Question

A machine gun fires 20 bullets per second into a target.each bullet weighs 150 grams and has a speed of 800 metre per second .calculate the force required to hold the gun in position

Answer 1

Let us say each bullet takes about 1/20 th of a second to come out of the barrel of the gun.  Each bullet then accelerates from rest to a speed of 800 meters in a time duration of 1/20 = 0.05 sec.

Acceleration of a bullet = a = (800 - 0 ) / 0.05 sec = 16000 m /sec²

Force necessary to give the bullet this acceleration = m a

           = (150 /1000) kg * 16000 m/sec²

           = 2400 Newtons

The bullets exert the same amount of force on the machine gun as the machine gun exerted on the bullets.

Force necessary to hold the gun = recoil force of gun = 2400 Newtons

Answer 2

Number of bullets per second(n) = 20 per second

Mass of bullet, m = 150g = 0.15 kg

Velocity, v = 800 m/s

Force required = nmv = (20/s) × 0.15 kg × 800 m/s = 2400 kg.m/s^2 = 2400 N

Force required is 2400 N