As shown in the figure (Figure 1), a superball with mass m equal to 50 grams is
ID: 1414023 • Letter: A
Question
As shown in the figure (Figure 1), a superball with mass m equal to 50 grams is dropped from a height of h_i = 1.5 m. It collides with a table, then bounces up to a height of h_f = 1.0 m. The duration of the collision (the time during which the superball is in contact with the table) is t_c = 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. Find J_y, the y component of the impulse imparted to the ball during the collision. Express your answer numerically, to two significant figures. Find the y component of the time-averaged force F_avg,y, in newtons, that the table exerts on the ball. Express your answer numerically, to two significant figures.Explanation / Answer
Vi = initial velocity just before hitting the table = - sqrt(2ghi) = - sqrt(2 x 9.8 x 1.5) = - 5.42 m/s
Vf = final velocity just after hitting the table = sqrt(2ghf) = - sqrt(2 x 9.8 x 1) = 4.43 m/s
m = mass of ball = 50 g = 0.05 kg
Impulse = I = m (Vf - Vi) = (0.05) (4.43 - (-5.42)) = 0.4925 kgm/s
b)
F t = I
F (0.015) = 0.4925
F = 32.83 N
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