You are to design a rotating cylindrical axle to lift 850-N buckets of cement fr

Question

You are to design a rotating cylindrical axle to lift 850-N buckets of cement from the ground to a rooftop 75.0 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 1.95 cm/s when it is turning at 7.2 rpm? (b) If instead the axle must give the buckets an upward acceleration of 0.385 m/s^2, what should the angular acceleration of the axle be? rad/s^2

Explanation / Answer

here,

weight of bucket, w = 850 N

height of rooftop, h = 75 m

velocity, v = 1.95 cm/s = 0.0195 m/s

angular speed, w = 7.2 rpm = 7.2 * 0.105 = 0.756 rad/s

Part a:
Since,
v = w * radius of axle

radius of axle,r = v/w

dia of axle = 2 * v/w

dia of axle = 2 * 0.0195/0.756

dia of axle = 0.051 m

dia of axle = 5.1 cm

Part b:
radius of axle, r = 0.051/2 = 0.0255

acceleration, a = 0.385 m/s^2

angular acceleration,alpha = a/r

angular acceleration,alpha = 0.385 / 0.0255

angular acceleration,alpha = 15.098 rad/s^2

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