tidal force energy analisis with calculus (help please)

woz

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 already answered part (a) but I'm not sure about part (b).

I´d appreciate some help.

Thanks

Attached Thumbnails

 

Tide

What exactly have you tried so far?

woz

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

HallsofIvy

Work= mass*height. The work done by the tide in raising the level of the water is the height the water is raised times the (average) height the water is raised. The potential energy then stored in that water is equal to the work done in raising that water.

Basically, what a "tidal power plant" does is open the gates and allow the tide to raise the level of the water in the bay. Then close the gates and use the stored water, at low tide, to run through dynamos, creating electricity.

Tide

Woz,

I'm sorry I couldn't get back to you sooner - Spring semester is pretty hectic for me.

It looks like you have gotten the help you need!

ishtiyaq123

I need help with same problem. will you help me with this