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Re: [Phys-L] defining energy

On 10/29/2013 08:48 AM, Philip Keller wrote:

I am going to be teaching this topic to my 11th graders soon. I have a
question about the definition of energy.

OK.

I know that the "ability to do
work" definition runs into trouble when you consider heat, engines and 2nd
law issues.

Quite so.

But what if I turn the definition around. Instead of saying
"energy is the ability to do work", I want to say:

Work is defined to be the product of force and displacement (in the same
direction).

Mostly OK. IMHO it might be slightly better say that F • dx is
an /example/ of what we call work ... rather than the "definition"
per se. See the "nitpick" section below.

Then, in different contexts, you can show that work = delta
(some quantity). Any such quantity is referred to as [blank] energy. Fill
in the blank with an adjective that fits the context.

That's on the right track, but it seems unnecessarily vague.

For one thing, remember the work/kinetic-energy theorem. That means
you should be able to fill in the [blank] with "kinetic".

So "energy" is not the ability to do work, but energies are the quantities
that are changed by work.

Also unnecessarily vague. I treat energy as primary and fundamental.
At the secondary level, there are various ways of /transferring/ energy,
of which work is one.

I'd draw the diagram.

________________ __________________
| | work | |
| energy in |--------------------> | energy in |
| region A | | region B |
| | heat | |
| |--------------------> | |
| | | |
| | advection | |
| |--------------------> | |
| | | |
|________________| |__________________|


========================================

One more thing: IMHO it is worth saying that energy is an
/abstraction/. Maybe that's obvious, but still I think it
is worth mentioning. Water is a tangible material thing,
whereas energy is an abstract thing.
-- The flow of water is /to a good approximation/ conservative flow.
++ The flow of energy is /exactly/ conservative flow, so far as
we can tell.

The same point applies to other conservation laws:
-- An electron is a tangible, material thing.
++ The notion of electrical charge is an abstraction.
-- The number of electrons is not conserved.
++ Electrical charge is conserved, exactly, always.

Students can handle abstraction, but it helps to alert them
to what's going on. Start with the conservative flow of water,
then abstract away the water, keeping the idea of conservative
flow. Start with Dennis's blocks, then abstract away the blocks.

========================================

Slight nitpick: It is better to think of F • dx as /one type/
of work. The other types such as pressure d(volume) and
voltage d(charge) are so closely related that any professional
would think of them as conceptually the same, but students are
prone to focusing on the literal definition rather than the concept.

Students *want* definitions. By the time they show up in physics
class, they've been trained for 10+ years that memorizing definitions
verbatim is good, whereas thinking about things is not allowed on
school grounds. They desperately need to learn the following idea:
/Words acquire meaning from how they are used/
not from some pithy legalistic definition.
However, don't expect students to believe that the first eleventeen
times you tell them.

Suggestion: I find it helps to say emphatically and explicitly
that it is more important to understand what energy /does/ rather
than trying to define what energy "is".

"Energy is as energy does."

Similarly, I would not get wrapped up in trying to "define"
work.

Semi-constructive suggestion: I would be tempted to say that
there are many types of work. For now we will focus attention
on F • dx. We can worry about other types of work later.

I call this semi-constructive, because it makes me feel
better, even though I have no expectation that students
will remember that I said it. Caveats like that are
more important in written documents than in conversation.

=====================================================

More importantly:

I consider it super-important for students to be able to
/reconcile/ new ideas with stuff they already know. This is
central to any form of critical thinking.

Therefore, it is important to explain to students that there
are two different definitions of energy ... two different
/technical/ definitions, not counting innumerable non-technical
and/or metaphorical usages.

The energy that folks worry about at the Department of Energy
is *not* the physics energy. The "DoE energy" is what a
physicist would call the "available" energy or "useful"
energy. This is an important concept, but it is *not* the
same as the physics energy.

In particular, when somebody says "please conserve energy by
turning off unused lights" they are using a different notion
of energy -- and a different notion of conservation -- than
the ones we will be using in this class.

The two definitions of energy are similar enough to be confusing,
yet different enough to get you into trouble. Figuring out
which is which is not always easy. I apologize, dear student,
for sticking you with this obnoxious burden, but there's no
way around it. Almost everything you have heard about energy
up to this point, in school and elsewhere, is probably referring
to the "available" energy. In this class, however, we will
focus attention on the real, total, honest-to-goodness physics
energy.

One thing's for sure: Understanding the "available" energy in
terms of the physics energy is a whole lot easier than vice
versa.



On 10/29/2013 10:49 AM, Richard Tarara wrote:

The Feynman 'Dennis the Menace' story is useful at this level (and beyond),

Yes indeed.

The story of Dennis and the blocks can be found at
http://www.feynmanlectures.caltech.edu/I_04.html#Ch4-S1

More generally, all of Feynman volume I is online, free for all.
http://www.feynmanlectures.caltech.edu/