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Force or acceleration first (was The sign of g)



The discussion of "g" seems to me to be a bit like the chicken & egg
question. There are two intertwined ideas that can't really be separated.
You either have to say "you will understand acceleration better after you
understand force" or " you will understand force better after you
understand acceleration".

Several people have argued that you need forces before it makes sense to
discuss g (or even a), but I don't agree. Perhaps its because I'm an
experimentalist, but I definitely see theories following from experiments.
In this case, the experiment is that I can drop 100 different objects,
measure x vs t, calculate a, and find that (within limits) all of them have
an acceleration downward of 9.8 m/s^2. I don't need to know anything about
"force" or "Second Law" or "gravity" to notice this pattern in nature.

I'm starting to see this as a theoretician vs experimentalist perspective
on the question. So instead of the biological question "Which came first,
the chicken or the egg?" we might ask "Which came first, the experiment or
the theory?"

My own answers are
* Two birds a lot like chickens mated and produced an egg. That egg
produced a bird that was enough different than either one that it was a new
species, that has come to be called a chicken. Thus the egg came first by
1/2 a generation. However, since that occurred millions of generations
ago, the half generation difference is of little practical concern. Eggs
lead to chickens and chickens lead to eggs. All modern chickens and modern
eggs are so completely intertwined that it makes little sense to talk about
one without the other.
* You need at least some observations of patterns before you think to form
a theory. However, we have become so accustomed to expecting patterns that
often we will make up theories because they are analogous to previous
theories, or just because they are mathematically elegant. Theories
suggest experiments, and experiments suggest theories. The two are so
completely intertwined that it makes little sense to talk about one without
the other.


For the case of g, the two perspectives might be summarized as follows:

Experimentalist: "Falling things are worth looking at, so we measured
several things falling, and all had a = 9.8 m/s^2. Taking into account N2,
let's try to come up with a theory of gravity that would cause such an
acceleration. WOW! That means F = mg and we have a simple explanation that
agrees with the data."

Theoretician: "Let's assume that gravity causes a force of a very simple
form, say F/m = g. Then according to N2, things should accelerate
downward uniformly. Let's try to confirm that. WOW! Everything we check
does fall with a = 9.8 m/s^2, so our original conjecture must have been
correct, and g = 9.8 m/s^2"

We measure things because we hope to find patterns. Or we propose patterns
and hope that measurements fit our predictions. Both are common and
acceptable ways for science to proceed. So it is perfectly reasonable that
g can be an experimental result to which we try to fit a theory of gravity,
or g can be a theoretical prediction that needs testing.

--------------------------------

There is a second related, but different, question - will the students
understand better with one approach over the other? The more common
textbook approach seems to be the "Experimentalist" approach - present an
experimental result that g = 9.8 m/s^2 and seek the theory to explain.
I've said about enough and I'm running out of free time, so I'll stop and
see what you all think about these ramblings.


Tim Folkerts


Department of Physics
Fort Hays State University
Hays, KS 67601
785-628-4501