force is no more real then energy, so you can't
privilege it on that basis.
Exactly.
Depending on what we mean by "real", we could say that both
are real, or neither.
A related question asks whether they are "abstract" or not.
The answer depends on context. There are lots of situations
where ideas move back and forth on the abstract-o-meter, i.e.
ideas can become more abstract or less abstract.
For instance: suppose I put two paving-blocks on the table.
Those pavers are 100% real and 100% concrete. (Literally,
they're made of concrete :-). Now, I could talk about the
properties of those two particular blocks, but it wouldn't
be very interesting, because you probably aren't going to
see those particular blocks ever again. It would be much
more interesting if I could talk about pavers in general.
But ... there is a tremendous leap from "these two pavers"
to "pavers in general"!!!! The latter is an abstraction.
Formally, it is an equivalence class.
Yes, talking about "energy in general" requires a certain
level of abstraction. But the same can be said of force
in general ... or pavers in general.
I really don't want to hear about "studies that show XX% of
college freshman are incapable of dealing with abstractions"
and therefore we should teach this-or-that first and something
else not at all. That's baloney.
-- Firstly, the degree of abstraction we are dealing with here
is within the reach of most four-year-olds. They learn from the
"See-N-Say" (tm) that the cow goes moo. It doesn't particularly
bother them that this is a statement about the equivalence class
of all cows.
-- Secondly, comparing energy to force, there is no significant
difference in the degree of abstraction. Some kids are familiar
with one and not the other ... or both or neither. Some teachers
are particularly fond of one and not the other ... or both or
neither.
As a teacher and as a citizen, I think that if kids escape from
school without knowing about energy, that's bad. And on the
other side of the same coin, if they escape from school without
knowing about force and acceleration, that's bad, too.
Here are some sample applications of these ideas:
1) If you want to analyze how an airplane turns (in particular,
assume a constant airspeed, and assume an ordinary level turn,
i.e. a turn in a horizontal plane) then you need to think about
force and acceleration. Energy is a secondary consideration.
(You might think energy would be a constant of the motion and
therefore completely uninteresting, but that's not quite right,
especially for steeply-banked turns.)
2a) If you want to analyze climbs and descents, you need to
think about energy. Sure, there are forces involved, but in
my experience, the more pilots think about the forces during
climb and descent, the more confused they get.
2b) On the playground swingset, it takes you N cycles to build
up a large amplitude. This is most easily understood in terms
of energy. The driving force is more-or-less the same each cycle;
it is the energy that accumulates.
I reckon this thread started because people wondered what I meant
when I wrote "energy is primary and fundamental". Let me clarify
that a bit: Energy is high on the list of things that are primary
and fundamental, but it is certainly not the only item on the list.
(It is not even at the top, as discussed below.)
M.E. pointed out that it is important for people (including students
and citizens in general) to have some understanding of the notion
of "rate of change" and even "rate of change of a rate of change".
I entirely agree with that. But I would hasten to add that those
are not the only items on the list of important notions.
I'm not saying that force is unimportant. I am saying:
-- Minor point: Energy needs more emphasis than it usually
gets.
-- Major point: The great conservation laws need more
emphasis than they usually get.
Let's be clear: My major point is not necessarily about energy.
You could take away energy and still make most of the point. The
point is about conservation. Conservation is a very big deal.
Newton's third law is tantamount to conservation of momentum.
That's important, and needs to be emphasized. The task that
chemists call "balancing the reaction equation" is mostly just an
exercise in applying 92 different conservation laws simultaneously
(at least in ordinary not-too-tricky cases). And then there's
paraconservation of entropy.
I don't see any reason to argue that energy is more important than
momentum. But it seems clear that conservation in general is more
important than energy or momentum separately, or any other conserved
quantity separately.
Is "conservation" an abstraction? Sure it is. So what? Most
people on this list teach at the high school level or higher.
According to the classical Piaget story, kids are supposed to
"get" the various types of conservation at various ages from 6
to 11. (Of course there is considerable kid-to-kid variation.) http://www.learningandteaching.info/learning/piaget.htm
If a high-school kid can't handle conservation, that's not a
problem the physics teacher can solve by rejiggering the
physics curriculum; it's a problem for the special-ed teacher
(and/or the clinical psychologist).
=================
As a not-very-elementary application of conservation laws, to
illustrate the power thereof, consider the following: at the
center of a large region of air, we have a balloon. Using
some complex arrangement of clockworks, we use the balloon
to launch a spherically-symmetric outgoing sound wave. The
details are arranged so that at time t = t1, the wave has a
square profile, i.e. it looks like this:
where "B" marks the position of the balloon. The curve is
a graph of pressure versus position. Assume the small-amplitude
limit, so everything is linear.
Prove that this wave cannot maintain its shape. Specifically,
show that the wavefunction cannot be written as
phi(r, t) = f(r - c t)
where f() is a function of one variable ... even though the
system is linear, and plane waves in the same medium can perfectly
well be written as
Phi(x, t) = F(x - c t)
That is to say, prove that the wave equation in polar coordinates
is necessarily dispersive, event though the corresponding wave equation
in rectangular coordinates is not dispersive.
Sketch roughly what the wave must look like at some time t >> t1.
HUGE HINT: There are two conservation laws in play here: conservation
of energy, and conservation of air molecules.
HUGE HINT: Scaling laws are very high on my list of important ideas,
right up there with the conservation laws. Derive a scaling law for
amplitude-versus-r using conservation of energy, then derive another
scaling law for the same thing (amplitude-versus-r) using conservation
of air. Two different scaling results for the same thing?!? What
does that tell you?
Note that energy is a big deal in this problem, but it is by no
means the only big deal.
This is obviously not a "September" activity, i.e. not in the same
category as the "swinging bowling-ball + face" activity. This is
more of a "May" activity, bringing together a whole bunch of ideas
about conservation, scaling, waves, energy, et cetera. I mention
it now, because having a goal for where I want to be in May helps
me figure out what I want to do between now and then.