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Re: [Phys-l] energy is well defined.

I'm new to the Phys-L list and I'm glad that one of the first topics I've
encountered is this one. I've finally learned that I've taught a large
number of students over the years some very wrong ideas about work and
energy. (I haven't gotten to the point of doing it right yet.)

What woke me up (unfortunately about 20 years after he wrote it!) was an AJP
paper (see below) by Bruce Sherwood explaining how badly one will foul up by
misapplying work and energy relations that 'work' for point particles to
extended bodies like cars and people.

Now I've found a more recent (but still almost ten years old) paper by
Arnold Arons that goes over the same sorts of snags and also shows how to do
things right. In the introduction he quotes Feynman and addresses whether
energy is some sort of 'stuff' or not --

[Arons--]
"There are basic epistemological insights that are also of fundamental
importance. It is worth quoting at this point what Feynman says so lucidly
and compellingly in his introduction of energy concepts:2

[Feynman--]
'There is a fact, or if you wish, a law governing all natural phenomena that
are known to date. There is no known exception to this law‹it is exact as
far as we know. The law is called the conservation of energy. It states that
there is a certain quantity, which we call energy, that does not change in
the manifold changes which nature undergoes. That is a most abstract idea,
because it is a mathematical principle; it says that there is a numerical
quantity which does not change when something happens. It is not a
description of a mechanism, or anything concrete; it is just a strange fact
that we can calculate some number and when we finish watching nature go
through her tricks and calculate the number again, it is the same.'

[Arons--]
"There are several crucial aspects of learning and understanding embedded in
this beautiful but cryptic statement. Energy is not concrete; it is not a
material substance; it is given meaning through the calculation of numbers.
(Many students coming out of introductory physics courses view both momentum
and energy as though they were substances‹something like the imponderable
fluids of phlogiston, caloric, and electric virtue of 18th century science.)
Furthermore, we must learn or discover how to define and calculate the
numbers that turn out to be conserved; the calculations are not to be
derived and are not immediately obvious on observation of relevant
phenomena. Genuine understanding on the part of students involves
assimilation of such insights, not just manipulating the formulas in
end-of-chapter examples."


It's worth repeating his statement, "Energy is *not* concrete; it is *not* a
material substance; it is given meaning through the calculation of numbers."
[The original had italics that don't come through in the cutting and
pasting.] I think this backs up the idea of energy being very much like
money that has already been mentioned in this discussion thread.

I encourage everyone to read Arons and Sherwood -- they both have several
very enlightening examples that will make you start thinking differently.

Steve Highland
Duluth MN

------------
Development of energy concepts in introductory physics courses
American Journal of Physics, Vol. 67, No. 12, pp. 1063­1067, December 1999

Arnold B. Arons
Department of Physics, University of Washington, Seattle, Washington 98195
Received: 28 January 1999; accepted: 22 April 1999

The work-energy theorem, derived from Newton's second law, applies to the
displacement of a particle or the center of mass of an extended body treated
as a particle. Because work, as a quantity of energy transferred in
accordance with the First Law of Thermodynamics, cannot be calculated in
general as an applied force times the displacement of center of mass, the
work-energy theorem is not a valid statement about energy transformations
when work is done against a frictional force or actions on or by deformable
bodies. To use work in conservation of energy calculations, work must be
calculated as the sum of the products of forces and their corresponding
displacements at locations where the forces are applied at the periphery of
the system under consideration. Failure to make this conceptual distinction
results in various errors and misleading statements widely prevalent in
textbooks, thus reinforcing confusion about energy transformations
associated with the action in everyday experience of zero-work forces such
as those present in walking, running, jumping, or accelerating a car.
Without a thermodynamically valid definition of work, it is also impossible
to give a correct description of the connection between mechanical and
thermal energy changes and of dissipative effects. The situation can be
simply corrected and student understanding of the energy concepts greatly
enhanced by introducing and using the concept of internal energy, that is,
articulating the First Law of Thermodynamics in a simple, phenomenological
form without unnecessary mathematical encumbrances. © 1999 American
Association of Physics Teachers. [S0002-9505(99)00312-8]

