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A cricket ball of mass $200g$ moving with velocity $15m{s^{ - 1}}$ is brought to rest by a player in $0.05s$. What is the impulse of the ball and average force exerted by the player?

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Last updated date: 05th Mar 2024
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IVSAT 2024
Answer
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Hint: Impulse is defined as the difference between the final momentum and the initial momentum of any object. In other words change in momentum is also known as Impulse.

Complete step by step answer:
Momentum is a measurement of mass in motion. It measures how much motion the mass is carrying during that time period. Whereas impulse is the term that quantifies the overall effect of a force acting over time. It measures the motion that the mass is carrying over an infinitesimally small period of time.In Newtonian mechanics, Impulse \[\left( J \right)\] is defined as the integral of a force$\left( F \right)$ over the time interval $\left( t \right)$ for which it acts. Which means,
$\vec J = \int\limits_0^t {\vec F.dt} $

Since force is a vector quantity, impulse is also a vector quantity. In simple terms, impulse is defined as the change in momentum that occurs in an object. Which means,
$\overrightarrow J = \Delta \overrightarrow p $
This equation is known as the impulse-momentum theorem. It helps relate both the quantities.
$ \Rightarrow \vec J = \overrightarrow {{p_f}} - \overrightarrow {{p_i}} $
$ \Rightarrow \overrightarrow J = m\overrightarrow v - m\overrightarrow u $
$ \Rightarrow \overrightarrow J = m\left( {\overrightarrow v - \overrightarrow u } \right)$
Where, $\overrightarrow {{p_f}} = $Final momentum of body,$\overrightarrow {{p_i}} = $Initial momentum of body,$m = $Mass of the ball$ = 200g = 0.2kg$ and $\overrightarrow v = $Final velocity of the ball$ = 0m{s^{ - 1}}$.
$\overrightarrow u = $Initial velocity of the ball$ = 15m{s^{ - 1}}$.

So,
$\overrightarrow J = 0.2\left( {0 - 15} \right)$
$\therefore \overrightarrow J = - 3Ns$
Therefore the impulse generated by the cricket ball is $ - 3Ns$.
Now, we know that,
$\overrightarrow F = m\overrightarrow a $
$\overrightarrow F = m\dfrac{{\overrightarrow v - \overrightarrow u }}{t}$
$ \Rightarrow \overrightarrow F = 0.2 \times \dfrac{{0 - 15}}{{0.05}}$
$\therefore \overrightarrow F = - 60N$

Therefore the force applied is $ - 60N$.

Note:Impulse gives us an idea about a very large force applied over a very small amount of time. Impulse is otherwise also known as impact. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. The best examples for impulse are hitting a ball with a bat, body falling from the sky, or any collision.
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