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Bowl and Rod (Posted on 2004-12-31) Difficulty: 3 of 5
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?

See The Solution Submitted by Bractals    
Rating: 2.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Gosh | Comment 9 of 18 |
(In reply to by )

I actually rummaged through my kitchen as well, and I found a mortar and pestle.  The pestle was about 3.5 times the length of the mortar radius, and it made about a 30 degree angle.  I found a straw, cut it to the right length and it also seemed to be about 30 degrees.  Which is one reason I am suspicious that I made an error either in my force diagram assumptions, or in the math.

But I still don't see how you can just draw it, and get the answer.  For one thing, if the rod is 3 times the radius and you place the rod with 1/3 sticking out, then the rod would be perfectly horizontal with 2/3 of it "being" the diameter at the top of the bowl.
  Posted by Larry on 2005-01-01 19:56:47

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