Question

A ball of mass m is dropped onto a floor from a certain height.The collision is perfectly elastic and the ball rebounds to the same height and again falls.Find the average force exerted by the ball on the floor during a long time interval.

Answer 1

A ball of mass m is dropped to a floor from a certain height, let 'h'

$\therefore$ $v_1=\sqrt{2gh}$

$v_1=0$

$v_2=-\sqrt{2gh}$

and $v_2=0$

$\therefore$ rate of change of velocity:

$F=\frac{m\times 2\sqrt{2gh}}{t}$

$\therefore v=\sqrt{2gh},s=h,u=0$

$\Rightarrow \sqrt{2gh}=gt$

$\Rightarrow t=\sqrt{\frac{2h}{g}}$

$\therefore$ Total time=$2\sqrt{\frac{2h}{g}}$

$\therefore F=\frac{m\times 2\sqrt{2gh}}{2\sqrt{\frac{2h}{g}}}=mg$