Impedance of rigid bodies in one-dimensional elastic collisions

Abstract

In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand efficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.

Descrição temporal de forças de colisão: um modelo didático para laboratório de física assistido por sistema embarcado

“…O campo Impulso é mostrado para fins didáticos, visto que ele equivale à integral da força, conforme indica a Eq. (9). Essa integral é aqui calculada numericamente como…”

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“…The case of a head-on elastic collision of two rigid balls with masses m 1 and m 3 offers an interesting analogy. To maximize the energy transfer from m 1 , which has nonzero initial energy E 1 , to m 3 , which has zero initial energy, one can position a rigid ball with mass m 2 = √ m 1 m 3 and zero initial energy, in between the two balls [6].…”

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“…An extension of the problem to multiple bodies was described by Kerwin in 1972 [3]. These phenomena, with surprising and counterintuitive results, are used regularly in many forms in classrooms as teaching demonstrations and novel methods [4] of analysing the problem of chain-collisions and are still of interest to teachers and students.…”