We describe a numerical procedure for plotting the force-versus-time curves in elastic collisions between identical conducting balls. A system of parametric equations relating the force and the time to a dimensionless parameter is derived from the assumption of a force compatible with Hertz’s theory of collision. A simple experimental arrangement consisting of a mechanical system of colliding balls and an electrical circuit containing a crystal oscillator and an electronic counter is used to measure the collision time as a function of the energy of impact. From the data we can determine the relevant parameters. The calculated results agree very well with the expected values and are consistent with the assumption that the collisions are elastic.

Topics
Electrical circuits, Oscillators, Rigid body dynamics, Elastic modulus, Alloys, Hooke's law, Multivariable calculus, Elastic collisions, Public policy and governance, Laboratories
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The curves were plotted using the ParametricPlot command of Mathematica 4.1, www.wolfram.com

© 2006 American Association of Physics Teachers.
2006
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