Question

A cricket ball of mass is 0.18kg is moving with a velocity of 10^ms-1 hits the bat and turned back with velocity 20ms^-1.The force acts on a ball for 0.01 second.The caluclate the average force exerted by the bat on the balls​

Answer 1

Given :

• Time (t) = 0.01 second
• Mass (m) = 0.18 kg
• Initial speed (u) = -10 m/s
• Final speed of the ball after being hit by the bat (v) = 20 m/s

To Find :

• The Average force exerted by the bat on the ball = ?

Solution :

First we have to find the Impulse :

→ Impulse = Change in momentum

→ Impulse = m(v - u)

→ Impulse = 0.18[20 - (- 10)]

→ Impulse = 0.18 (20 + 10)

→ Impulse = 0.18 × 30

→ Impulse = 5.4 kg.m/s

Now,lets find the average force exerted by the bat :

→ Force = mass × acceleration

→ Force = (change in momentum) ÷ (time)

→ Force = 5.4 ÷ 0.01

→ Force = 540 N

• Hence,the average force exerted by the bat is 540 N.

Answer 2

Explanation:

$\frak Given = \begin{cases} &\sf{Time,\ t\ =\ 0.01\ seconds.} \\ &\sf{Mass,\ m\ =\ 0.18kg.} \\ &\sf{Initial\ speed,\ u\ =\ -10m/s.} \\ &\sf{Final\ speed\ of\ the\ ball\ after\ being\ hit\ by\ bat,\ v\ =\ 20m/s.} \end{cases}$

To find:- We have to find the average force exerted by the bat on the ball ?

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf\pink{\underline{Impulse\ =\ Change\ in\ momentum.}}$

___________________

$\frak{\underline{\underline{\dag Now,\ we\ will\ find\ the\ impulse:-}}}$

$\sf : \implies {Impulse\ =\ Change\ in\ momentum} \\ \\ \sf : \implies {Impulse\ =\ m(v\ -\ u)} \\ \\ \sf{Impulse\ =\ 0.18[20\ -\ (-10)]} \\ \\ \sf : \implies {Impulse\ =\ 0.18(20\ +\ 10)} \\ \\ \sf : \implies {Impulse\ =\ 0.18\ ×\ 30} \\ \\ \sf : \implies {\purple{\underline{Impulse\ =\ 5.4kg.m/s}}}\bigstar$

___________________

$\frak{\underline{\underline{\dag Now,\ finding\ the\ average\ force\ exerted\ by\ the\ bat:-}}}$

$\sf : \implies {Force\ =\ mass\ ×\ acceleration} \\ \\ \sf : \implies {Force\ =\ \dfrac{Change\ in\ momentum}{Time}} \\ \\ \sf : \implies {Force\ =\ \dfrac{5.4}{0.01}} \\ \\ \sf : \implies {\purple{\underline{Force\ =\ 540N.}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ average\ force\ exerted\ by\ the\ bat\ is\ 540N.}}$