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Sun 6 Jan, 2013 05:06 pm

QUESTION

A steady stream of 15 balls per second (50 grams each), rolls from a horizontal table and falls through a height of 1 m onto the top of a scale. The scale responds slowly and so reads the average force which in this case is 6N. TO WHAT HEIGHT H DO THE BALLS REBOUND? (they each make only one collision with the scale) Please provide full solution.

SOLUTION

Impulse times number per second = force.

impulse = force / number per second

impulse = 6N / 15/s

impulse per ball = 0.4 kg m/s

v^2 = 2 a x

v = sqrt(2 a x)

v = sqrt(2 9.81m/s^2 1m)

v = sqrt(19.62m^2/s^2)

v = 4.42m/s (down)

p(f) - p(i) = dp = impulse

p(f) = impulse + p(i)

p(f) = 0.4 kg m/s + (0.05kg (-4.42m/s))

p(f) = 0.4kg m/s - 0.221 kg m/s

p(f) = 0.179 kg m/s

v(f) = p(f) / m

v(f) = 0.179 kg m/s / 50g

v(f) = 4.02 m/s

v^2 = 2 a x

x = v^2 / 2 a

x = (4.02m/s)^2 / 2*9.81m/s^2

x = 0.82m