Re: Spring potential energy without Work (sort of)

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

On Monday, October 15, 2001 9:40 PM, RAUBER, JOEL wrote:

> > Is this hand-waving somehow worse than the hand-waving
> > performed to get
> > v_f^2 = v_i^2 + 2 a Delta x?
>
> [snip]
>
> Furthermore, average velocity doesn't require handwaving, algebra and
> geometry alone serve to derive this for constant
> acceleration; at least if
> you believe geometry implies that the midpoint of a linear line is its
> average value, (and don't call that handwaving).  But we're
> getting into the
> realm of taste here, IMO the result is less natural for Delta
> x^2; in the
> sense that I think it requires knowing the desired answer in
> a slightly more
> profound way than the Delta v^2.
>
> I readily admit that formally the arguments are identical.

I know you feel it is a matter of taste but I'm curious as to why
you think the result is less natural for Delta x^2?

> > *[since F = kx, then
> > F_avg*Delta x = k (x_i + x_f)*(x_f - x_i)/2 = 1/2 k Delta (x^2).]
> Good!  We don't need calculus for the linear spring! And I
> suppose this
> answers, perhaps not in pleasing way, Ludwik's question.
>
> Of course, I'll next say, let's consider a non-linear spring, . . .

Are you saying to consider a situation where one cannot use current
methods (i.e., algebra, geometry, graphing, etc.) to determine the
average* force?  Well, of course there must be *some* advantage to
knowing calculus.  :)

* average over space (not time)

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| rcohen@po-box.esu.edu      East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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