Ac 2012-2947: Applying Dynamics to the Bouncing of Game Balls: Experimental Investigation of the Relationship between the Duration of a Linear Impulse during an Im- Pact and the Energy Dissipated

This paper discusses experiments done as a class assignment in a Dynamics course in order to investigate the relation between the duration of a linear impulse and the energy dissipated during impact. After analysis had been presented in lecture on the relation between work and energy and on the connection between linear impulse and linear momentum, a series of distinct but related projects was assigned as hands-on applications of the results of analysis. In project one, it was shown that the height to which a dropped ball rebounded depended upon the height from which it was dropped. The ratio consisting of the rebound height divided by the drop height was found to decrease with increasing drop heights. This pattern held true with basketballs, tennis balls, ping pong balls, volleyballs, and racket balls. In project two, the rebound height of a basketball was investigated as a function of the inflation pressure of the basketball. It was determined that the rebound height increased with increases in the inflation pressures. In project 3, experiments that would allow for the collection of data to help explain the results of projects one and two were designed and carried out. The relationship between the mechanical energy dissipated by a ball bouncing off a rigid surface and the duration of the impact was investigated analytically and experimentally. Three different kinds of balls were used: basketballs, tennis balls, and ping pong balls. Data were collected using digital cameras and processed using software freely available on the web. For each of the tested balls, analysis and experimental data agreed. They showed that when the duration of impact increased, so did the amount of energy that was dissipated. Similarly, when the duration of impact decreased, so did the amount of energy that was dissipated. Consequently, for each tested ball, the longer the duration of the impulse, the more energy was dissipated.