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[Phys-L] Re: Newton's Equation - 2 or 3 variables?



Gene Mosca wrote:

F=ma is a two variable equation. Mass is not a variable in this
equation

There are two points of view on this, and I can sympathize with both.

1) The original remark about three-variable equations was made in
the context of Piagetan development. I would say that for some
introductory pedagogical purposes (but not all), in some scenarios
(but not all), it makes sense to emphasize the variability of F
and a, and de-emphasize the variability of m.

BTW, as a minor point: I changed the subject line from "terms"
to "variables". The discussion, all along, has been about
variables. The word "term" has a few rather specific meanings,
none of which is synonymous with "variable".
http://mathworld.wolfram.com/Term.html

2) This list is not restricted to discussing things at the
introductory level. As an issue of principle, m is just as much
of a variable as F or a. Several lines of evidence support this
point:

1) Let's rewrite the law as m=F/a. This version can be used to
determine the hitherto-unknown mass of some object. Surely if
everything on the RHS is considered variable, the LHS must be,
also.

2) Consider the derivation of the Tsiolkovsky rocket quation
http://www.answers.com/topic/tsiolkovsky-rocket-equation
Both the result and the method of derivation are amusing, and
IMHO highly recommended for inclusion in a calc-based physics
course. A crucial part of the excercise is to account for
the changing mass of the rocket.

3) As a truly fundamental conceptual point, it is important to
distinguish _conserved_ from _unchanging_. Conservation means
that the amount of X within a given region cannot change *except*
by flowing across the boundaries of the region. It is a horribly
common mistake for people to say X is conserved when all they
really meant is that X is unchanging.
-- It is perfectly possible to have a quantity that is unchanging,
even though it is not conserved.
-- It is perfeclty possible to have a quantity that is changing,
even though it is conserved.

I find it helpful to visualize these ideas in terms of the continuity
of world lines, as discussed at
http://www.av8n.com/physics/conservative-flow.htm
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