A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed –v. The impulse imparted to the ball by the wall is
To find the impulse imparted to the ball by the wall, we need to use the impulse-momentum principle, which states that the impulse experienced by an object is equal to the change in momentum of the object.
The momentum of an object is defined as the product of its mass and velocity. In this case, the ball's initial momentum before hitting the wall is +mv, as it is moving in one direction (let's call it the positive direction) with velocity +v.
After hitting the wall, the ball rebounds and moves in the opposite direction (negative direction) with velocity -v. Therefore, its final momentum is -mv.
The change in momentum is the difference between the final momentum and the initial momentum:
Change in momentum = Final momentum - Initial momentum
= (-mv) - (+mv)
= -mv - mv
= -2mv
Thus, the impulse imparted to the ball by the wall is -2mv. The negative sign indicates that the direction of the impulse is opposite to the initial direction of motion of the ball.