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Using Microsoft Windows to Compare the Energy Dissipated by Old and New Tennis Balls

Abstract Sound waves produced by bouncing tennis balls are recorded using software commonly available in Microsoft Windows XP and successive times at which the ball impacts a solid surface are extracted from the resulting wave forms. Time intervals between consecutive impacts are related to the energy dissipated by impacts during bouncing. The collected data are analyzed in Microsoft Excel and used to deternline the quality of the bounces that can be expected from both new and used tennis balls.

1. Introduction

Experienced tennis players distinguish old tennis balls from new tennis balls by assessing the extent to which the balls dissipate energy during impact with the tennis court. Such bouncing tests relate directly to the concept of the collision of particles, a unit that appears in many curricula that are relevant to the education of physics and engineering maj ors [3,9, 101. In this article, we illustrate how we have used software commonly available in Microsoft Windows XP to demonstrate and analyze energy dissipation that occurs when a tennis ball bounces off the court during a game. We collected data directly from bouncing tennis balls and used them to illustrate a practical application of the coefficient of restitution that students learn in the dynamics of impacts and collisions.

The technique of measuring the coefficient of restitution using the sound produced when a ball strikes a solid surface is not new. It consists of releasing a ball from rest and letting it fall on a rigid surface on which it bounces repeatedly until it stops. The sound produced by successive impacts is recorded and analyzed to give the time intervals separating consecutive impacts. These time intervals are related to the coefficient of restitution. Bernstein used this procedure in 1977[131. Smith, Spencer, and Jones automated this process using a microcomputer in 1981 [141. Stensgaard and Laegsgaard adapted it to a PC in 2001 l151. Aguiar and Laudares[ 161extended the work of Bernstein [131, Stensgaard, and Laesgaard [15] and used data related to the coefficient of restitution of a bouncing ball to determine of the acceleration of gravity in 2003. Foong, Kiang, Lee, March and Paton [11J applied this work to an examination question aimed at determining how long it took a bouncing ball to bounce an infinite number of times in 2004.

The rest of this paper is organized in the following maimer: first we model the mechanics of a bouncing ball and introduce the coefficient of restitution; then, we summarize how this model is combined with the conservation of energy, the coefficient of restitution, and the kinematics of a particle in free fall to yield practical results, which are presented in tabular form; they show how energy dissipation during impact is related to rebound heights, to the time intervals between consecutive impacts, and to the coefficient of restitution; next, we discuss three experimental methods that are suggested by the analytical results obtained; finally, we design and carry out tests that use these methods to determine the energy dissipated by a bouncing tennis ball.

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Njock-Libii, J. (2010, June), Using Microsoft Windows To Compare The Energy Dissipated By Old And New Tennis Balls Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--15818