation, or use it in realistic
applications. Students do not get a feel for numbers and solutions when
they are never forced to convert 2 radical(5) to a decimal number.

John M. Clement
Houston, TX



John Clement wrote:

... the standard math text treatment of pool table physics ...

I didn't know there _was_ a standard math-text treatment
of pool-table physics. It doesn't seem like a suitable
topic for a math class.

A fascinating treatise on the physics of real pool tables
by Ron Shepard can be found at
http://www.playpool.com/anonftp/pub/APAPP/apappTotl.pdf

... claims that the standard math text treatment of pool table
physics is wrong.

I'll bet it is!

The standard math text treatment uses a mirror over the
edge of the bumper and has the player aim at the virtual image.
However this is wrong. The mirror must be moved in by about
the radius of the ball.

Yes, for starters.

Of course this is assuming an elastic
hard collision model with no friction.

And various other assumptions.
Spin (which depends on friction) is a big part of
real-world pool.

I suspect this has already been discussed or is written up
in one of the physics journals or textbooks.

If you're asking about the mirror result in particular, I
imagine it's not publishable by itself. Too obvious.

Would anyone have a source for this?

Oddly, Shepard doesn't have much to say about cushions.

The "point of aim" is discussed at
http://web.ndak.net/~bolton/billiards2.html