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 0.400 m/s2, what should the angular acceleration of the axle be?
Solution 22E Step 1 of 2: a)We have relation v = r 2 cm/s = R( 7.5)(1 min)( 2 rad) min 60 s 1 rev 2 cm/s = R(0.785) 2 R = 0.785 R = 2.55 cm D = 2R = 2 × 2.55 = 5.09 cm