Take a glass that is partially filled with water and drop a cork into it. The cork won't float in the center, but keeps drifting to one side and attaching itself to the side of the glass.
Without swirling the water, how can you make the cork float in the center?
(In reply to re(3): spoiler
Thank you, JLo, for recklessly dicing with a hangover to clear the matter up. I think I know now where my earlier reasoning went wrong: I neglected the pressure gradient in the water due to gravity.
In reality the pressure of the water at the top of the convex surface will be slightly lower than at the rim. As a consequence, the cork will sink in (very) slightly more when it is at the centre. The centre of mass of the displaced water also is slightly farther under the surface when the cork is in the middle, but by a lesser amount. So the water loses more potential energy than the cork gains when it moves to the centre, and the centre position is energetically preferable.
Posted by vswitchs
on 2006-10-05 02:09:51