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A motor rotates a pulley of radius 25cm ...

A motor rotates a pulley of radius `25cm` at 20rpm. A rope around the pulley lifts a `50kg` block, What is the power output of the motor?

Text Solution

Verified by Experts

The tension in the rope is equal to the weight since there in no acceleration. Thus `T=500 N` therefore, `tau=TR=(500)(0.25)=125 Nm`

Angular velocity, `omega=(2piN)/60(2pi(20))/60=(2pi)/3 rad s^(-1)`
The power required is
`P=tau omega=(125 Nm^(-1))((2pi)/3 rads^(-1))=261 W`
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