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Three Balls in a Bowl (Posted on 2005-09-07) Difficulty: 5 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolution! supp value for h^2goFish2005-11-20 11:26:33
Solution!goFish2005-11-20 11:23:58
re: Red HerringsgoFish2005-11-20 09:47:17
Some ThoughtsRed Herringsbrianjn2005-11-20 08:36:57
re: How about Two Balls in a BowlgoFish2005-11-17 04:20:11
re: How about Two Balls in a BowlgoFish2005-11-11 04:17:20
QuestionHow about Two Balls in a BowlLeming2005-11-10 09:20:51
re: not enough info?Larry2005-11-05 19:45:00
Solutionnot enough info?dave2005-10-14 01:06:58
Solution too long but possiblegoFish2005-09-20 22:39:06
re(2): Hugo's Challenge from CBbrianjn2005-09-20 00:59:22
re: Hugo's Challenge from CBHugo2005-09-19 18:33:45
Some ThoughtsThose Non-equalitiesCeeAnne2005-09-18 15:18:55
Hugo's Challenge from CBbrianjn2005-09-18 12:28:23
~ conservation of energy; first thoughtsLarry2005-09-08 01:38:48
re: Some thoughts and a questionHugo2005-09-07 21:12:46
Some ThoughtsMore thoughtsLeming2005-09-07 20:50:03
Some ThoughtsSome thoughts and a questionLeming2005-09-07 20:47:28
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