Question

A rubber ball of mass 50 g falls from a height of 5 m and rebounds to a height of 1.25 m. Find the impulse and the average force between the ball and the ground if the time for which they are in contact .

Answer 1

mass,m=50g=0.05kg
Height=5m
Rebound height=1.25
Initial velocity of the ball = u=0m/s
Let the final velocity = vm/s
g=9.8m/s²; h=5m
Using v²=u²+2gh we get,
v²=0+2×9.8×5
∴, v=√98=9.9m/s
In the second time,
Final velocity=0m/s
h=1.25
Using, v²=u²-2gh [as the ball goes against gravitational acceleration]
0=u²-2×9.8×1.25
thus, u=4.94m/s
Now, Impulse= change in linear momentum
=mv-m(-u)
=0.05×(9.9+4.94)
=0.742Ns

Force=Impulse/Time
=0.742/Time
Time is not given in the question..