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Re: [Phys-L] "conservative force" --> misnomer --> misconception



On 01/14/2014 10:32 AM, Herbert Schulz wrote:

My impression is that the definition of a `Conservative Force' is
that `The Work done by a Conservative Force when going around any
closed loop is zero (\oint\vec{F}\dot\vec{dr}=0).

This then implies that it can be written as the gradient of a
function (called -U where U is called the Potential Energy function
for that force.

Exactly. Proof by construction. You can integrate F to find U,
and you can differentiate U to find F.

That's all nice and logical. The problem is, pedagogy is not
always logical.

1) The first problem is that students often assume that a "conservative
force" is somehow related to the idea of conservation of energy.

I know where that comes from. It's because students tend to assume
that names are meaningful. All too often, teachers -- who ought to
know better -- assume the same thing. In this case, though, the word
"conservative" is the opposite of meaningful, the opposite of helpful.
As Voltaire pointed out, the Holy Roman Empire was neither holy, nor
Roman, nor an empire.

I strongly recommend saying non-grady instead of non-conservative,
so that students are not led into temptation.



2) On top of that, students often assume that non-conservative forces
are dissipative i.e. thermodynamically irreversible.

I know where that comes from, too. It comes from over-reliance on
friction as an example of a non-grady force.

I strongly recommend using the field in a betatron as a better
example. It is clearly non-grady, and also clearly reversible
and non-dissipative.

An ordinary transformer is another example, although it makes it
slightly harder to see what's going on.



On 01/13/2014 06:23 PM, Paul Lulai mentioned:

http://prettygoodphysics.wikispaces.com/

It is a place for folks to share notes, labs and other items.

That's basically a Good Thing.

There are several energy units there. Alas many of them say wrong
things about conservative forces, seriously polluting the discussion
of conservation of energy.

That's what provoked me to tilt at this particular windmill today.

I tend not to get very excited when students have misconceptions.
That's to be expected. OTOH when the teachers and the reference
materials are pushing misconceptions, I take that more seriously.