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Re: [Phys-l] Statics conundrum



Bob,
I added a couple of simpifying assumptions to make the problem you
stated what amounts to a pretty standard strength of materials (a.k.a.
mechanics of materials) problem, namely: the strings remain elastic
throughout, that is they obey Hooke's Law (stress equals Young's modulus
times strain), the strings are initially vertical, and the amount of
stretching is so small that the deviation of the strings from the
vertical after the slow smooth release is negligibly small (I use a
small angle approximation). The solution hinges on the fact that under
these assumptions, the stretch of a string is proportional to the
tension in it, and what I call the principle of consistent deformations
which in this case means that if you know the stretch of two of the
strings in the final configuration, then the geometry of the
configuration uniquely determines the stretch of the third.
<http://www.anselm.edu/internet/physics/phys-l/staticsProb.pdf>
is a link to a scan of a pencil on paper solution, valid for small
amounts of elastic stretch only, to the specific problem you stated
below.
Jeff

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Bob Sciamanda
Sent: Sunday, March 14, 2010 7:57 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Statics conundrum

Perhaps it will help to specify a particular situation:
Let the beam be hung from three strings of identical properties
(length,
etc), at the two ends of the beam and at L/4. Slow, smooth,
simultaneous
release all along the beam.
Can we determine the tensions in the strings? Why not? How do the
strings
"know what to do"? (I speak as the student that I am.)

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/