The change in the magnitude of the ball's momentum, directly related to the net force during the collision, is 0.099 kg·m/s.
(a) The magnitude of the change in the ball's momentum can be found using the momentum equation: Change in momentum = Final momentum - Initial momentum.
The momentum (p) is given by the product of mass (m) and velocity (v): p = mv.
So, for the falling phase, the initial momentum is m × v_fall, and for the rebounding phase, the final momentum is m × v_rebound. The change in momentum is then:
Change in momentum = m × v_rebound - m × v_fall.
Substitute the given values:
Change in momentum = (0.022 kg)(2.0 m/s) - (0.022 kg)(-2.5 m/s).
Change in momentum = 0.099 kg·m/s.
(b) The change in the magnitude of the ball's momentum is the absolute value of the change in momentum calculated in part (a):
Change in magnitude of momentum = |Change in momentum|. Change in magnitude of momentum
= 0.099 kg·m/s.
(c) The quantity calculated in part (b), the change in the magnitude of the ball's momentum, is more directly related to the net force acting on the ball during its collision with the floor. This is because force is related to the rate of change of momentum, or acceleration (F = ma). In the context of the collision, the change in the magnitude of momentum represents the impulse exerted by the floor, and impulse is directly related to force. A greater change in momentum implies a greater force acting on the ball during the collision.