On Sat, Dec 11, 2010 at 12:34 PM, Andy Latto <andy.latto@pobox.com> wrote:
So the answer to the original question of "why don't physicists get the problem of Newton's Cradle with a double-mass ball hitting the stationary balls" may be "It's an ill-posed problem"! If we model it as a series of non-simultaneous collisions, then after the big ball hits the second ball, it's still moving in the same direction, at speed V/3. So it will be involved in more collisions. All the collisions are nearly simultaneous, and the answer will depend on what order they occur in, so I don't see any way to give a unique answer.
How about assuming the balls are springy enough that they compress sufficiently so they're all in contact simultaneously? And if we assume they are close enough to touching that they all start compressing simultaneously? This seems like the natural assumption to make in the absence of more knowledge about the details of the spacing. Maybe there's still some assumption that needs to be made about the spring constant of the bigger ball compared with all the smaller balls. And maybe I should stop babbling and sit down and do some actual math, given the name of this list. Speaking of which, I should send another post on a different topic, with a little math in it. So I will do that. --Joshua