An inquiring student that has a mass of 65.0 kg is watching a crane with a wrecking ball demolish a building next door. The wrecking ball is swinging parallel to the property fence between her house and the neighbor’s. In an effort to estimate the length of the cable on the wrecking ball the student fashions a pendulum from a rock and a string. Her pendulum turns out to be 0.500m long. She then observes that the wrecking ball completes one oscillation in the same amount of time that it takes the rock to complete 5 cycles. What is the length of the cable on the wrecking ball?

Answer 1

for rock:
T = 2 pi sqrt (L/g)
T = 2 pi sqrt (.5/g)

for ball Tb = 5 T
so
5 T = 2 pi sqrt (Lb/g)
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10pi sqrt (.5/g) = 2pi sqrt (Lb/g)

5 sqrt (.5) = sqrt(Lb)

25 (.5) = Lb

Lb = 12.5