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An engineering firm is designing a ski lift. The wire rope needs to travel with a linear velocity of 2.0 meters per second, and the angular velocity of the bullwheel will be 10 revolutions per minute. What diameter bullwheel should be used to drive the wire rope?

Respuesta :

Answer:

The diameter of the bull-wheel is 3.82

Explanation:

Given that,

Velocity = 2.0 m/s

Angular velocity = 10 rev/m

[tex]\omega=10\times\dfrac{2\pi}{60}[/tex]

[tex]\omega=1.0472\ rad/s[/tex]

We need to calculate the diameter of bull-wheel

Using formula of angular velocity

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

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

Put the value into the formula

[tex]r=\dfrac{2.0}{1.0472}[/tex]

[tex]r=1.91\ m[/tex]

The diameter of the bull-wheel

[tex]D=2r[/tex]

[tex]D=2\times1.91[/tex]

[tex]D=3.82\ m[/tex]

Hence, The diameter of the bull-wheel is 3.82 m.

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