Re: Fun problem
- From: Richard Saam <rdsaam@xxxxxxx>
- Date: Tue, 25 Apr 2006 01:48:30 +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
Conditions for particle getting out of hole
Maybe something like "QM particle in the box"
2g/D = v^2 n^2 / r^2
g = gravity accleration
D = hole depth
v = initial particle horizontal velocity
n = integer
r = hole radius
Richard
.
- References:
- Fun problem
- From: Igor Khavkine
- Fun problem
- Prev by Date: Re: Fun problem
- Next by Date: Re: Super Copenhagen Interpretation (Consistent Histories)
- Previous by thread: Re: Fun problem
- Next by thread: Re: Fun problem
- Index(es):
Relevant Pages
|
|
