Discussion of the Question 05/97
The question was:When you throw a stone at a glancing angle into the water it skips several times before sinking. Can you increase the number of skips by modifying the angle or velocity at which the stone is thrown? Can you increase it by choosing a stone of special weight or shape? Is there a limit to the number of skips?
(11/96) Y. Tsori from Tel Aviv U. wrote (slightly edited):
The number of skips n depends upon the following factors:
1) The angle of glancing theta.
2) mg (where m is the mass of the stone).
3) mu - the friction coefficient between the stone and the water. I assume friction with the air is negligible.
4) The initial speed of the stone, v.
I assumed that the shape of the stone is given, and does not change. From dimensional analysis, it is clear that... n can only depend on the angle theta.
(11/96) Y. Kantor: The "friction coefficient" must be defined carefully. Let's say that friction force depends on velocity of the stone, viscosity (of the water) and size of the stone. Whatever the combination, clearly we can create a dimensionless quantity from the weight of the stone and the friction force. Thus the angle theta is not the only dimensionless quantity in the problem.
(11/98) Christian von Ferber from Duesseldorf U. (e-mail ferber@thphy.uni-duesseldorf.de) wrote:
When the Rhine flooded our garden at the time, I had the opportunity to test the question about the jumping stone. An important ingredient is the angular momentum of the stone. Without spinning it will never jump. Also the jumps follow a curved line. I suspect that the spin stabilizes the angle between the (flat) stone and the water surface. It also results in 'violating' the law of reflection when the stone jumps off the surface again. As the stone will not be reflected any more, when it has lost the angular momentum, the question seems to be connected with 5/96 "motion of the hockey puck" and at least as complicated, as in addition hydrodynamics comes into play.
Back to "front page"