Given a solid bowl (an idealized hemisphere, the opening facing straight up), let a slender rod rest in the bowl supported at two points: a point on the bowl's edge, and some point on the bowl's interior surface.

The bowl's edge exerts a force on the rod which is perpendicular to the rod's length.

The bowl's interior exerts, on the rod's end, a force which is perpendicular to the bowl's surface (at the point where they meet).

If the rod's length is three times the radius of the bowl, what is the angle between the rod, and the plane of the bowl's edge?

(In reply to FBD by nikki)

Your explanation was (again) excellent and easy to follow.
Though I would have preferred to exchange
Fgx = mg*cos(-90-t) with
Fgx = -mg*cos(90-t)
Same for Fgy = mg*sin(-90-t)
But this would only be a mean old man's critic :-) , the result is the same.
And you got to the same result as Larry's PE method.

Very nice proof nikki, I liked it a lot.

Posted by Hugo on 2005-01-06 20:56:55