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The concept of potential energy.



On Fri, 12 Oct 2001, Ludwik Kowalski wrote:


But can this theorem (of conservation of energy) be used to show
(without leaning on the
concept of work) that PEspr=0.5*k*x^2?


Dear Ludwik:

I think that most of our discussions would vanish if we take some time
to agree on a definition of the terms we use.

For example, when somebody talks about "potential energy", what comes
to my mind is the definition of potential energy.

(To avoid subscripts, allow me to write U instead of PE.)

What is U, then? I was thaught that

"The so called potential energy, is a scalar function U(x,y,z)
that has the following property: grad U = - force."

Of course you may write this in not so compact but more
clear fashion.

If we agree that this is a good definition of potencial
energy, then it follows that

Delta W = - grad U dot ds

As you see, it will be very difficult to isolate the
analysis of the notion of potential energy and the notion of work.

Dario Moreno


P.S. I agree with Sciamanda's sugestion of studying "the effect
of a force summed over time" before "the effect of a
force summed over distance". That is the sequence used in
many countries in Europe ... and in Mexico.