Question

what does newtons third law say about why momentum is conserved in collisions?
unequal forces act for unequal times, so the change in momentum for both objects must be equal.
equal forces act in equal times, so the change in momentum for both objects must be equal.
equal forces act for unequal times, so the change in momentum for both objects must be equal.
unequal forces act for unequal times, so the change in momentum for both objects must be unequal.

Explanation:

Newton's third law states that for every action, there is an equal and opposite reaction. In a collision, the force exerted by one object on another (\(F_{12}\)) is equal in magnitude and opposite in direction to the force exerted by the second object on the first (\(F_{21}\)), i.e., \(F_{12}=-F_{21}\). The time of contact (\(\Delta t\)) between the two objects during the collision is the same for both. According to the impulse - momentum theorem, \(\Delta p = F\Delta t\). For the first object, \(\Delta p_1=F_{12}\Delta t\) and for the second object, \(\Delta p_2 = F_{21}\Delta t\). Since \(F_{12}=-F_{21}\) and \(\Delta t\) is the same for both, \(\Delta p_1=-\Delta p_2\), which means the change in momentum of the two objects are equal in magnitude (and opposite in direction).

Answer:

Equal forces act in equal times, so the change in momentum for both objects must be equal.