On Dec 13, 2010, at 7:33 PM, Gary Antonick wrote:
am not sure I'm following completely. I've tried this experiment now with several different model cradles (all with 1st ball mass 2m and remaining balls mass m) and get the same result each time: the last ball flies out and the remaining balls barely move. The balls clearly do *not* swing out in a fan pattern predicted by pairwise collisions.
then the balls come together and interact again. after this *second* set of collisions the the pairwise model seems accurate (because the balls started off slightly apart)— the balls fan out in the predicted pattern.
Experiments should be taken seriously. By "fan pattern predicted by pairwise collisions" I assume you mean this pattern of final velocities: 2 balls 1/3 4/3 3 balls 1/9 4/9 4/3 4 balls 1/27 4/27 4/9 4/3 etc. Another thing to bear in mind. In the standard cradle the number of collisions for 2,3,4,... balls is 1,2,3,... But for your modification the number of collisions (pairwise model) goes like 1,3,6,10,... so a non-ideal coefficient of restitution degrades the kinetic energy more. Veit