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Re: Can this be true?



(Please excuse the duplicate post. I'm resending with a more
descriptive subject line. /GAC)

What if the string had mass, but was horizontal? Wht if the string was
supported from below, not from above (the string is perfectly straight
and plumb)? What if the string is not acted on by gravity? Change the
assumptions; we change the answer.

Real bodies break at imperfections (stress concentrations). Perfect
bodies don't break, or we wouldn't call them perfect.

There is no paradox here. The problem is accepting an idealization
("exactly the same all along") as describing reality ("a true
statement"). We can reach any conclusion we want if we make
sufficiently unrealistic assumptions. It is quite easy to reach
unrealistic conclusions from ideal (unreal) assumptions (e.g.,
"perfectly incompressible fluid," "frictionless surface," "all things
being equal," "if I were king of the world," "if pigs could fly,"
etc.).

As a physics teacher, it's important that help the students understand
the difference between reality and models of reality. Models are not
reality. Models only approximate reality. Models are tools which help
us describe (understand?) reality. Any model will fail to accurately
describe reality or even contradict itself if we extrapolate it far
enough. The goal is help students learn how to model and recognize the
limits of the model.

Glenn A. Carlson, P.E.
St. Charles County Community College
St. Peters, MO


Subject: Re: Can this be true?
Date: Wed, 11 Aug 1999 15:54:17 -0400
From: Maurice Barnhill <mvb@UDEL.EDU>

He forgot to say massless, therefore the tension is highest at the
highest point and the string breaks there. If there is more than one
highest point, it breaks simultaneously at each of them. Moreover,
there must be a highest point (or two highest points) if the hanging
mass is not accelerating.

Carl C. Gaither wrote:

Hello--

While working on the books I came across the following quote. It seems
to me to be quite an interesting statement. Does anyone know if this
can actually be a true statement? The statement is:

If a piece of string were exactly the same all along, however thin it
was, however great the weight hung on it, and however much you jerked
it, it could not break--it wouldn't know where to break.
The Collected Works of Paul Valéry
Valéry, Paul
Volume 14
Analects (p. 322)

--
Maurice Barnhill, mvb@udel.edu
http://www.physics.udel.edu/~barnhill/
Physics Dept., University of Delaware, Newark, DE 19716