Question

A ball is thrown from a height 50m and it sinks in the sand at 5cm find the force reflected by sand.

Answer 1

The force reflected by the sand is 98.1m N (m is mass of ball)

First we will calculate the velocity of the ball, when ball just hit the sand.

By the law of energy conservation

v=$\sqrt{2gh}$

Plugging the values in the above equation

v=$\sqrt{2×9.81*50}$=31.32 m/s

Now we will calculate the change in kinetic energy when the ball sinks in the sand

ΔKE=0.5m[(v_{f})^2-(v_{i})^2]

Since the ball finally stops, therfore its final velocity is 0

Plugging the values in the above equation

ΔKE=0.5*m(31.32^2-0)=490.5m Joule

Now we can calcualte the force applied by the sand

Change in energy=Force×Displacement

490.5m=Force×5

Force=98.1m N

Here, m is the mass of the ball.