Question

A ball bounces to $80$% of its original height. What fraction of its potential energy is lost in each bounce?

• A. $0.20$
• B. $0.60$
• C. $0.40$
• D. $1$

Answer 1

Answer: (A)

$0.20$

Given,

$h^{\prime }=\frac{80h}{100}$

where, $h=$ original height

The kinetic energy of a ball striking the ground is equal to the potential energy of a ball at height $h$,

$K=mgh$

The kinetic energy due to rebounce is given by

$K_r=mg{h}^{\prime }$

Loss of kinetic energy, $\Delta K=K-K_r$

$\Delta K=mgh-mg{h}^{\prime }$

$\Delta K=mg(h-\frac{80h}{100})$

$\Delta K=\frac{20}{100}mgh=0.20mgh$

Fractional loss, $\frac{\Delta K}{K}=\frac{0.20mgh}{mgh}=0.20$

The correct option is A.