Question

Explain in terms of the conservation of momentum why the ratio of the masses of a bullet and a gun must be carefully considered

Answer 1

Answer on Question #39461, Physics, Mechanics | Kinematics | Dynamics

Question:

Explain in terms of the conservation of momentum why the ratio of the masses of a bullet and a gun must be carefully considered.

Answer:

The law of conservation of momentum:

$$m \vec {v} + M \vec {u} = 0$$

where $m, M$ are masses of gun and bullet, $\vec{v}, \vec{u}$ are their velocities.

Or

$$m v = M u$$

Therefore, speed of gun equals:

$$u = \frac {m}{M} v$$

So, if the ratio of the masses of a bullet and a gun will be large, the recoil of gun will be large too.