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Direction of Friction

A cylinder of...

Question

A cylinder of weight $W$ and radius $R$ is to be raised onto a horizontal step of height $h$ as shown in figure. A rope is wrapped around the cylinder and pulled horizontally with force $F$ . Assuming the cylinder does not slip on the step, find the minimum force $F$ necessary to raise the cylinder.

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Solution

Clockwise moment $=$ anti $-$ clockwise moment
$F (R + h) = m g \times R$
$F = \frac{m g R}{R + h}$

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