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Tipping Tube (Posted on 2005-06-23) Difficulty: 4 of 5
A man places a circular tube upright on a table. He then places a solid ball into the tube followed by a smaller solid ball. The tube stays upright. He removes the balls and places them again with the smaller ball being placed in first. The tube tips over. In both cases the man holds onto the tube until the balls come to rest and then lets go. The radii of the balls are 2.6 and 3.4 centimeters. The length of the tube is 18.0 centimeters and its thickness (external radius minus internal radius) is 0.1 centimeter. The balls and tube are made of the same material - so their weights are proportional to their volumes. Assume the points of contact between the balls, table, and tube are frictionless. What are the minimum and maximum values for the internal radius of the tube?

See The Solution Submitted by Bractals    
Rating: 3.7500 (4 votes)

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re: What I think I know | Comment 6 of 11 |
(In reply to What I think I know by Jer)

Jer, I don't find an influence of the small sphere on the moments or torques that are working on the cylinder and I think there should be one.  Maybe I overlooked it or it is somewhere in the 'work omitted ' part.

The large sphere pushes downwards on the small sphere and this small sphere will be pushing against the cylinder wall with a force that can be found by taking the horizontal part of the vector-force excerted on the small sphere.  Let's call this force F 

Now imagine a line through the point where F touches the cylinderwall and a point on the opposite side of the cylinder, where it touches the ground surface.  You can now make two vectors (Sum of which is F), one along the line and one perpendicular to that line.  The perpendicular part creates a  moment/torque that will try to tip the cylinder.

Unfortunately I am not smart enough/ too lazy to do the calculations.

  Posted by Hugo on 2005-06-24 10:04:38
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