The bounce of a ball

Abstract

In this paper, the dynamics of a bouncing ball is described for several common ball types having different bounce characteristics. Results are presented for a tennis ball, a baseball, a golf ball, a superball, a steel ball bearing, a plasticene ball, and a silly putty ball. The plasticene ball was studied as an extreme case of a ball with a low coefficient of restitution ͑in fact zero, since the collision is totally inelastic͒ and the silly putty ball was studied because it has unusual elastic properties. The first three balls were studied because of their significance in the physics of sports. For each ball, a dynamic hysteresis curve is presented to show how energy is lost during and after the collision. The measurement technique is quite simple, it is suited for undergraduate laboratory experiments, and it may provide a useful method to test and approve balls for major sporting events.

Force-versus-time curves during collisions between two identical steel balls

“…In this case the usual technique that allows us to study the evolution of the contact force uses a piezoelectric film placed between the colliding bodies. [3][4][5][6][7] This technique can be applied to both elastic and inelastic collisions and the force-time curve is obtained in real time; its disadvantage is that it is intrusive because the film may significantly change the coefficient of restitution.…”

“…Indeed, the collision can be described as one between mass points interacting by springs. 7,11,12 If these springs behave like Hooke's-law springs, the collision time would be independent of the impact speed. However, experiment shows that the collision time depends on the impact speed and the assumed form of F takes this fact into account.…”

Proposta experimental do estudo de colisões entre bolas de borracha e superfície plana

“…As medições, tanto das alturas, como das velocidades, podem ser realizadas usando-se técnicasópticas [6,19] ou imagens [20,21]. O tempo necessário para inversão da velocidade (ou sentido de deslocamento) tambémé uma grandeza importante no estudo das colisões e pode ser medido a partir de experimentos com dispositivos piezelétricos [11,12], imagens de alta velocidade [11,20] ou contato elétrico [11,22]. A deformação da bola durante o impacto (compliance) e determinada pelaárea de contato na forma de círculo que decorre da deformação da bola ao chocar-se com a superfície plana (Equação 7).…”

“…Este tema, em particular, tem sido estudado por Cross [12] e pode ser abordado e adaptado em nível adequado de compreensão para alunos de cursos introdutórios de física básica.…”

An estimate of spherical impactor energy transfer for mechanical frequency up-conversion energy harvester

“…Therefore, the total energy before and after the impact, including any energy dissipated during the impact (if any is assumed), is conserved. [31][32][33] The Hertzian contact law presented in (1) can be used to develop a simple model of the impactor and how it interacts with a target. Then, traditional vibration theory can be used to generate the response of the entire target, including any energy harvesting components.…”