Question

A ball of mass 100 g dropped on the ground from 5 m bounces repeatedly. During every bounce 64% of the potential energy is converted into kinetic energy. Calculate the following: 

(a) Coefficient of restitution. 

(b) Speed with which the ball comes up from the ground after third bounce. 

(c) Impulse given by the ball to the ground during this bounce. 

(d) Average force exerted by the ground if this impact lasts for 250 ms. 

(e) Average pressure exerted by the ball on the ground during this impact if the contact area of the ball is 0.5 cm²

Answer 1

Given that, for every bounce, 64% of the initial energy is converted to final energy. 

i. Coefficient of restitution in case of inelastic collision is given by,

ii. From equation (1),

∴ v = – eu 

∴ After first bounce, 

v₁ = – eu

after second bounce,

iii. Impulse given by the ball during third bounce, is,

iv. Average force exerted in 250 ms,

v. Average pressure for area