Coefficient of restitution

The coefficient of restitution (COR) of two colliding objects is a positive real number between 0.0 0.0 and 1.0 1.0 representing the ratio of speeds after and before an impact, taken along the line of the impact. When a basketball which has the restitution coefficient of e e with the floor falls free from the height of h , h, the bounce height is h h' as above left(A). The above right(B) shows the bounce height h h' as a function of the drop height h . h. What is e ? e?

0.64 0.8 0.6 0.4

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2 solutions

Tanuja Iyer
Mar 26, 2014

Velocity just before striking ground v= 2 g h \sqrt{2gh} Velocity immediately after the bounce v' = 2 g h \sqrt{2gh'} e = v'/v = 2 g h / 2 g h \sqrt{2gh'} / \sqrt{2gh} = h / h \sqrt{h'/h} = 0.64 / 1 \sqrt{0.64/1} .... from graph e = 0.8

Tanya Gupta
Mar 24, 2014

H and h are functions of v2....while we just need the ratios of v...therefore on taking square root we get the answer to be 0.8

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