Question

Question #edbe4

Answer 1

See the explanation that follows...

Explanation:

Before the gun is fired, none of its mass is moving, and so, the total momentum of gun and bullet is zero.

The bullet is then propelled from the barrel of the rifle with a very small mass but a large velocity, and so, has a certain momentum, which I will write `mV` (small m, large V, okay?)

The law of conservation of momentum requires that the total momentum of the gun and bullet remains zero after the complex forces involved in the explosion of the gunpowder have sent the bullet on its way. So, the gun, having a large mass, M must move in the opposite direction with a velocity v, such that:

`mV = -Mv` (the - sign referring to the opposite direction of the gun).

You can show that the law of conservation of mass is a consequence of Newton's third law by the way, which also predicts that the gun receives a backward force when it applies a forward force to the bullet.