-----


Pseudowork and real work
American Journal of Physics -- July 1983 -- Volume 51, Issue 7, pp. 597-602

Bruce Arne Sherwood
Computer-based Education Research Laboratory, Department of Physics and
Department of Linguistics, University of Illinois at Urbana­Champaign, 252
Eng. Res. Lab., 103 S. Mathews, Urbana, Illinois 61801

(Received 7 January 1982; accepted 28 July 1982)

In teaching mechanics, we should more clearly distinguish between an
integral of Newton's second law and the energy equation. This leads to
greater clarity in the notions of system, work, and energy. A reorientation
of the treatment of work and energy would not only provide benefits in the
mechanics course but would also produce better connections between the
mechanics and thermodynamics courses. ©1983 American Association of Physics
Teachers

Here are the couple of "puzzles" he starts out with--

"When a car accelerates from rest, it appears that the kinetic energy is
equal to the work done by the frictional force exerted by the road, acting
through the displacement of the car. Yet the frictional force does no work,
and the car's kinetic energy comes from the burning of gasoline, not from
the road."
"When a block slides down an incline with friction, it is often said that
the kinetic energy is equal to the work done by gravity minus the work done
by the frictional force. Yet one knows that the block gets warmer, and
there is the uneasy feeling that this increase in thermal energy ought to
appear explicitly in the work-energy equation."






Well Ken,

I have given a fairly concise definition to my class and I would like to
see if it stands up to the listserv.

Energy - a conserved substance like quantity that can be transferred
from one body to another or transformed from one form to another.

That is the basic definition I use to get the students thinking about it
as a conserved quantity. It also allows for the transfer of the energy
from body to body and from form to form. We also talk about the forms
objects store energy in. A moving object stores Kinetic energy. This is
to show that energy is constantly being shifted around from one form or
body to another. Let me know what you think.

Leon

Ken Fox wrote:
I don't know if anyone else has read John's notes on Energy. They are very
interesting to me and quickly are over my head. ( 2 hot potatoes can do more
work as long as we keep the cold one as well, I think.)

I want to teach energy to my high school students and would love a
definition and was excited to be told that it is well defined. Then I read
the part of the notes named "Definition of Energy" and several sentences
jumped out at me:
1."It is more important to *understand* energy than to *define* energy. We
can and will define it, but the definition is not super-simple nor
super-concise. The concept of energy is so fundamental that there is no
point in looking for a concise definition in terms of anything more
fundamental."
2."Energy is somewhat abstract. There is no getting around that. You just
have to get used to it ­ by accumulating experience, seeing how energy
behaves in various situations. As abstractions go, energy is one of the
easiest to understand, because it is so precise and well-behaved."
3."The most important thing about energy is its role in the law of
conservation of energy,...."

I am still looking for the well defined statement of energy, suitable for my
neophytes, but I feel better that what have done in my classes for 40 years
falls into these 3 statements.

Ken Fox



On Feb 16, 2008 8:53 AM, John Denker <jsd@av8n.com> wrote:


In the context of
http://www.av8n.com/physics/energy-counterexample.htm

On 02/16/2008 06:51 AM, carmelo@pacific.net.sg wrote:


How about heat or thermal energy generated when sands are continuously
falling at constant rate on a moving conveyor belt?

Well, how about it?


Electromagnetic
energy generated by friction to what extent measurable?

What about it?


Zero-point energy measurable?

Yes, it is measurable. What's the point?


Energy is *well* defined as "capacity to perform work" or "ability to
perform work"?

No, that's not a good definition, for reasons explained in detail at
http://www.av8n.com/physics/thermo-laws.htm#sec-workability

Note that the existence of a bad definition does not disprove
the existence of a good definition.


It is, of course, better for the students to learn from something
concrete, then to abstract...

Maybe that's why Feynman started with an exceedingly concrete
example of conservation (Dennis and the blocks) before
abstracting away the concreteness.

Maybe that's why
http://www.av8n.com/physics/thermo-laws.htm#sec-energy
also starts with a series of more-or-less concrete examples
before abstracting away the concreteness.