Explosion and total momentum

Problem

Explosion and total momentum. A rocket travels at velocity $v$ with total momentum $\vec p$. It explodes into three pieces. Explain in a few lines why the sum of the momenta of the pieces stays equal to $\vec p$, even though each piece goes in a different direction.

Solution

The explosion is produced by forces internal to the rocket. By Newton’s third law, every push between two fragments is accompanied by an equal and opposite reaction: in the vector sum these forces cancel in pairs. Since there are no external forces (or they are negligible), the total momentum cannot change: $\ev{\vec p_1 + \vec p_2 + \vec p_3 = \vec p}$ The individual pieces can fly off in any direction, but their vector sum remains $\vec p$. Equivalently: the centre of mass of the fragments keeps moving at the same velocity $v$ as the rocket before the explosion.

Links

Topics: Centre of mass Concepts: Explosion · Conservation of momentum · Newton’s third law