Re: [Phys-l] nifty question

[brian whatcott <betwys1@sbcglobal.net>]

 On 9/22/2010 9:56 AM, Carl Mungan wrote:
> 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

I am lacking  the critical insight. I may not even have the question 
properly
 addressed.
Suppose I hang a light string between pylons, so that the curve is  
described by
 y = cosh(x)   for x [-2..2]   The midpoint is evidently at 0,1   Now I 
add a very
heavy weight to the center point so that the string has two straight 
sections.

The CoG of the ensemble is inevitably lower. That cannot be the question 
that
Carl intends to frame. Perhaps he is asking, for the center weighted,
 what happens to the CoG of the string ALONE?   Here I expect he means us
 to answer that the CoG rises, but I come to this graphically.

 I am certainly missing the glorious simplicity. Could it be we are 
intended
 to visualize a property of an object with  least potential energy, so 
that a
central weight which pulls the center down, with some expenditure of work,
invokes a reactionary  work in the up direction?

One can certainly invoke analytical models of cables or chains of this kind
with or without perturbations to track the dynamics, but this is certainly
the sledgehammer wielded for something that needs no more
 (I can suppose ) than a toffee hammer?
Help me out..
Brian W