In a recent post on sci.physics.research, Igor Khavkine proposes a fun problem (requiring no more than high school classical mechanics) whose solution, he claims, is ‘a little surprising and intriguing’. Here is the problem:
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.
Some people have already chimed in with comments, but you may want to try your hand at it first!
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