Re: definition of energy (without work?)

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

On 26 Oct 1999 21:59:45 -0500 John Denker wrote:

> Ludwik Kowalski wrote:
> > A definition does not have to be perfect to be useful. You can say, in
> > an elementary school, that "flowers and animals are living things" and
> > then proceed with "what do they have in common?", etc. Yes, there
> > are microorganisms, and dead flowers, etc. But this is for later.
>
> I agree!  Well said!
>
> Chuck Britton wrote:
>
> > Energy is too important to be limited by a definition.
> > As are ALL of the most important words in ANY field of study.
>
> I agree that understanding energy is important, and I agree that our
> understanding must not rest on a short, cute definition.  But it is an
> overreaction to abandon definitions altogether.
>
> Previously I argued that the cutesie definition of energy as "the ability
> to do work" was just plain wrong on technical grounds.  Now I would
> like to argue that it is wrong on broad pedagogical grounds, to wit:
>
> As the saying goes, "Learning proceeds from the known to the unknown."
>
> Alas, anybody who doesn't know the definition of _energy_ is exceedingly
> unlikely to know a definition of _work_ that is adequate to give meaning to

> the cutesie definition.
>
> ===================
>
> Here is how I generally introduce the concept of energy:
>
> Energy has many forms.  Examples include
> * the kinetic energy of an object, which is
>    ordinarily proportional to its mass and to the square of its velocity;
> * the gravitational potential energy of an object,
>    which is ordinarily proportional to its mass and to its altitude;
> * the mechanical potential energy of a spring;
> * the chemical energy in a fuel;
> * electromagnetic energy;
> * nuclear energy;
> * heat;
> * et cetera. ....

Sequences in physics teaching, such as mechanics before
thermo, or work before energy, were not influenced by "the
width of a Horse's ass" (see last Leigh's message). They
evolved by attempts of teachers to promote learning. The
order in which things were historically discovered and
explained had strong influences, it corresponds to
something "real and natural" in learning humans.

As a learning and teaching human I prefer to introduce new
concepts as simple products (area, work, momentum), or
as simple ratios (speed, density, electric field) of previously
defined quantities. I would be less comfortable with axiomatic
introduction of 0.5*k*x^2 or 0.5*m*v^2 or mass times
acceleration times distance. The F*d is easier to grasp than
the m*g*d.

Energy is a basic concept in physics but I do not know
how to introduce it logically without work. I do not want to
say "just accept this formula because I say so", and because
"it will turn out to be very useful". 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. Those who discover things do not know
how useful the discoveries will be. Keeping things as simple
as possible is important to me.

"Ability to do work" is not a working definition. It is an
attempt to generalize. Working definitions (based on
mathematical derivations) come separately for each form
of energy, one after another. 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, (or the v^2
instead of v^4), without first introducing the concept of
work and its unit? Work is the essential link between the
force-based approaches and the energy-based approaches.
I am still waiting for the promised essays on how to
introduce energy without work to novices.
Ludwik Kowalski