A machine gun has a mass of 20kg. It fires 35 g bullets at the rate of 4 bullets per second, with a speed of `400 ms^(-1)`. What force must be applied to the gun to keep it in position?

Explanation

Mass of gun , M=20 kg
Velocity of bullet , `v= 400 ms^(-1)`
If V be the velocity of recoil , then
`V=(mv)/(M)=(0.035 xx 400)/(20) ms^(-1) = 0.7 ms^(-1)`
Time taken to fire one bullet , ` t=(1)/(4)` second
If F be the average force required to hold the gun in position, then
`F xx t`= change in momentum of gun or `F xx t = MV`[`:.` Initial momentum of gun is zero ]
`:. F=(MV)/(t)=(20 xx 0.07)/(1//4)N = 56 N`
Aliter: Number of bullets fired per second, n = 4 momentum given to the bullets per second = nmv
Same momentum per second is gained by the gun. This gives the force acting on the gun and also the force applied to keep the gun in position. So, `F= nmv= 4 xx 0.035 xx 400 = 56N`