Re: definition of energy (without work?)

[John Denker <jsd@MONMOUTH.COM>]

At 11:08 AM 10/27/99 -0400, Ludwik Kowalski wrote:
> Sequences in physics teaching, such as mechanics before
> thermo, or work before energy, ...
> evolved by attempts of teachers to promote learning.

True, with allowances for imperfections...

> The
> order in which things were historically discovered and
> explained had strong influences,

Definite influences, but not always helpful influences.

> it corresponds to
> something "real and natural" in learning humans.

Thomas Kuhn and others would disagree with that.  If you look at the actual
history of science, it is full of false starts and blind alleys.  We would
do students a tremendous disservice to reproduce all of that.  Often it is
better to cut to the chase.

> Energy is a basic concept in physics

We agree!

> but I do not know
> how to introduce it logically without work.

I'm surprised.

To me, energy is primary.  Energy is fundamental.  Work is a particular
type of energy conversion (not even the general case).

> I do not want to
> say "just accept this formula because I say so", and because
> "it will turn out to be very useful".

That is a noble objective.

It may help to de-personalize it.  We should not ask the students to take
an oath of allegiance to you, or to me, or to the textbook.

But we can ask them to trust (within limits) the experiments.  We can say
"the following expression for energy is well-attested by experiments."

> Ideally, I prefer the
> usefulness to be visible today, not tomorrow. Usefulness
> in the future may guide me but I do not want to lean on it
> as an argument.

Fine.

> Those who discover things do not know
> how useful the discoveries will be. Keeping things as simple
> as possible is important to me.

Simplicity is another noble objective.

But this objective sometimes partially conficts with the previous noble
objective (i.e. avoiding "just accept this" arguments).

Most of the time when children ask "what makes the hallway light come on"
they do *not* want a physics explanation about electromagnetic induction in
generators at the power plant and blah and blah and blah.  Usually they
want an answer of the form "there's a switch just around the corner by the
side door."  Usually this is _accepted_ without challenge.  If there is a
challenge, the wise comeback is not "accept it because I said so";  the
wise comeback is "let's do the experiment".  Trying to prove it from
physics and logical first principles would be a disaster.

> "Ability to do work" is not a working definition. It is an
> attempt to generalize.

To generalize what?  I don't get it.  It seems like energy is the general
case, and work is the less-general case.

> Just focus on the way in which
> the KE is derived as a useful quantity to grasp my point.
> How would I justify the 0.5 factor instead of 1 ...
> without first introducing the concept of
> work and its unit?

A brilliant question!

But before you pounce on the obvious answer, check whether you are prepared
to explain why
   E = .5 p v           for ordinary objects
while
   E =    p v           for light (v = c).

If a child really wants to know, I'm happy to explain why that .5 appears
where it does.  It is profound and beautiful.  It cuts to the core of our
understanding of how the universe is put together.  But it is not simple,
so I ask them to be sure they really want to know.  I would rather tell
them "we have excellent experimental evidence that the .5 belongs there,
good enough for present purposes" -- rather than telling them some "just so
story" analogous to Kipling's yarn about how the leopard got his spots.

> Work is the essential link between the
> force-based approaches and the energy-based approaches.

I still don't see it.

> I am still waiting for the promised essays on how to
> introduce energy without work to novices.

Why wait?  Why not grab _The Feynman Lectures on Physics_ and read volume I
chapter 4.

Feynman is quite up-front about the appeal to experiment;  see for example
the middle paragraph on page 4-4.


______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com