Re: ENERGY BEFORE Q

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

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.