I reckon everybody on this list has graded papers like this:
The student was asked to derive the Kepler 1-2-3 law. The
student writes down "E = m g h" and nothing more, and turns
in the paper, expecting to get points because what he wrote
down was true.
Well, it may be true, and it may be the right answer to some
*other* question ... but it is not the answer to the question
that was asked, and is not even particularly closely related.
I mention this because on 09/01/2011 06:05 AM, Bernard Cleyet
asked about:
The discussion of the cars is cute, and it might even be the
right answer to some *other* question, but it is not the
answer to the question that was asked.
For one thing, cars don't ordinarily push on each other;
they accelerate and decelerate mainly by transferring momentum
to/from the road (and maybe the ambient air). The situation
is very different in a gas: the particles push on each other
quite a lot. You could fix the car model by imagining that
the cars push on each other, but this was not mentioned in
the document in question.
However, that would leave us with a more fundamental issue:
The cars accelerate and decelerate by using their engines
and brakes to add energy to the system and remove energy
from the system. This is verrry unlike what happens in a
gas. I don't see any good way to fix this problem with
the car model. This energy issue is quite central to the
question that was asked, since Bernoulli's equation can
be interpreted as a statement about the enthalpy. http://www.av8n.com/physics/bernoulli.htm
Thirdly: The car model is a more-or-less valid way of
explaining the /continuity/ equation in one dimension.
Alas, if we are to have any hope of applying this to
the question that was asked, we need to understand what
happens in two or more dimensions, and this is quite a
bit more involved.
Fourthly, if we are to connect the continuity equation
to the Bernoulli equation, we need some more information.
The document doesn't explain how to do this. It seems
to implicitly make an appeal to the ideal gas law, but
that is still not enough information, because we don't
know the temperature. If we assume constant temperature,
then the document implies that the pressure and density
are inversely proportional to the first power of the
velocity ... which is the wrong answer. If we don't
assume that, we need to make some other assumptions about
the equation of state of the cars, which the document
doesn't even hint at.
The document doesn't state (let alone derive) the correct
form of the Bernoulli law.
Et cetera.
====================
Again I ask: Whatever happened to the idea of "check
your work"?
When a child hands you a piece of refrigerator art, it is
bad manners to critique it. It is pointless to observe
that it is not a good likeness by professional standards,
let alone an artistic portrait by the standards of da
Vinci or Holbein.
On the other hand, if an adult produces a pre-schematic
drawing, you have to worry.
Also, when an adult critiques other work and claims that his
version is better, then I reckon it is fair to critique his
version.