[Phys-L] Re: Energy is primary and fundamental? (was RE: First Day Activities or Demos)

[jsd at AV8N.COM (John Denker)]

Dan Crowe wrote:
> Some physicists advocate starting a first course in physics at the high
> school level with energy and energy conservation, ....
>
> How do you define energy without reference to force or work?

1) As a starting point, give an example of energy, namely
        m g h

[The idea of using this as "the" archetypal energy goes back
to at least Boltzmann (1898) if not earlier ... I'm not a
historian.]

Conceptually and operationally, m is based on an arbitrary
artifact (the standard kg).  These two objects over here are
a half kg apiece, because when bolted together they act just
the same as the 1 kg object, as we can verify using the mgh
energy of an equal-arm balance or pulley.  The rule is, mass
is additive when we combine objects (neglecting binding energy
divided by c^2, which is truly negligible in this context).

In more detail, my take on how to define mass:
  http://www.av8n.com/physics/mass.htm
and how to define energy:
   http://www.av8n.com/physics/thermo-laws.htm#sec-energy

I assume the kids have enough of an intuitive notion of what
distance is that I don't need to make too much of a fuss
about the operational meaning of h.  Mumble something about
rulers.  Three one-foot rulers add up to one yardstick in
much the same way as the two half-kg objects added up to
one one-kg object.

For first-day purposes, g is just some constant of proportionality.
It is constant to a sufficient approximation over classroom length
scales and time scales.

2) Less obviously but almost as importantly for the swinging-
ball demo, there is kinetic energy.
At the very least, you need to sketch a graph of KE versus
velocity, and make the point that KE is at its minimum
when v is zero.  For the purposes of the swinging ball demo,
you don't need to quantify KE (other than zero KE), so you
don't need to quantify v (so long as you can recognize v=0).

3) Later you can quantify KE.  This requires being able to
quantify velocity.  Since we can already quantify distance,
it suffices to quantify time (using a stopwatch).

At this point you can play a theory game.  The aforementioned
constant g has dimensions of acceleration, and by Einstein's
equivalence principle it is indistinguishable from an
acceleration, so you can theorize about how long it takes a
mass to fall a distance h, how much velocity it picks up (due
to acceleration) and how much KE it picks up (in accordance
with conservation of energy).  That is, you do not necessarily
need to impose .5 m v^2 by fiat, or get it empirically, because
if you believe in dimensional analysis and/or the equivalence
principle, you can predict it for free (and then check it
empirically).

4) Moving right along, the next step is to quantify Hookean
spring energy, .5 k x^2.  I would approach this empirically;
it is, after all, not a deep law of nature, just an approximation.

5a) You can go quite far down this road, including the formula
for the period of a pendulum as a function of length (in the
small-angle limit) ... just using energy and a little bit of
geometry.

5b) Ditto for the period of a mass on a spring.  Insert story
about John Harrison and the technical, commercial, and
geopolitical importance of chronometers.

Insert tangent about longitude at sea being gauge-invariant
and time being gauge invariant ... but if you can break one
invariance (using a chronometer) you break the other for
free.  At this point 90% of the students will have no idea
what this tangent is about, but that's OK.  Tell 'em it's OK
to have questions that cannot be answered until later.  They're
in good company;  just recently figured out the answer to some
questions that had been bugging me since high school.  Literally.
And even better company:
   http://www.av8n.com/physics/pierre-puzzle.htm

I emphasize that you can get this far without mentioning force.
In items (3) and (5) we used acceleration without any need for
force.

========

It may come as no surprise that when I introduce force, I talk
a lot about momentum.  Force is momentum per unit time.  Newton's
third law is equivalent to conservation of momentum.

Momentum is right next to energy on the list of primary and fundamental
things.

I haven't got time to go into details right now ... I need to go
have some fun in the lab ... but on many, many occasions I've
walked into a room where smart people were hopelessly confused
by this-or-that force-balance problem.  Then I suggest that they
reformulate it as a momentum-flow problem and a few minutes later
the whole problem has gone away.