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I've been thinking lately about hanging cables. I came across the
following neat question (which has a simple answer).
Consider an ideal (ie. cannot stretch, and can bend freely) cable
suspended from two points of equal height (that are closer together
than the cable's length). The cable adopts the shape of a catenary
(hyperbolic cosine).
Now suppose you hang a weight from the center of the cable. Does the
cable's center of mass move up, down, or remain at the same height?
Have fun thinking about it! If you see the simple solution, don't
give it away too quickly! -Carl