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Re: CAUSATION IN PHYSICS



At 11:10 AM 10/15/00 -0400, Tom McDonald wrote:
... better but lazier students who were firmly convinced that since F =
ma, they could describe force as the product of mass and acceleration and
did so on a test.

Question: Describe what a force is.

Answer: mass times acceleration.

Oh, great. Now we can have a discussion of what "is" is.

I agree with Tom that the student gave a wise-guy answer. IMHO it is
roughly equivalent to the following:
Question: Describe what the Venus de Milo is.
Answer: A piece of marble.

In some narrow, wise-guy sense, the Venus de Milo "is" a piece of
marble. But the student should have known the unwritten rules of the
test: when asked for a description, give an interesting and/or useful
description, not a trivial or tautological description.

The student needs to understand that F=ma is _not_ a tautology -- and he
needs to communicate that understanding on the test.

There are many things that a force "is".
-- A force "is" mass*acceleration, but also
-- a force "is" (d/dt) momentum,
-- a force "is" pressure*area,
-- a force "is" energy/distance,
.. et cetera.
To the extent that the student described _one_ of the things a force "is",
he should get _partial_ credit.

My argument was [...]
F and ma were two different concepts.

Exactly so. There is an operational definition of force which is separate
from the operational definition of acceleration.

that equality did not imply identity,

That's not a particularly good way to express the key idea.

Perhaps a better approach would be to argue (as Tom says below) that F and
ma are not _conceptually_ identical, while conceding that they are
_numerically_ identical (within the level of approximation appropriate for
this course).

In particular, the key conceptual point is that F _might not_ be exactly
equal to ma. It might be only an approximation. Physics is full of
approximations. We definitely could carry out experiments to measure how
accurately F approximates ma.

And, yes, (cringe) I argued that force causes acceleration.

Not the correct argument.

My students would argue back that the symbol = means *the same*, and we
would go around and around.

The student is 100% right about that part of the argument.

Perhaps after the recent discussion I might be more inclined to say that
force is *associated with* acceleration of a mass, but surely no one has
said or is thinking that they are conceptually identical. Right?

Right!