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Re: [Phys-l] nifty question



I thought this question was too hard for me, but John's comment gave me a clue. I still am not sure, but if I am right, then the answer to this question reminds me of the reasoning used to show that the electric field inside a conductor is zero... if there were a field available to push the charges, there's nothing stopping them from going where they are pushed! So they must already be there.

But this may be better desciibed as a random free association than as an analogy. I'm just saying one problem reminded me of the other. And of course, I may just be wrong. But isn't one way to derive the shape of a catenary to assume that it takes the shape with the lowest potential energy? If so, then I'm on the right track.
________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of John Mallinckrodt [ajm@csupomona.edu]
Sent: Thursday, September 23, 2010 11:57 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] nifty question

... and then, of course, there is the modification that actually
makes the problem a lot easier:

Push or pull anywhere, in any direction. Allow the cable to slide,
or not.

John Mallinckrodt
Cal Poly Pomona

On Sep 23, 2010, at 7:58 AM, curtis osterhoudt wrote:

I'd like to propose a tiny modification to Carl's puzzle, one which
(I think)
makes it a lot harder:

Pull up in the center, instead of down. Whether you let the
cable slide
side-to-side at the point of pulling is up to you.



/**************************************
"The four points of the compass be logic, knowledge, wisdom and the
unknown.
Some do bow in that final direction. Others advance upon it. To bow
before the
one is to lose sight of the three. I may submit to the unknown, but
never to the
unknowable." ~~Roger Zelazny, in "Lord of Light"
***************************************/




________________________________
From: Carl Mungan <mungan@usna.edu>
To: phys-l@carnot.physics.buffalo.edu
Sent: Wed, September 22, 2010 8:56:38 AM
Subject: [Phys-l] nifty question

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
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l