Question
A machine gun fires the bullets of mass 30 gm at the rate of 20 bullets per second with speed 400m/s. Find the force required to keep the gun in position.
Solution
Mass of bullet is, m = 30 gm = 0.03 kg
Velocity of bullet, v = 400 m/s
Frequency of firing the bullets is, n = 20 bullets/second
Change in momentum of one bullet is,
mv = 0.03 x 400 = 12 Ns
Change in momentum of 20 bullets is,
12 x 20 = 240 Ns
As 20 bullets are fired in one second, therefore 240 Ns is change in momentum of bullets in 1 second.
Since change in momentum of body in one second is equal to force acting on the body, therefore force exerted by gun on the bullets is 240N.
Now according to Newton’s third law, the bullets exert equal and opposite force on the gun.
Thus the force required to hold the gun is 240N.
