# Question #19991

Oct 2, 2015

An impulse of $50 N s$ is needed to keep the gun in position

#### Explanation:

The gun fires 600 bullets per minute, which is the same as 10 bullets per second. Each bullet has mass $25 g$, which is equal to $0.025 k g$. 10 bullets, each of mass $0.025 k g$ leaving the muzzle at $200 m / s$ have a momentum, $m v$ of:
$\implies 10 \times 0.025 k g \times 200 m / s = 50 k g m / s$

The force required to change momentum is called impulse. It is the product of force and time, $F \times t$, that is required to cause a change in momentum of $\Delta m v$. It is derived as shown:
$F = m \times a$
$\implies F = m \times \left(\Delta v / t\right)$
$\therefore F \times t = m \times \Delta v$

Here, your value of $m v$ is $50 k g m / s$ and hence your value of $F \times t$ should be $50 N s$