Re: definition of energy

[John Denker <jsd@MONMOUTH.COM>]

At 06:36 PM 10/26/99 -0500, 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!

At 01:34 PM 10/26/99 -0400, 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.

The interesting thing about energy is that it cannot be created or
destroyed.  It can often be converted from one form to another, but the
total energy does not change.

What's more, any conversions must take place *locally*.  That is, energy
cannot magically disappear from one region of space and appear in another
region.  If the energy in a region is decreasing, there must be a flow of
energy across the boundary of that region.

======

If necessary I can boil that down about a factor of two, but not much more
without heavy lossage.  Trying to get a useful definition of energy in a
few words ("energy is blah blah blah") is a doomed enterprise.

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