Re: Fun problem
- From: "John Bell" <john.bell@xxxxxxxxxxxxxxxxxx>
- Date: Mon, 24 Apr 2006 21:29:18 +0000 (UTC)
Igor Khavkine wrote:
I recently ran into a fun problem from an old Russian physics olympiad.
I found the solution a little surprising and intriguing. The problem
requires no more than high school classical mechanics and some
ingenuity. Here it is for your amusement.
Consider a point particle sliding on a flat table (ignore friction).
The table has a cylindrical hole of finite depth (vertical walls, flat
bottom). The particle can approach the hole with different velocities
and with different impact parameters (the particle's motion need not be
directed toward the center of the hole). As the particle falls into the
hole, it starts bouncing off the walls and the bottom (assume elastic
collisions). Sometimes it gets stuck in the hole forever, sometimes it
escapes (bounces out). Determine the relation between the depth of the
hole, its radius, the particle's initial velocity, and impact parameter
necessary for the particle to escape after it falls in.
Enjoy!
Igor
Firstly, the particle will not even fall into the hole unless we invoke
a gravitational field relative to the table.
If we do, then loss in gravitational potential energy on reaching the
bottom will then be reflected by a corresponding gain in upward kinetic
energy, if we assume perfectly elastic collisions. Therefore, I see no
reason why the particle should not eventually get out again.
Consequently I think you have defined too few parameters for the
problem to make sense (or too many).
John Bell
http://global.accelerators.co.uk
(Change John to Liberty to respond)
.
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- From: Igor Khavkine
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