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Re: [Phys-L] proportional reasoning, scaling laws, et cetera

I can't imagine anyone (except for a few cranky professors) thinking that the mass of the car has magically doubled. Most reasonable people would realize that saying the "mass of the car doubled" is just a shorthand for comparing two situations - one with a car of original mass and one with a car of twice the mass - all other things being equal. The part that is not real world is the assumption that the coefficient of friction will remain the same - not the doubling of the car's mass.

I find that these "what-if" questions using simple proportional reasoning are great for probing if the students are really understanding the material well enough to make predictions on their own. If they cannot respond to a "What if I make ______ twice as big" type question, it may be because they can't do proportional reasoning, but it's more likely to be due to their not understanding the physics.

Bob at PC

________________________________________
From: phys-l-bounces@mail.phys-l.org [phys-l-bounces@mail.phys-l.org] on behalf of Brian McInnes [bmcinnes@pnc.com.au]
Sent: Wednesday, May 16, 2012 6:24 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] proportional reasoning, scaling laws, et cetera

Bill Nettles wrote

Instead of "the mass of the car doubles" we could say 2 cars, one
with twice the mass of the other, etc.

The situation described is a car travelling around a circular track.
In the original formulation its mass magically doubles; your
alternative replaces the car by two cars but that surely in a
different problem or, rather, the original problem done twice.

You say it's a matter of discerning what is important not in solving a
problem. I say that it is important that the problems we present to
the students are grounded in the real world where momenta, kinetic
energies, masses and track radii don't change by magic. Problems in
physics should be real problems and not mathematical manipulations.
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