Calculating Hydrostatic Force of a Submerged Semicircle

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To calculate the hydrostatic force on a submerged semicircle, the problem involves a semicircle with a radius of 5 ft and a distance of 2 ft from the water surface to the top. The weight density of water is given as 62.5 lb/ft³. The force is derived using the integral of the product of weight density and the area element, leading to an initial calculation of approximately 1.4 * 10^4 N. However, there is uncertainty regarding the integration limits and the expression (7 - x), which may need reevaluation. The correct answer is stated to be 1.2 * 10^4 N, indicating a potential error in the initial calculation.
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Homework Statement



There is a semicircle submerged in the water. The distance between the surface and the top of the semicircle is 2 ft, and the radius is 5 ft. Find the hydrostatic force.

The answer is 1.2 * 10^4 N.

Homework Equations



y = sqrt(25 - x2)

The Attempt at a Solution



w = 62.5

dA = sqrt(25-x2)dx
dF = w(7-x)sqrt(25-x2)dx
F = w∫(7-x)sqrt(25-x2)dx, limits of integration: 0, 5

Calculated and got this answer:
F ≈ 1.4 * 10^4 N

I think the (7 - x) part is wrong, or maybe the limits of intg.
 
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