Is a Paper Strip Contracted on a Table a Parabola?

[SAZAR]

When you take a paper strip, put it on the flat surface (table), and contract it so it stands up - is it parabola or something else?

 

[tiny-tim]

Hi SAZAR!

You mean you push the ends towards each other, so that the rest of the paper bends naturally?

I think that's a catenary … see http://en.wikipedia.org/wiki/Catenary#The_inverted_catenary_arch

 

[SAZAR]

no.

I meant when you place a paper strip on a desk, then press the ends of the paper strip with index fingers, and then slide them toward each other with paper strip ends stuck to the fingers, so the section of the paper strip between fingers lifts up from the desk and forms a curve.

 

[tiny-tim]

Isn't that what I said?

Anyway, still a catenary. ​

 

[SAZAR]

In the example with paper strip I described the index fingers are not placed at the ends of the paper strip - they are placed some distance away from the ends of the paper strip, so the elastic forces of the paper strip are at work at the point where index fingers are.

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The catenary pictures (examples) on wikipedia show things hanging or bulging at sharp angle from ends of the structure bending.

In example I described, however, the structure continues beyond - the direction of the part beyond is horizontal - not in direction of the curve (it transits from horizontal to the curve)...

 

[Elucidus]

If I am understanding your description correctly, the resulting arching curve is flat underneath the fingers and then bugles upwards in the center. If this is correct, then the curve is definitely not a parabola.

I strongly suspect it is a very complicated curve that may involve trigonometric and/or exponential factors. Even worse still, if the ends are pushed sufficiently close, I believe the curve stops being a function as is balloons out past where the fingers are ( much like a light bulb shape or the letter $\Omega$).

Am I way off base here?

--Elucidus

 

[SAZAR]

I'm interested only in the case when elastic forces of the paper are still at work, not when paper "breaks" and fold at sharp angle.
Imagine that finger-nails face each other, so the nails pin the paperstrip to the surface of the desk while paper slides e.i. contracts which make it bulge - still maintaining its elastic properties (not "breaking").

Try it yourself - take any paper you have there - do what I described. What is that curve you get when you watch it from its profile? ...

 

[SAZAR]

Anyway - would it have at least some properties of parabola? (such as a single focal point; at least in some cases)