I'm working on a few questions that apply calculus to physics questions.

I seem to be having issues with this one question(been at it for awhile)

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An anchor weighing 100lb in water is attached to a chain weighing 3lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 25ft.

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So this is what i've attempted:

Knowing that and that in these units a lb is a force unit,

I've sliced the chain horizontally so it has thickness

So my next step is to calculate the work done on this strip to lift it, plus the weight of the anchor, to the top. Then ill integrate the formula i get for the work on the strip across the total length of the chain. That is, from 0 to 25.

My problem is getting the work done on this strip. Work = Force * Distance

or in this case Work = Mass * Distance.

I know that Distance will be = (25-y) but what is the mass of the chain? It is obviously 3lb/ft * but how do i account for the anchor at the bottom? Must i account for the remaining chain attached below the strip?

Any quick help here is greatly appreciated.