Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] A suspended metal rod



On 05/11/2013 05:34 PM, LaMontagne, Bob wrote:

I ran a quick analysis using the sum of the forces in the x and y
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.

Here is my answer to the original question:

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 I
was quite embarrassed.

Did any of the students answer the way I did?

The moral of the story is don't make up
quickie problems for an exam.

You know what they say about lemons and lemonade. This is a big-time
teachable moment.

In the real world, whenever somebody hands you a problem, more-or-less
the first thing you should do is check to see how badly ill-posed it is.

It's been so long since I saw a well-posed problem I almost forget what
they look like. Problems like that tend not to make it to my desk;
they get solved much earlier in the pipeline.

Pedagogically speaking, it would have been better to train then how to
deal with such things /before/ assigning the question, but better late
than never. Some helpful hints can be found at:
http://www.av8n.com/physics/ill-posed.htm
especially
http://www.av8n.com/physics/ill-posed.htm#sec-how-to