From Hilbert Space to Dilbert Space

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Math behind Mythbusters
How to Model Newtons Cradle. I read this before seeing Newton's Crane Cradle in which the Mythbusters supersize the system. The model assumes conservation of momentum and that the collision is elastic, i.e. kinetic energy is conserved. Assume also that one steel ball cannot pass through another and the solution is determined by simple algebra.

The model is reasonably accurate for a smail cradle, though not perfect.. Some momentum and energy are lost by air friction and transmission to the mounting structure, and untimately to the Earth as a whole. Furthermore some energy is lost in deforming the shape of the balls: The collisions are not perfectly elastic. All of these effects intensify as the size of the system increases. Before the last test in the show Jamie noticed that even his specially designed wrecking balls were slightly flattened by the previous runs. At that point I knew their final changes were not going to significantly alter the result.

Having read Allain's article just hours before the show, I was struck by how much clearer it was than the explanations on television. A couple conservation principles and some simple algebra go a long way.


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