# Thread: Work done to lift chain w/ weight attached

1. ## Work done to lift chain w/ weight attached

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 $\displaystyle W = F * D$ and that in these units a lb is a force unit,

I've sliced the chain horizontally so it has thickness $\displaystyle \Delta y$

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 * $\displaystyle \Delta y$ 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.

2. I know this might be more physics than calculus is - there a better place to be posting this?

3. bump.. anyone have any clues for me?

4. $\displaystyle int_{r=0}^{r=25} (100 + 3 (r)$

this would be the answer.. thanks anyways guys!

5. total work = work to raise the chain + work to raise the anchor

the force required to raise the anchor is not variable ...

$\displaystyle W_{total} = \int_0^{25} (25-y)3\, dy + 2500$