Question

A machine gun fires n bullets per second and the mass of each bullet is m. if the speed of bullets is v, what is the force on the machine gun?

Answer 1

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 on the gun is=nmu.
The force is directed opposite to the direction of the bullets.

Answer 2

We know that Force is directly proportional to change in momentum.

Momentum of the bullets => ( mass of one bullet × speed of one bullet ) × no. of bullets fired per unit time

Mass of one bullet=m

Speed of the bullet=v

No. of bullets fired=n

And time taken=1 second

So Force => m×v×n/1 second

=>mnv

Hope it helps....

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