physics question

Question

A 3kg basketball compresses by 0.02m when released from a height of 2m. What is the spring constant of the the basketball? If the basketball only rebounds to a height of 1.8m. How efficient is the basketball?

Answer 1

A 3kg basketball compresses by 0.02m when released from a height of 2m. What is the spring constant of the the basketball? If the basketball only rebounds to a height of 1.8m. How efficient is the basketball?

In this question we have to use law of conservation of energy

m= 3kg, x= 0.02 m , h= 2m

KE gained by falling ball = Loss in PE ( assuming 100% efficient fall)

1/2mv² = mgh= 1/2 kx² Where k = spring constant

This gives 2mgh/x² = k

where x = Compression of spring , so k = 2*3*9.8*2/0.02*0.02 N/m

Now as the rebound is not 100% efficient

It rebounds only up to 1.8 m

Rebound efficiency = out put / In put = mgh ₂/mgh_{1 =} h₂/h ₁ = 1.8/2.0 = 0.9

So Rebound Efficiency is 90%