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 Another method, Another answer by Larry)

Hi Larry,

I think that if you tried your other method again that you will get the same answer as this method. Remember when balancing forces you can pick any direction - perpendicular to gravity, parallel to gravity, perpendicular to the rod, parallel to the rod, etc. Remember when balancing torques you can pick any pivot point on the rod - either end, the midpoint, where it touches the edge, etc. Try them all and pick the simplest equations.

 

Posted by Bractals on 2005-01-04 22:09:15