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Question

A machine gun fires n bullets per second each of mass m. If the speed of each bullet is v, then the force of recoil is?


Solution

Since, the momentum of gun and bullet together was zero before firing, so, after firing:
momentum of bullets+momentum of gun=0
momentum of the gun=-momentum of the bullets
momentum of bullet for each fire=mu
since, n bullets are fired per second.
Change in momentum of bullet per second=nmu
Therefore, change in momentum of gun per second is =-nmu[since direction of gun and bullet are opposite]
since, Force=rate of change of momentum
Force on gun= -nmu
Therefore Force of recoil is=nmu.
The force is directed opposite to the direction of the bullets.

 

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