## tidal force energy analisis with calculus (help please)

I´ve been trying to solve this problem but I have been unable. I was able to solve part (a) but I can´t do part (b) I´d appreciate a lot if someone helped me.

the problem is the following:

Tidal power plants use "tidal energy" to produce electrical energy. To construct a tidal power plant, a dam is built to separate a bay from the sea. The amount of natural energy produced depends on the volume of the bay and the tidal range -- the vertical distance between high and low tides.

the basin is formed by a 3d rectangle with dimensions: 1000ft wide, 500 deep and 25 ft in height. The curve inside that 3d rectangle that is given by the function:
y= x(square)/40000 --> this is y=x*x/40000.

(a) Consider a basin with a rectangular base, as shown in the figure. The basin has a tidal range of 25 feet, with low tide corresponding to Y=0. How much water does the basin hold at high tide.

(b) The amount of energy produced during the filling (or the emptying) of the basin is proportional to the amount of work requiered to fill (or empty) the basin. How much work is requiered to fill the basin with seawater? (Use a seawater density of 64 pounds per cubic foot.)

I´d appreciate some help.

Thanks
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 I solved (a) integrated the curve to get the area below it. Then multiplied that by the depth to get the volume under the curve then I got the volume of the 3d rectangle by multiplying 1000x500x25 and subrstracted the volume undert he curve from this. THis way I believe I got the volume of water that enters the damn. I tried part (b). But I didn't use calculus in this part, I just did the standard W=Fd . I got the mass with the density and volume. I used the 1000 ft in the d and in the Force I used the earth's gravity as acceleration. I don't think this is right. Can you help me please? IF you don't understand the drawing let me know and I'll draw one myself\ thanks a lot

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