Calculating Hydrostatic Force of a Submerged Semicircle

[tylu234]

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.

 

[tylu234]

bump, test in 20 minutes