Re: Fun problem
- From: "John Bell" <john.bell@xxxxxxxxxxxxxxxxxx>
- Date: Thu, 27 Apr 2006 21:16:04 +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
Perhaps this question would make more sense if you:
1) Specify a less than 100% efficiency in elastic collisions
2) Specify a finite height of the particle
3) Specify a gravitational field.
1) will admit the possibility that the particle can get trapped
2) will then re-admit the possibility that the particle can escape
regardless
3) will (a) ensure that the particle can fall into the hole in the
first place and
(b) introduce some relevance to the depth of the hole.
You would then also have a question with some physical significance.
John Bell
http://global.accelerators.co.uk
(Change John to Liberty to respond)
.
- References:
- Fun problem
- From: Igor Khavkine
- Fun problem
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