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On 05/11/2013 05:34 PM, LaMontagne, Bob wrote:/snip/
I ran a quick analysis using the sum of the forces in the x and yHere is my answer to the original question:
directions, checked my results, and they appeared to work. Many of my
best students agreed with my answers. However, two of my best
students got a different answer for the tensions - and they agreed
with each other. I checked their results and their arithmetic was
fine. However, they solved the problem using torques about the two
ends of the rod.
The problem is ill-posed.
Lemma: In an equilibrium situation, the cables have to hang at
the same angle. Mirror images.
Proof: The bar has no net force along the axis of the bar,
so the forces at each end have to have equal and opposite
x-components.
The bar has no net torque around its middle, so the forces at
each end have to have the same y-component.
Therefore the setup must be unphysical. To proceed, one has to
drop at least one element of the statement of the problem. You can
get almost any answer you like, depending on which element(s) you
decide to drop, especially if you drop the implied (but not quite
explicitly stated) requirement that the system is in equilibrium.
It took me a quite few minutes to figure out what was wrong - and IDid any of the students answer the way I did?
was quite embarrassed.