You are to design a rotating cylindrical axle to lift 800 N buckets of cement fr

Question

You are to design a rotating cylindrical axle to lift 800 Nbuckets of cement from the ground to a rooftop 78.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise.

a) What should the diameter of the axle be in order to raise the buckets at a steady 2.00

cm/s when it is turning at 7.5 rpm?

b) If instead the axle must give the buckets an upward acceleration of 0.400

m/s2, what should the angular acceleration of the axle be?

Explanation / Answer

Each revolution of the axle will lift the bucket one circumference. At 7.5 rpm, that means 7.5*?*D cm/min (D in cm) or 7.5*?*D/60 cm/sec so
7.5*?*D/60 = 2.00, D = 120/(7.5*?) = 5.09 cm/s

The tangential acceleration of the axle is 0.400 m/s

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