# Force calculations on a hemisphere

1. May 15, 2005

### stevemir

I need to find the force on a hemisphere below a certain height H in water. The hemisphere is resting at the bottom. The radius of the hsphere is r. I think i need to use dF = dPdA and use spherical coordinates to integrate but do not know how to form the triple integral required!

2. May 15, 2005

### Staff: Mentor

Doing the integration is one way to solve it, but not the easiest. Make use of Archimedes' principle to find the buoyant force on a submerged half-ball.

But if you'd like to do the integral, be sure to take advantage of cylindrical symmetry. (I assume the axis is vertical.) And realize that only the vertical components of the force elements remain (the horizontal components cancel).