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3 years ago

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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 grou

nd. 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

1 answer:

Ronch [10]3 years ago

8 0

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

$v = r\omega$

$r=\dfrac{v}{\omega}$

Where, v =velocity

r = radius

$\omega$ =angular velocity

Put the value into the formula

$r=\dfrac{2.00}{7.5\times\dfrac{2\pi}{60}}$

$r=2.54\ cm$

We need to calculate the diameter of axle

Using formula of diameter

$d=2r$

$d=2\times2.54$

$d=5.08\ cm$

Hence, The diameter of the axle is 5.08 cm.

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A (20, 15, 0 ) m

B (0, 0, 7) m

$\overrightarrow{F_{1}}=8\widehat{i}+29\widehat{j}+32\widehat{k}$

$\overrightarrow{F_{2}}=48\widehat{i}-59\widehat{j}-22\widehat{k}$

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Work done is defined as

$W = \overrightarrow{F}.\overrightarrow{S}$

$W = \left ( 56\widehat{i}-30\widehat{j}+10\widehat{k} \right ).\left (-20\widehat{i}-15\widehat{j}+7\widehat{k} \right )$

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W = - 600 J

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