Question

A 240 g ball travelling at 54km/h strikes the palm of a cricketer and is stopped on 0.5 seconds find the force exerted by the ball on the head​

Answer 1

☞ To Find :

The Force exerted by the ball.

☞ Given :

• Mass of the ball $\rightarrow m = 240g\:or\:0.24g$

• Final velocity $\rightarrow v = 54 kmh^{-1}\:or\:15ms{-1}$

• Time Taken $\rightarrow t = 0.5 s$

• Initial velocity $\rightarrow u = 0$

☞ We know :

• $\mathtt{F = ma}$

where,

➝ F = force exerted

➝ m = mass

➝ a = acceleration

• $\mathtt{a = \dfrac{v - u}{t}}$

Where,

➝ a = acceleration

➝ v = final velocity

➝ u = initial velocity

➝ t = time taken

☞ Concept :

To find the force applied ,first we have to find it's acceleration as.

$\because f \propto a$

Hence ,

To find it's acceleration, we can use the given information of final velocity and Intial velocity and the time taken.

• $\rightarrow v = 54 kmh^{-1}\:or\:15ms{-1}$
• Time Taken $\rightarrow t = 0.5 s$
• Initial velocity $\rightarrow u = 0$

Putting the value in the formula,

$\mathtt{a = \dfrac{v - u}{t}}$

we get,

$\mathtt{\Rightarrow a = \dfrac{15 - 0}{0.5}}$

$\mathtt{\Rightarrow a = \dfrac{\cancel{15}}{\cancel{0.5}}}$

$\mathtt{\Rightarrow a = 30 ms^{-2}}$

Hence the acceleration produced is $30 ms^{-2}$

☞ Solution:

From the given values of mass and Acceleration ,we can find the force exerted on the head.

We know that ,

$\sf{F = ma}$

Here ,

m = $0.24 kg$

a = $30 ms^{-2}$

Putting the value in the formula ,we get :

$\sf{\Rightarrow F = 0.24 \times 30}$

$\sf{\Rightarrow F = 7.4 N}$

Hence ,the force exerted is 7.4 N.

Extra information :

• Acceleration due to gravity on a planet's surface ...

$g = \dfrac{GM}{r^{2}}$

Where ,

g = acceleration due to gravity

G = universal gravitational constant

r =distance between the planets.

M = mass of the planet.

• Acceleration due to gravity , second formula

$g = G\dfrac{m_{1}m_{2}}{r^{2}}$

Where ,

g = acceleration due to gravity

G = universal gravitational constant

r =distance between the planets.

m = mass of the body

Answer 2

HERE IS UR ANSWER DEAR,

GIVEN:

mass (m) = 240 g

= 240 /1000

= 0.24kg

initial velocity (u) = 54 km /hr

= 54 ×5/18 m/s

= 15 m/s

final velocity (v) = 0

time (t) = 0.5 sec

TO FIND:

Force (F)

SOLUTION:

by using kinematic equation of motion

v= u +at

a= v-u/t

a = 0-15/0.5

a= -30 m/s²

according to Newtons second law of motion,

F=ma

F= (0.24)(30)

F= 7.2 N

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