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Re: [Phys-l] Errata for FCI?



On 11/03/2010 10:43 AM, I wrote:
In particular, if we hypothesize that the intent was to ask about
buoyancy, this is not the right way to do it. The question embodies
wrong physics in the sense that the buoyancy is independent of
pressure /per se/, as you can see from the following: Make a plot
using density and pressure as the axes. (The contours of constant
temperature are hyperbolas on this plot.) On this plot, contours
of constant buoyancy are parallel to the contours of constant density
and perpendicular to the contours of constant pressure!

If we hypothesize that the intent was to check whether the students
can visualize the pressure as a scalar field and the pressure gradient
as a vector field ... well, let's just say that the level of the
question is inconsistent with the rest of the FCI.

I was in a hurry and didn't clearly or fully explain what I meant.
Let me try again:

We can describe "the" pressure as a scalar field, i.e. P(x) for
all x, where x is the position.

We can expand this as a Taylor series:
P(x) = P(0) + ∇P(0) • x + ....
\ \
\ \--- pressure gradient
\
\--- baseline pressure

My point is that the baseline pressure contributes nothing to
the buoyancy. The pressure /gradient/ i.e. ∇P(x) is a vector
field, and ∇P(0) is the lowest-order term that actually contributes
to the buoyancy.

In the introductory class, I don't recommend explaining buoyancy
in terms of pressure, because if you want them to understand the
_concept_, the lowest-order concept that connects to the answer
is the pressure /gradient/. That's unnecessarily overcomplicated.

Constructive suggestion: As previously discussed, there
are force-balance and momentum-conservation arguments that
get you directly to Archimedes' principle without any need
to mention pressures on surfaces.

The FCI question that started this thread looks to me like
one of those questions that is most easily answered by playing
word-games, i.e. by matching the words of the question against
the words of some "definition" that was learned by rote ...
all without regard to actual concepts.

I get really tired of "Conceptual" books and "Conceptual" exams
that pay only lip service to actual concepts and instead rely
heavily on rote regurgitation. I object to using "conceptual"
as a euphemism for "superficial" i.e. "not requiring much if
any deep thinking". Forsooth, I consider the concepts and the
principles to be the /most/ thoughtful, deep, and sophisticated
part of any subject.