If a particle with mass $m$ collides with a wall at right angles, and the collision is perfectly elastic. The particle hits the wall at $v\ ms^{-1}$. There is no friction or gravity.
So the particle will rebound at $-v\ ms^{-1}$?
What will the change in momentum be?
I did:
$$initial\ momentum = final\ momentum$$
$$mv = m(-v)$$
$$mv = -mv$$
But this doesn't seem right because it's like saying $1=-1$?
Best Answer
The initial and final momentum are not the same because the ball is not an isolated system. The wall exerts a force on it. In principle the ball and the wall (and the planet it's connected to!) form an isolated system with a conserved momentum, but you'd have to take into account how much the wall moves after the collision.
The change of momentum is final momentum - initial momentum, and you have the correct values for the initial and final momentum.