Re: [Phys-l] Equations

[Jack Uretsky <jlu@hep.anl.gov>]

Hi all-
	I do do not disagree with anything that Mike says,
although I think that the point may be made more forcefully
by recognizing the fundamental ambiguity embedded in an
equal sign (sometimes resolved by use of an identity symbol).
	"F=ma" states a relationship among three, separately
measurable physical quantities.  It relates three previously
unrelated clases of experiments.
	w = integral(F dot dx) defines a mathematical
quantity, w.  If you have separate way of measuring w (not
assumed here), than this meaning of the equal sign becomes
identical to the first meaning.  In the absence of such a
"separate way", then w has meaning only through the definition
and the equal sign could be replaced by an identity sign.
				Regards,
					Jack

On Thu, 27 Apr 2006, Michael Edmiston wrote:

> I haven't thought about it enough to try to answer John Denker's
> questions, but I admit that in teaching I agree with John Clement.  I
> always write it a = F/m and I tell students that writing it this way
> ought to help them grasp it better than writing F = ma.
>
> Quite a few students who encountered F = ma in high school have told me
> it never made sense to them until they viewed it as a = F/m.  Therefore
> I am convinced that students generally view equations as effect = (some
> function of cause).  If that is the common student way of viewing it, we
> might as well try to capitalize on that.
>
> Along the way I try to show students other ways of viewing equations.
> For example another way to view an equation is (idea or property) =
> (definition).  I view work that way:  w = integral(F dot dr) is the
> definition of work.
>
> I think there are some equations that are more nebulous.  Should the
> work-energy theorem be written as deltaE = w or should it be w = dE.
> Again, from my experience, students seem more receptive to deltaE = w
> and they view it that a change in the energy of something was caused by
> work having been done on that something, or that the something did work
> on something else.  But it is clear a few students debate which is cause
> and which is effect.  Could it be that something naturally changes
> energy and work is the result?  An example where they think this way is
> water naturally flows over a waterfall and spins a turbine.  Here the
> work done on the turbine is the effect and the change in gravitational
> energy of the water was the cause.
>
> Of course there are multiple steps involved in this example and I can
> challenge their thinking by saying that gravity did work (cause) on the
> water giving it kinetic energy (effect) and then the turbine did work on
> the water (cause) reducing its kinetic energy (effect).
>
> Some students never get to this level of seeing physics equations.
> However, if I can get students to discuss whether they are viewing
> physics equations as definitional or as cause/effect; and if
> cause/effect then which side is cause and which side is effect, then I
> think we have arrived at a higher level of appreciation of physics.
> Therefore this discussion of how equations are viewed is very
> worthwhile, especially if we focus on getting students to think about
> what equations might mean rather than nitpicking too much on the deeper
> philosophical issues of cause/effect.
>
>
> Michael D. Edmiston, Ph.D.
> Professor of Physics and Chemistry
> Bluffton University
> Bluffton, OH 45817
> (419)-358-3270
> edmiston@bluffton.edu
>
>
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