Question

a machine gun has a mass of 5 kg . it fires 50 gram bullets at the rate of 30 bullets per minute at a speed of 400 m/s. what force is required to keep the machine gun in position

is we have to use the the action reaction law at the end ??

Answer 1

The gun of mass 5 kg force change the bullet's momentum from zero (initially at rest ) to the final value of
P_f = mv = (50 / 1000) * 400 =20 kg m/s
time taken = 30 bullets are fired in 1 min = 60 second
1 bullet fired in = 60/30 = 2 second
Force = dp/dt = 20 / 2 = 10 N
From Newton's third law, there must be an average backward force of bullets of the gun of magnitude 10 N. To keep the gun in place the shooter must exert a force of magnitude 10 N in the forward direction.