In a collision where no external impulses act, how is momentum before related to momentum after?

In a collision where no external impulses act, how is momentum before related to momentum after?

• A. Total momentum is conserved: p_before = p_after.
• B. Momentum is redistributed among the objects but the total changes.
• C. External impulses are needed for momentum to change.
• D. Kinetic energy is conserved.

Answer: (A)

Momentum is mass times velocity, a quantity that adds up for all objects in a system. When nothing from outside the system pushes on it, the forces during a collision are internal, acting only between the objects themselves. These internal forces can swap momentum from one object to another, changing each object’s velocity, but they cannot change the total momentum of the whole system. So the total momentum before the collision equals the total momentum after the collision. That means the overall p_before and p_after are the same, even though individual objects may end up moving differently after the impact. The idea isn’t about all energy staying the same, but about the momentum sum staying constant when external impulses are absent. As for the other ideas: momentum being redistributed among objects but the total changing would require an external impulse; without one, the total doesn’t change. External impulses are not required for momentum to change inside the system—it’s the external impulse that would change the system’s total momentum. And while kinetic energy can be conserved in perfectly elastic collisions, it isn’t guaranteed by the absence of external impulses, since energy can be transformed between kinetic and other forms during the collision.

Momentum is mass times velocity, a quantity that adds up for all objects in a system. When nothing from outside the system pushes on it, the forces during a collision are internal, acting only between the objects themselves. These internal forces can swap momentum from one object to another, changing each object’s velocity, but they cannot change the total momentum of the whole system. So the total momentum before the collision equals the total momentum after the collision.

That means the overall p_before and p_after are the same, even though individual objects may end up moving differently after the impact. The idea isn’t about all energy staying the same, but about the momentum sum staying constant when external impulses are absent.

As for the other ideas: momentum being redistributed among objects but the total changing would require an external impulse; without one, the total doesn’t change. External impulses are not required for momentum to change inside the system—it’s the external impulse that would change the system’s total momentum. And while kinetic energy can be conserved in perfectly elastic collisions, it isn’t guaranteed by the absence of external impulses, since energy can be transformed between kinetic and other forms during the collision.