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?

A machine gun has a mass of 20kg. It fires 35 g bullets at the rate of

1.	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?
Answer» Solution :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`= changein 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`