A perfectly happy ball is one that bounces to its original height when dropped on a massive, rigid surface. A completely unhappy ball does not bounce at all. In the former case, the coefficient of restitution (COR) is unity. In the latter case, the COR is zero. It is shown that when an unhappy ball collides with a happy ball, the COR increases from zero to unity as the stiffness of the happy ball decreases from infinity to zero. The COR is independent of the mass of each ball. The implication of reducing the COR of a tennis ball, as a possible means of slowing the serve in tennis, is also considered. It is shown that (a) the COR for a collision with a racket varies with the impact point and is a maximum at the vibration node near the center of the strings, and (b) the serve speed is reduced by only about 20% if the COR for a bounce on the court is reduced to zero.
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November 2000
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November 01 2000
The coefficient of restitution for collisions of happy balls, unhappy balls, and tennis balls Available to Purchase
Rod Cross
Rod Cross
Physics Department, University of Sydney, Sydney, NSW 2006 Australia
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Rod Cross
Physics Department, University of Sydney, Sydney, NSW 2006 Australia
Am. J. Phys. 68, 1025–1031 (2000)
Article history
Received:
June 07 1999
Accepted:
February 28 2000
Citation
Rod Cross; The coefficient of restitution for collisions of happy balls, unhappy balls, and tennis balls. Am. J. Phys. 1 November 2000; 68 (11): 1025–1031. https://doi.org/10.1119/1.1285945
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