If the coefficient of restitution is 0.5,what | vedclass

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(D) The initial kinetic energy of the ball just before impact is $K_i = \frac{1}{2} m v_i^2$.After the collision,the velocity of the ball is $v_f = e

Vedclass · Accepted Answer

$75$

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(D) The initial kinetic energy of the ball just before impact is $K_i = \frac{1}{2} m v_i^2$.After the collision,the velocity of the ball is $v_f = e v_i$,where $e$ is the coefficient of restitution.The final kinetic energy is $K_f = \frac{1}{2} m v_f^2 = \frac{1}{2} m (e v_i)^2 = e^2 K_i$.The loss in kinetic energy is $\Delta K = K_i - K_f = K_i - e^2 K_i = K_i(1 - e^2)$.The percentage loss in energy is $\frac{\Delta K}{K_i} 	imes 100\% = (1 - e^2) 	imes 100\%$.Given $e = 0.5$,the percentage loss is $(1 - (0.5)^2) 	imes 100\% = (1 - 0.25) 	imes 100\% = 0.75 	imes 100\% = 75\%$.

If the coefficient of restitution is $0.5$,what is the percentage loss of energy on each rebounding of a ball dropped from a height?

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