Question

A rubber ball of mass $50g$ falls from a height of $1m$ and rebounds to a height of $0.5m$. Find the impules and the average force between the ball and the ground if the time for which they are in contact was $0.1s$

Answer 1

Given that,

Ball of mass = $50g$

Height = $1m$

Rebound to height = $0.5m$

Time = $0.1s$

Now,

Initial velocity of the ball $=um/s$

Let the final velocity $=vm/s$

Using equation of motion

$v^2=u^2+2gh$

$v^2=0+2\times 9.8\times 0.1$

$v=\sqrt{1.96}$

$v=1.4m/s$

In the second time,

Final velocity=0m/s

Now, Using equation of motion

$v^2=u^2-2gh$

$0=u^2-2\times 9.8\times 0.5$

$u^2=9.8$

$u=3.1m/s$

Now, Impulse= change in linear momentum

$=mv-m(-u)$

$=m(v+u)$

$=0.05\times (1.4+3.1)$

$=0.225Ns$

Now, the Force=Impulse/Time

$F=\frac{impulse}{time}$

$F=\frac{0.225}{0.1}$

$F=2.25N$

Hence, the impulse is $0.225Ns$ and force is $2.25N$