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       #Post#: 105--------------------------------------------------
       SUSPENDED ROPE TRICK
       By: eba95 Date: July 30, 2010, 6:25 am
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       Suspended Rope Trick
       What is the shape of a suspended
       rope? Is there some function that
       describes it?
       Answer: it's the cosh curve!
       Presentation Suggestions:
       This may be seen quite dramatically
       by putting up a transparency of the
       catenary
       y = cosh x
       and suspending a rope in front of the
       transparency projection so that the
       rope shadow can be compared!
       Now, someone may object and say
       that the curve of x2 will also give a
       good approximation. If they do this,
       you can talk about how the Taylor
       series of cosh begins with a
       quadratic 1 + x2/2, so it is not
       surprising!
       The Math Behind the Fact:
       Calculus and modeling are useful
       here: by breaking the rope into lots
       of little chunks, and modeling the
       forces on each chunk, one can obtain
       a differential equation whose
       solution is the cosh curve.
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