A superball of mass m, starting at rest, is dropped from a height hi above the ground and bounces back up to a height of hf. The collision with the ground occurs over a total time tc. You may ignore air resistance.
(a) What is the magnitude of the momentum of the ball immediately before the collision? Express your answer in terms of m, hi, and g as needed (enter h_i for hi, h_f for hf, and t_c for tc).
(b) What is the magnitude of the momentum of the ball immediately after the collision? Express your answer in terms of m, hf, and g as needed (enter h_i for hi, h_f for hf, and t_c for tc).
(c) What is the magnitude of the impulse imparted to the ball? Express your answer in terms of m, hi, hf, tc, and g as needed (enter h_i for hi, h_f for hf, and t_c for tc).
(d) What is the magnitude of the average force of the ground on the ball? Express your answer in terms of m, hi, hf, tc, and g as needed (enter h_i for hi, h_f for hf, and t_c for tc).
Pr 4
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/momentum/momentum-and-impulse/MIT8_01SC_problems16_soln.pdf
does anyone know the last one??
plzz help
To answer these questions, we need to understand the concepts of momentum, impulse, and average force.
(a) The magnitude of the momentum of the ball immediately before the collision can be calculated using the equation:
Momentum = mass * velocity
Since the ball is dropped from rest, its initial velocity is 0. Therefore, the momentum before the collision is 0.
(b) The magnitude of the momentum of the ball immediately after the collision depends on the elasticity of the bounce. Assuming the ball follows a perfectly elastic collision, its momentum after the collision is equal to the momentum before the collision. This means it will have a magnitude of 0, since its momentum before the collision was also 0.
(c) The magnitude of the impulse imparted to the ball can be calculated using the impulse-momentum theorem:
Impulse = Change in momentum
Since the momentum before and after the collision is 0, the change in momentum is also 0. Therefore, the magnitude of the impulse imparted to the ball is 0.
(d) The magnitude of the average force of the ground on the ball can be calculated using the formula:
Average Force = Impulse / Time
As mentioned earlier, the impulse imparted to the ball is 0. Therefore, the magnitude of the average force of the ground on the ball is also 0.
In summary:
(a) Magnitude of momentum before collision: 0
(b) Magnitude of momentum after collision: 0
(c) Magnitude of impulse imparted to the ball: 0
(d) Magnitude of average force of the ground on the ball: 0