Question

A bullet of mass 10 g is fired with a rifle. The bullet takes 0.004s to move through the barrel and leaves it with a velocity of 400m/s. Calculate the force exerted on the bullet by the rifle.

Answer 1

Answer:

v=300 ms

−1

; u=0 ,t=0.003 s ,m=0.01 kg

Force exerted by the bullet on the rifle =

time

m(v−u)

F=1000 N

Explanation:

hope it helps you

Answer 2

To Find :–

The Force exerted by the rifle .

Given :–

• Mass of the body = 10g

• Velocity of the bullet = 400 m/s

• Time taken = 0.004 s

We know :–

First Equation of Motion :-

$\boxed{\underline{\bf{v = u + at}}}$

Where :-

• v = Final Velocity

• u = Initial Velocity

• t = Time Taken

• a = Acceleration Produced

Force :–

$\boxed{\underline{\bf{F = ma}}}$

Where :-

• m = Mass of the body

• a = Acceleration Produced

• F = Force exerted

Concept :–

First we have to find the Acceleration Produced by the bullet as without the acceleration ,we can't find the force exerted by the bullet.

Solution :–

Acceleration Produced :-

Given :-

• Initial Velocity (u)78 = 0 m/s

• Final Velocity (v) = 400 m/s

• Time Taken (t) = 0.004 s

Using the First Equation of Motion and substituting the values in it ,we get :-

$:\implies \bf{v = u + at} \\ \\ \\ :\implies \bf{400 = 0 + a \times 0.004} \\ \\ \\ :\implies \bf{400 = a \times 0.004} \\ \\ \\ :\implies \bf{400 = a \times \dfrac{4}{1000}} \\ \\ \\ :\implies \bf{400 \times 1000 = a \times 4} \\ \\ \\ :\implies \bf{\dfrac{400 \times 1000}{4} = a} \\ \\ \\ :\implies \bf{100 \times 1000 = a} \\ \\ \\ :\implies \bf{100000 = a} \\ \\ \\ \therefore \purple{\bf{a = 100000 ms^{-2}}}$

Hence, the acceleration Produced is 100000 m/s².

Force Exerted :-

Given :-

• Mass (m) = 10 g or 0.001 kg

• Acceleration Produced = 100000 m/s².

Using the formula and substituting the values in it,we get :-

$:\implies \bf{F = ma} \\ \\ \\ :\implies \bf{F = 0.001 \times 100000} \\ \\ \\ :\implies \bf{F = \dfrac{1}{1000} \times 100000} \\ \\ \\ :\implies \bf{F = 1 \times 100} \\ \\ \\ :\implies \bf{F = 100} \\ \\ \\ \therefore \purple{\bf{F = 100 N}}$

Hence, the force on the bullet by the rifle is 100 N.