As shown in the figure (Figure 1) , a superball with mass m equal to 50 grams is

Question

As shown in the figure (Figure 1) , a superball with mass m equal to 50 grams is dropped from a height of hi=1.5m . It collides with a table, then bounces up to a height of hf=1.0m . The duration of the collision (the time during which the superball is in contact with the table) is tc=15ms . In this problem, take the positive y direction to be upward, and use g=9.8m/s2 for the magnitude of the acceleration due to gravity. Neglect air resistance.

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

Express your answer numerically, to two significant figures.

Explanation / Answer

According to the given problem,

First find the y component of the momentum, Pbefore,y, of the ball immediately before the collision.
= 0.05* 2*9.8*1.5 = 0.27 kg-m/s

Now, Find the y component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table. = 0.05* (2*9.8*1.0) = 0.22 kg-m/s

Finally,

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

Favg,y= [0.22 -(- 0.27)]/0.015 = 32.7 N = 33 N

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