You are to design a rotating cylindrical axle to lift 775-N buckets of cement fr

Question

You are to design a rotating cylindrical axle to lift 775-N buckets of cement from the ground to a rooftop 69.5 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 1.65 cm/s when it is turning at 7.8 rpm?
(b) If instead the axle must give the buckets an upward acceleration of 0.450 m/s2, what should the angular acceleration of the axle be?
Thanks.

Explanation / Answer

Given speed of the bucket , v = 1.65 cm /s = 0.0165 m/s Angular velocity , = 7.8 rev / min = 7.8 rev / min * (1 min /60s) * (2 rad / 1 rev)                            = 0.8164 rad / s a) From the relation, v = r                            r = ( 0.0165 m/s) /  0.8164 rad / s = 0.0202 m      Diameter of the axle is , d = 2 r = 2(0.0202m ) = 0.04 04 m                                           d = 4.04 cm b) Acceleration of the bucket is, a = 0.450 m/s^2                 From the relation, a = r                                              = a / r = (0.450 m/s^2) / 0.0202 m                                              =   22.27 rad /s^2 Thus, the angular acceleration of the axle is 22.27 rad/s^2

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