Momentum
Intermediate
Conservation of Momentum
Source: High school physics (Chinese)
Problem Sets:
momentum - 1110
Problem
When a rifle is fired, the bullet exits the barrel and the rifle recoils. The rifle's mass is 3 kg, and the bullet's mass is 50 g. The bullet's muzzle velocity is 600 m/s.
If the rifle is not braced against the shoulder, what is its recoil velocity?
V = -10 m/s
The system consists of the rifle and the bullet. Since there are no external horizontal forces, the total momentum of the system is conserved. The initial momentum is zero.
Let $m$ and $v$ be the mass and velocity of the bullet, and $M$ and $V$ be the mass and velocity of the rifle.
$$p_i = p_f$$ $$0 = mv + MV$$The recoil velocity of the rifle is:
$$V = - \frac{m}{M}v$$Substituting the given values, with $m = 50 \text{ g} = 0.05 \text{ kg}$:
$$V = - \frac{0.05 \text{ kg}}{3 \text{ kg}}(600 \text{ m/s})$$