Question

a gun of mass 3 kg fires a bullet of mass 30 g. the bullet takes 0.003 s to move through the barrel of the gun and aqquires a velocity of 100 m/ s. calculate
a) the velocity with which the gun recoils
b) the force exerted on gun man due to recoil of the gun​

Answer 1

Answer:

Given that,

Mass of the gun = m_1 = 3 kg

Mass of the bullet = m_2 = 30 g = 0.03 kg

Time taken by the bullet to love through the barrel of the gun = t = 0.003 s

Acquired velocity by the bullet = v_2 = 100 m/s

We need to Find : a) velocity by which gin recoils and b) force exerted on gun man due to recoil of the gun

Solution :

We know by law of conservation of momentum that,

m_1v_1 = m_2v_2

Hence, Substituting the given values,

⇒ 3*v_1 = 0.03*100

⇒ 3v_1 = 3

⇒ v_1 = 3/3

⇒ v_1 = 1 m/s

Now, initial velocity of the gun = 0 m/s

And the final velocity = 1 m/s

Time = 0.003 s

We know, Acceleration = v-u/t

⇒ Acceleration = 1-0/0.003

⇒ Acceleration = 1/0.003

⇒ Acceleration = 333.33 m/s²

We know, Force = ma = 3*333.33 = 999.99 = 1000 N

Hence, a) velocity by which gin recoils = 1 m/s² b) force exerted on gun man due to recoil of the gun = 1000 N.

Answer 2

ANSWER :

1. The velocity with which the gun recoil is $\sf - 1 \: m/s^{2}$
2. The force exerted on gun man due to recoil of the gun is 1000 N.

GIVEN :

• Mass of gun = 3 kg.
• Mass of bullet = 30 g.
• Time, t = 0.003 sec.
• Velocity, v = 100 m/s.

TO CALCULATE :

1. The velocity with which the gun recoils.
2. The force exerted by the gun man due to recoil of the gun.

FORMULA :

• $\sf Force \: = \: \dfrac {\Delta p}{\Delta t}$

SOLUTION :

Net force on gun and bullet, system is zero.

$\hookrightarrow \sf 3 \: \times \: v \: (30 \times 10^{-3}) \: \times 100 \: = \: 0$

$\hookrightarrow \sf 3v \: = \: - (30 \: \times \: 10^{-1}$

$\therefore \boxed{\sf V \: = \: - 1 \: m/s^{2}}$

$\bold\red{Force \: = \: \dfrac {\Delta p}{\Delta t}}$

$\hookrightarrow$ $\sf \dfrac {m(v \: - \: 0)}{0.003}$

$\hookrightarrow$ $\sf \dfrac {3 \: \times \: 1}{0.003}$

$\therefore \boxed{\sf F \: = \: 1000 \: N}$