Answer to Question #87980 in Mechanics | Relativity for Amoo Emmanuel

Question

A machine with a mass 4kg fires a 45g bullet at a speed of 100m/s. Find the recoil speed of the machine gun

Answer 1

We can find the recoil velocity (or speed) of the machine gun from the law of conservation of momentum (the total initial momentum of the machine gun and the bullet is zero, because they both are initially at rest):

$$p_{total(initial)} = p_{total(final)},$$ $$p_{total(initial)} = 0,$$ $$M_{gun}v_{gun} + m_{bullet}v_{bullet} = 0,$$ $$M_{gun}v_{gun} = -m_{bullet}v_{bullet},$$ $$v_{gun} = -\dfrac{m_{bullet}v_{bullet}}{M_{gun}}.$$

From this formula we can calculate the recoil velocity of the machine gun:

$$v_{gun} = -\dfrac{0.045 kg \cdot 100 \dfrac{m}{s} }{4.0 kg} = -1.1 \dfrac{m}{s}.$$

The sign minus indicates that the recoil velocity of the machine gun directed in the opposite direction to the velocity of the bullet.

Answer:

$v_{gun} = 1.1 \dfrac{m}{s}.$