perplexus.info :: Science : Three Balls in a Bowl

Three Balls in a Bowl (Posted on 2005-09-07)

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 two balls,

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 centers.

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 ?

No Solution Yet Submitted by Bractals

Rating: 3.8000 (10 votes)

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Puzzle Thoughts

Comment 19 of 19 |

h =

{Sqrt[(-(a^2*b^2*c^2) - 2*a^2*b^2*c*d - 2*a^2*b*c^2*d - 2*a*b^2*c^2*d - a^2*b^2*d^2 + 2*a^2*b*c*d^2 + 2*a*b^2*c*d^2 - a^2*c^2*d^2 + 2*a*b*c^2*d^2 - b^2*c^2*d^2)/(a*b*c*(a + b + c))]}

Posted by K Sengupta on 2023-08-15 21:07:17

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