Question

A 33 kg gun is standing on a frictionless surface. The gun fires a 55.7 g bullet with a muzzle velocity of 318 m/s. The positive direction is that of the bullet. Calculate the momentum of the gun immediately after the gun was fired

Answer 1

Answer on Question#39212 – Physics – Other

A 33 kg gun is standing on a frictionless surface. The gun fires a 55.7 g bullet with a muzzle velocity of 318 m/s. The positive direction is that of the bullet. Calculate the momentum of the gun immediately after the gun was fired

Solution:

This is a conservation of momentum problem.

Before gun fires, the total momentum in the system is 0 (gun is standing). After the gun was fired, total momentum of the system is sum of momentum of the gun and momentum of the bullet (along X-axis):

$$x: 0 = p_{\text{gun}} + p_{\text{bullet}} \Rightarrow$$ $$p_{\text{gun}} = -p_{\text{bullet}} = -mv = -55.7 \times 10^{-3} \text{kg} \cdot 318 \frac{\text{m}}{\text{s}} = -17.7 \text{kg} \cdot \frac{\text{m}}{\text{s}}$$

Answer:

momentum of the gun immediately after the gun was fired is equal to $-17.7 \text{kg} \cdot \frac{\text{m}}{\text{s}}$