A modern aluminum sculpture consists of a hollow cylinder that is capped on one end by a solid hemisphere. The cylinder has an outer diameter of 100 cm and thickness of 1 cm, and the hemisphere has the same diameter as the outside of the cylinder.
If, on a level surface, the sculpture balances in stable equilibrium at any point on its hemispherical surface, how long is the cylinder, and what is the minimum ceiling height in the museum to permit the sculpture to assume any stable position?
(In reply to
re(2): soln by Steven Lord)
I think that because the center of gravity of the object is always directly above the point of contact with the table (unless fully on its side when it is only true for the point of contact where half sphere meets cylinder), the slightest push would start rotation at a constant angular velocity but no acceleration once the "push" was ended.
Now that I think about it, the cylinder would eventually strike the table and then recoil. The object would (if no friction and no loss of energy) roll back and forth 180 degrees at a time like a windshield wiper or a metronome.
Good discussion.
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Posted by Larry
on 2025-01-24 10:17:35 |
re(3): soln
