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 __________________________________
Is there a good source to find measured values for coefficients of restitution? I found a paper with measurements of the coefficient of restitution for steel balls against a steel plate, at velocities between 2.2 and 3.5. The coefficient of restitution (COR) is velocity-dependent, but the maximum is only .62 at 2.2 meters per second. These seem very low. I suppose the balls are hollow, and this increases the coefficient of restitution(?) If someone with a Newton's cradle could take a video and single-step through, it should be possible to figure it out. To be more explicit about Veit's point, in the Newton's cradle with one ball of double weight, the first ball (4/3 in the perfectly elastic case) emerges as the result of (n-1) collisions, while the second ball (4/9) is the result of those plus (n-2) additional collisions, etc. Even if the coefficient of restitution is say .95, the effect would be severely dampened for say a 5 ball Newton's cradle. I understand that there is a strange behavior of the COR at low velocities, going up and down and up, or something like that. An anomalies of that sort could also ruin the effect. Bill Thurston On Dec 13, 2010, at 8:46 PM, Veit Elser wrote:
...
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.
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