Question

A ball hits the ground and loses 20% of its momentum. Coefficient of restitution is

Answer 1

Answer:

Let us consider,

the mass of the ball be “m”

the initial velocity be “Vi”

the final velocity be “Vf”

We know,

Momentum = m * V

Therefore,

Initial momentum = m * Vi ….. (i)

And,

Final Momentum = m * Vf = m * (Vi – 20% * Vi) = m * (8/10)Vi ….. (ii)

As the ball hits the ground it loses its momentum by 20%. In both the equations (i) & (ii), since the mass of the ball will not change, so after losing the initial velocity by 20%, the final velocity “Vf” becomes 80% of initial velocity “Vi” i.e.,

Vi = Vi and Vf = 8/10 Vi ….. (iii)

The coefficient of restitution “e” is given by

e = (relative velocity of separation) / (relative velocity of approach) ….. (iv)

on substituting the values from (iii) in (iv), we get

e = (8/10)Vi / Vi = 8/10 = 0.8

Hence, the coefficient of restitution is 0.8.