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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

Respuesta :

Answer:

The diameter of the axle is 5.08 cm.

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

[tex]v = r\omega[/tex]

[tex]r=\dfrac{v}{\omega}[/tex]

Where, v =velocity

r = radius

[tex]\omega[/tex]=angular velocity

Put the value into the formula

[tex]r=\dfrac{2.00}{7.5\times\dfrac{2\pi}{60}}[/tex]

[tex]r=2.54\ cm[/tex]

We need to calculate the diameter of axle

Using formula of diameter

[tex]d=2r[/tex]

[tex]d=2\times2.54[/tex]

[tex]d=5.08\ cm[/tex]

Hence, The diameter of the axle is 5.08 cm.

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