MyOpenMath Assessment rums Calendar Gradebook Log Out 8 Koric> Assessment 6 Flui

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MyOpenMath Assessment rums Calendar Gradebook Log Out 8 Koric> Assessment 6 Fluid Force and Centroid Tram Nguyen Due Mon 03/19/2018 10:00 The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y- 0.1a2 and below the line y (Here, distances are measured in meters.) The water level is 36 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. kg m3 772 Preview Points possible: 10 Unlimited attempts. Message instructor about this question Submit

Explanation / Answer

To find the force, you multiply density, gravity, area and depth. Because the area and depth are variable, you need to take an integral. Because the dam goes up/down, we'll make the limits of integration y-values, which means our equation must be in terms of y also.

Limits of Integration: The total depth of the water is 188 (220-32). We measure from the bottom up, so limits of integration are 0 to 188.

The depth in the equation is changing, and is equal to (188-y).

You solve the area equation for 'y', so that is (2y)^(.5). *You have to multiply the area by 2 so you get both halves of the equation.

Overall, you integrate (9.8)(1000)(188-y)2(sqrt2y) from 0 to 188.

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