Question

A ball of mass 100g falls from a height of 5m and rebounds to a height of 1.25m. Calculate the impulse and the average retarding force on the vehicle, if the time is constant is 0.1s.Taking g=10meter per second square​

Answer 1

The impulse is 1.5 kg-m/s and the retarding force is 15 N.

Explanation:

Given that,

Mass of the ball, m = 100 g = 0.1 kg

Initial height, h = 5 m

Initial velocity will be :

$u=\sqrt{2gh} \\\\u=\sqrt{2\times 10\times 5} \\\\u=10\ m/s$

Final height, h'=1.25 m

Final velocity will be :

$v=\sqrt{2gh'} \\\\v=\sqrt{2\times 10\times 1.25} \\\\v=5\ m/s$

As it rebounds, final velocity will be negative, v = -5 m/s

Impulse is given by change in momentum as :

$J=m(v-u)\\\\J=0.1\times (-5-10)\\\\J=-1.5\ kg-m/s$

Retarding force is :

$F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{-1.5}{0.1}\\\\F=-15\ N$

So, the impulse is 1.5 kg-m/s and the retarding force is 15 N.

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