Re: ENERGY BEFORE Q

[Bob Sciamanda <trebor@VELOCITY.NET>]

Ludwig,
You could avoid the concepts of force and work by introducing a Lagrangian
approach - which you pull out of the air as primitive :-)    Even here
though, the concepts of generalized forces/work are required in the
general case.

Call it what you will, the space integral of the Newtonian force is the
genesis of the mechanical energy concept.  To avoid work (by any name) is
to avoid force and the Newtonian model, and begin anew with some abstract
energy concept (or Lagrangian or Hamiltonian) which hangs in the air as
primitive.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Ludwik Kowalski" <kowalskiL@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, October 12, 2001 4:03 PM
Subject: Re: ENERGY BEFORE Q


> I agree with Bob (see below) that the impulse-momentum
> theorem, and the conservation of p, may help prepare
> students for dealing with the idea of conservation of another
> quantity E=KE+PEgrv+PEspr, in the idealized world of
> two conservative forces.
>
> But can this theorem be used to show (without leaning on the
> concept of work) that PEspr=0.5*k*x^2? I was not able to do
> so through simple algebraic manipulations. Can somebody
> show how to prove that PEspr=0.5*k*x^2?
>
> We all know how simple the proof is when the idea "PEspr is
> the work required to compress the spring" is used together with
> the experimental force law (Hooke). Work is the average F,
> which is k*x/2, times the distance, x. Thus, PEspr=0.5*k*x^2.
> Without work the proof seems to be more difficult. If we agree
> on this then we have a good argument against the "do not lean
> on the concept of work" suggestion.
> Ludwik Kowalski
>
> Bob Sciamanda wrote:
>
> > My approach to much of this has been be-labored in past incarnations
> > of this thread.  Let me this time add that an approach which I have
often
> > (fruitfully) taken is to immediately follow Newton's laws with the
> > impulse-momentum theorem and the consequent conservation of linear
> > momentum  (this is "naturally" motivated by the students' queries
about
> > N3).
> > After this exploration of the implications of the TIME integral of
F=ma,
> > it can be made quite "natural" to investigate the SPACE integral of
N2.
> > Thence to the work-energy theorem, conservative forces . . . etc.
> >
> > My motivation is to lift as little as possible "out of the air", but
to
> > rather explore in a somewhat "natural" manner.  But at the same time,
> > all of this is preceded by the admission that our intuition is not
really
> > this clever . . . we are using the hindsight provided by the giants
> > upon whose shoulders we teeter.