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The concept of potential energy.



Dear friends:

Some days ago, just in the middle of a posting, Ludwik
Kowalski asked "can this theorem be used (WITHOUT LEANING ON THE
CONCEPT OF WORK) that the potential energy ( of a spring ) is
0.5 * k * x^2 ? "

My first impulse was to answer simply NO, but trying
to be more useful, I added a few comments. Judging from the reactions
to my posting I feel the need to add some more lines.

1) I was trying to help to the understanding of a concept,
NOT TO ADVICE YOU OR ANY OTHERS about how to teach it. This is simply
because I do not know your students, nor the level of the course you are
aiming to, nor the amount of time you have at your disposal, nor etc.

2) How to teach ? I am sure you have many good examples
in your own library. To the many times cited Feynman and Aarons, let
me add Eric M. Rogers. His book "Physics for the the Inquiring Mind"
is a treasure that every physics teacher should have close by. In it
one can find MANY new ideas for teaching many topics. Energy before
work? He has it. How to teach addition of vectors? He has it. How
to teach relativity? He has it. What is a good experiment? He has
it. Feynman defines "potential energy as a function that gives
as the work done ... etc." (It is this close association between
energy and work that prompted my reply to Ludwik).

3) For many years, curricula have been organized in a
purely logical way. Many of them start with mechanics, under the
impresion that "mechanis is easy" and that "mechanics is the birth
place" of many fundamental concepts, like "energy". This may be a
good way to organize a treatise, but certainly it is not the best
way to start a conversation with children. Rogers begin by talking
about the amount of fuels we need to acomplish several tasks, PSSC
starts with optics, and so on.


4) In a latter posting, I found "you define your
concepts when you introduce them. Right?"
I certainly did not define "time"
the first time I lectured about kinematics. This may
degenerate into another discussion topic, but if it does, let's
try to be specific when our opinions are about how to teach and
when they constitute only our epistemological rumblings.

Dario Moreno.