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Its a situation where I'm pulling a box with weight W up utilizing a pulley with radius r and a sliding friction coefficient μ. What is the minimum force on the rope downward on the rope needed to lift the box?

The question says to use an integration technique, and says to show that it's We

^{πμ}.

I'm not quite sure how to think about this; and knowing that I need to use an integration technique to solve it is throwing me off as well.

I'm quite knowledgeable of single variable calculus and I'm not looking for an answer, I'm just looking for some help in how to think about this problem, and perhaps some guidance pointing me in a direction to go about solving this problem or dealing with this situation.

Thank you.