Here is a problem I have been developing. Maybe somebody can
tell me if it can be solved or if more information is needed.
Three solid balls of radii a, b, and c are placed in a bowl
whose inner surface is a hemisphere of radius d.
The following information is known:
1) a < b < c < d,
2) d is large enough so that each ball touches a point on
the inner surface of the bowl,
3) a is large enough so that each ball touches the other
4) the balls are made of the same material so that their
weights are proportional to their volumes,
5) the forces that the balls exert on each other and the
bowl are directed along the lines determined by their
After the balls come to rest, what is the angle between
the plane determined by the centers of the balls and the
horizontal in terms of a, b, c, and d ?
i think balls could be made that all squish together and touch the lid of the bowl then the plane would be maximized for the hemisphere.
another solution with smaller balls is also possible so i think this needs more info
Posted by dave
on 2005-10-14 01:06:58