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?

(In reply to What I think I know by Jer)

Jer,

I agree with what you have, up to the displacement of the spheres.  I have that displacement equal to sqrt(24r).  I arrived at max radius of 4.5135cm and min of 3.4 cm to cause the tube to tip (or topple).  No elegant equation though. Working on that.

Edited on June 24, 2005, 12:20 am

Posted by Leming on 2005-06-24 00:12:18