# Momentum

As shown in the figure (see attachment), a superball with mass m equal to 50 grams is dropped from a height of h1= 1.5 m. It collides with a table, then bounces up to a height of h2= 1.0 m. The duration of the collision (the time during which the superball is in contact with the table) is tc= 15 ms. In this problem, take the positive y direction to be upward, and use g = 9.8 m/s^2 for the magnitude of the acceleration due to gravity. Neglect air resistance.

a). Find the y component of the momentum, of the ball immediately before the collision.

b). Find the y component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table.

c). Find the y component of the time-averaged force F in newtons, that the table exerts on the ball.

d). Find Jy, the y component of the impulse imparted to the ball during the collision.

e). Find Kafter - Kbefore, the change in the kinetic energy of the ball during the collision, in joules.

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#### Solution Preview

a) Mass of the ball = 50 g

Initial velocity of the ball = u = 0

Displacement of the ball when it hits the table = - 1.5 m (negative because upwards is +ve)

Acceleration of the ball = a = - 9.8 m/s^2

Applying v^2 - u^2 = 2as we get : v^2 = 2 (- 9.8) (-1.5) = 29.4 or v = + 5.42 m/s

As the ball is moving downwards just before collision with the table, v = - 5.42 ...

#### Solution Summary

Step by step solution provided.