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conservation of energy



Here's my take on conservation of energy:

There are various ways of stating the principle of conservation
of energy.

Indeed there are many principles that involve some sort of
conservation of some sort of energy ... which is unsurprising
and indeed completely reasonable, for the following reason:
If you start with a general principle, you can generate a
huge number of corollaries simply by restricting the domain
of validity. Within the appropriate domain, each of these
corollaries is perfectly valid.

When I was 10, I clearly understood the principle of conservation
of pulley-pulling. I had enough rope and enough pulleys to
make block-and-tackle systems with a wide range of mechanical
advantage factors. I knew that if the factor was higher, less
force would be involved in hoisting things, but I would need
to pull a proportionately longer section of rope....... This
is the principle of conservation of energy, restricted to
ropes and restricted to potential (not kinetic) energy only.

To repeat: I like corollaries. Corollaries are good.

But I draw the line when somebody worships some narrow
corollary and tries to pass it off as "the only" general
law. That's unacceptable.

-- As an example of a reasonably general formulation of
the principle of conservation of energy, consider this:
The energy in a region cannot change except by the
flow of energy across the boundary of the region.
Specifically, the decrease in energy in the region
is equal to the flow of energy outward across the
boundary. Since this is a conservative flow, the
flow outward across the boundary of this region
must simultaneously be accounted as a flow inward
to an adjacent region.
For details, see
http://www.av8n.com/physics/conservative-flow.htm
and for an application that illustrates the power of
this way of formulating things, see
http://www.av8n.com/physics/euler-flow.htm
This formulation was recommended by Feynman (remember
Dennis and his blocks?) and is pretty much obligatory
if you want to do relativity and/or fluid dynamics
(see e.g. Misner/Thorne/Wheeler).

-- I am fully aware that intro physics is mostly about
pointlike particles and not so much about regions with
boundaries. But starting from the region/boundary
formulation above, we obtain _immediate_ corollaries
applicable to point particles.

-- The work/KE theorem is not "the" principle of conservation
of energy. Not even close.

-- You can derive various work/KE theorems, using intro-level
physics.

-- The reasonably general forms of the law of conservation
of energy cannot be derived using elementary means, not
as consequences of the work/KE theorem or otherwise.
(They can be related to time-invariance of the equation
of motion via Noether's theorem, but that's not something
you're likely to cover in September in an intro-level
course.)

Instead, for an intro-level course, my recommendation is
to take the law of conservation of energy as primary and
fundamental. (I wouldn't quite call it axiomatic, because
it remains subject to experimental test. But it is an
input to the intro-level understanding of physics, not an
output.)

-- In particular, I don't know whether to laugh or cry when
I see statements of the form "the _only_ way to change the
energy of a system is to do work" [emphasis in the original].
Gimme a break. That is about as narrow and infantile as
my pulley-pulling corollary.

By way of counterexample, consider my flashlight as a system.
Far and away the most significant way in which the energy of
this system increases is via the flow of fresh batteries
across the boundary of the system. Far and away the most
significant way in which the energy of this system decreases
is via flow of heat (and to a lesser extent light) across
the boundary of the system. None of these contributions
can be categorized as work, not according to any reasonable
definition of the term "work".