Question

A machine gun has a mass of 20 kg. It given 35 g bullets at the rate of 400 $bullets$/$second$ with a speed of 400 $m{s}^{-}$ ${}^1$, what force must be applied to the gun to keep it in position?

Answer 1

Here the thrust force due to firing$=F_{th}=V_{rel}\frac{dm}{dt}$

$V_{rel}$=velocity of bullet with respect to gun velocity=400m/s (given)

thus thrust force is experienced by person holding the gun

$\frac{dm}{dt}=400\times \frac{35}{1000}$

(mass of a bullet multiplies bullet firing rate)

$F_{th}=400\times \frac{dm}{dt}=400\times (400\times \frac{35}{1000})$

$⟹F_{th}=5600N$