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Dan Crowe wrote:http://www.av8n.com/physics/thermo-laws.htm#sec-energy
in physics at the high
Some physicists advocate starting a first course
school level with energy and energy conservation,....
force or work?
How do you define energy without reference to
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:
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.