Two bodies interacting
Physics Narrative for 14-16
How momentum is exchanged in some collisions
Pairs of objects interact, by collision or explosion.
As there is only one interaction, the
contact time is the same for both objects. That's the duration for which the force exerted by one acts on the other.
Newton's third law links the force-pair, one member of which acts on one object, and one member of which acts on the other object. The actions of the forces are opposite in direction but equal in magnitude.
So both the force and the duration for which the force acts are identical for both objects. The product of force and duration is the impulse, and is equal to the change in momentum.
The impulses are equal and opposite so the change in momentum of one object is equal in magnitude but opposite in direction to the change in momentum of the other. What is taken from one is necessarily added to the other and so momentum is conserved. But you already knew that because you had reached the same conclusion using a separate argument, using symmetry.
Note that there is no requirement that the distances over which the forces act is equal, so the energy shifted to or from kinetic stores may (
an elastic collision), or may not (
an inelastic collision), be conserved. Energy is conserved, but we may need to look in other stores in addition to kinetic stores.