Question

A metal ball falls from a height $1m$ on a steel plate and jumps up to a height of $0.81m$. Find the coefficient of restitution.

Answer 1

we know that if ball is dropped from a height , h , velocity of particle just before hitting the ground will be $v=\sqrt{(}2gh)\Rightarrow v=\sqrt{(}2g)$

and if particle is projected with u , then it reaches a maximum height H then , $u=\sqrt{(}2gH)\Rightarrow u=\sqrt{(}1.62g)$

Now we know that, coefficient of restitution $e=\frac{v_2-v_1}{u_1-u_2}=\frac{0-\sqrt{(}1.62g)}{-\sqrt{(}2g)-0}=\sqrt{(}0.81)=0.9$