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 N buckets 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 0.400m/s2, what should the angular acceleration of the axle be?

Explanation / Answer

v = Rw

w = 7.5 rpm = 7.5 * 2pi/60 rad/s

v = 2cm/s

R = 2.546 cm

D = 2R = 5.09 cm

part b )

alpha = a/r

r = 2.546 cm = 2.546 x 10^-2 m

alpha = 0.400/2.546x10^-2 = 15.7 rad/s^2

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