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.

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?

If instead the axle must give the buckets an upward acceleration of 0.400 m/s^2, what should the angular acceleration of the axle be?

Please be as detailed as possible! Thank you!

## Answers (1)

tangential speed of the circumference of axle = V = 2.00 cm/s = 0.02 m/s

angular velocity of axle = w = 7.5 rpm = 7.5/60 rps = (7.5/60)(2π) = 0.785 rad/s

R = radius of axle

V = wR

R = V/w = 0.02/0.785 = 0.0255 m

D = = 2R = (2)(0.0255) = 0.051 m ANS-1

2.

a = αR

α = a/R

a = 0.4 m/s²

R = 0.0255 m

α = 0.4/0.0255 = 15.7 rad/s² ANS-2