Answer to Question #165872 in Physics for Maya

Question

1     A bullet with mass 0.005 kg is fired from a rifle of mass 5 kg. The bullet has a speed of 400 m/s towards the right.

a   Explain why the rifle jumps backward (recoils) as the bullet is fired.

b   What is the momentum of the bullet?

c   What must be the momentum of the rifle as it recoils?

d   How fast is the initial backwards movement of the rifle?

Answer 1

(a) The rifle jumps backward (recoils) as the bullet is fired because of the conservation of momentum. When the rifle is fired, the bullet gains forward momentum and the rifle gains backward momentum. That's why rifle recoils.

(b) The momentum of the bullet can be found as follows:

$$p_b=m_bv_b=0.005\ kg\cdot400\ \dfrac{m}{s}=2\ \dfrac{kgm}{s}.$$

(c) According to the law of the conservation of momentum, the momentum of the rifle as it recoils equals in magnitude to the momentum of the bullet, but directed in the opposite direction to the motion of the bullet:

$$p_r=2\ \dfrac{kgm}{s}, backward.$$

(d) We can find the recoil velocity of the rifle from the law of conservation of momentum:

$$m_bv_b+m_rv_r=0,$$ $$v_r=-\dfrac{m_bv_b}{m_r}=-\dfrac{0.005\ kg\cdot400\ \dfrac{m}{s}}{5\ kg}=-0.4\ \dfrac{m}{s}.$$

The magnitude of the recoil velocity of the rifle equals 0.4 ms^-1. The sign minus means that the recoil velocity of the rifle directed backward.