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 stead

Answer 1

The diameter of the axle is 5.08 cm.

Step-by-step explanation:

Given that,

Force = 800 N

Distance = 78.0 m

Suppose we need to find 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.

We need to calculate the radius of axle

Using formula of linear velocity

`v = r\omega`

`r=(v)/(\omega)`

Where, v =velocity

r = radius

`\omega`=angular velocity

Put the value into the formula

`r=(2.00)/(7.5*(2\pi)/(60))`

`r=2.54\ cm`

We need to calculate the diameter of axle

Using formula of diameter

`d=2r`

`d=2*2.54`

`d=5.08\ cm`

Hence, The diameter of the axle is 5.08 cm.