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Re: Why work before energy in texts



Hi all-
I've followed bits and snatches of this discussion, which has
stimulated me to go back and look at how some of the old masters dealt
with this issue. In other words, I peeked in Sommerfeld's <Mechanics>.
Sommerfeld, right off the bat, introduces Newton's laws.
Discussing the second law, he says: "We must now seek to get a clear idea
of the concept of force." After noting that we have an intuitive
qualitative idea, he discusses the use of gravity to measure forces
quantitatively. Then he adds:
The same is true for the concept of force as for all
other physical concepts and names: word definitions have
very little meaning; physically significant definitions
are obtained as soon as wee prescribe a way of measuring
the quantity in question.

After discussing the third law he turns to a new idea, saying, "Having
introduced the concept of force, we shall at this point introduce that of
work with the definition
dW =<F>.<ds>=FdsCos(<F>,<ds>).
[my notation is "<>" means vector quantity and ( , ) means the angle
between two vectors]

Later, discussing the motion of a mass point, he arrives at energy
as a constant of the motion - that is, as a constant of integration.

So in my opinion, John's <dicta>, below, are excessively intolerant and
represent just one among a variety of credible views about how to teach
this stuff.

Regards,
Jack

On Tue, 16 Oct 2001, John S. Denker wrote:

At 11:07 AM 10/16/01 -0700, kowalskil wrote:
4) In my classes F is first defined loosely as a
measurable push or pull of any kind.

Good. That's the right approach.

This is good enough to solve static equilibrium problems.

That's an understatement. It's much better than that.

Later
Fnet becomes "the cause of an acceleration." Is using
the concept of force also a blunder?

Yes, it's a blunder, for reasons previously discussed in detail and
summarized at
http://www.monmouth.com/~jsd/physics/causation.htm


In going "from
known to unknown" should we teach force before energy,
or the other way around?

Neither.

The question seems to be based on a false premise, namely the notion that
every concept in physics has to be derived from some other concept. Rather
than tackling the energy question directly, let's first discuss F=ma. It
is _not_ true that F is defined in terms of ma. F=ma is _not_ an axiom nor
a tautology. To say it in more positive terms: We have an operational
definition of force. We have an operational definition of mass. We have
an operational definition of acceleration. In Newtonian mechanics, the
equality between F and ma is a law, an approximate law, based on empirical
observations. We can design experiments to test whether F does equal ma to
some greater or lesser degree of accuracy.

Newton's laws of motion are NOT sufficient to derive the law of local
conservation of energy. Any alleged derivation thereof is just plain
wrong, and easily disproved.

Disproof by counterexample: Newton's three laws of motion are consistent
with Newton's law of universal gravitation. Newtonian gravitation does not
uphold local conservation of energy.

Should ALL mechanical problems be solved by energy
approaches because energy is "more basic" than F?

No.

Why not?

Because real physics is not like high-school geometry, where the name of
the game was to deduce everything in the world from four axioms.

I am ready to accept this kind of physics,

I'm not asking you to. When I wrote that "energy is primary and
fundamental" perhaps there was a misunderstanding. To put it in context:

-- Time is primary and fundamental.
-- Length is primary and fundamental;
acceleration is related to length and time.
-- Energy is primary and fundamental.
-- Momentum is also primary and fundamental;
force is intimately related to momentum and time.
-- Mass is primary and fundamental.
-- Electric charge is primary and fundamental.
-- Et cetera.

(Work doesn't even show up on the list.)


--
Franz Kafka's novels and novella's are so Kafkaesque that one has to
wonder at the enormity of coincidence required to have produced a writer
named Kafka to write them.
Greg Nagan from "The Metamorphosis" in
<The 5-MINUTE ILIAD and Other Classics>