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Re: [Phys-l] teaching energy



I think this is quite a nifty discussion. It is hard to imagine
a more appropriate topic for phys-l.


On 10/03/2006 09:48 AM, Robert Cohen wrote:
I've been skimming through the posts and I think there are three points
of view:

1. Energy is associated with fields.
2. Energy is associated with objects.
3. Energy is associated with systems of objects.

I agree.

All three viewpoints are valid, and can be considered a chain of
successive approximations, in the order (1), (3), (2).

Item (1) i.e. fields is the modern, mainstream, deluxe model. It
is a model, not carved in stone, and not without dubious elements
if you look closely enough. The crucial disadvantage is that it
is complicated, waaay too complicated for an introductory class.
The advantage is that it is consistent with ideas of /local/
conservation of energy.

Item (3) i.e. the energy of the /system/ is the canonical Newtonian
approach. This was the state of the art from 1666 to 1915, and is
still good enough for any terrestrial practical application AFAIK.

It can be consistent with local conservation of energy, in the weak
sense of the term "consistent", if we restrict it to situations
where the length scales are short, the time scales are long, and the
velocities are small compared to c. (In more general situations it
would not be consistent with local conservation.)

This sort of conditional consistency is the rule (not the exception)
in introductory physics. A familiar example is KE = .5 m v^2, which
is not consistent with relativity, except in the low-velocity limit.

Item (2) is an approximation to item (3), useful when we take every
system of interest to be a two-body system, with one body being
the earth. We then call the other body "the object". We treat
the earth as infinitely massive in comparison. As a consequence
of these assumptions:
-- the earth is considered immovable;
-- the reduced mass of the system is equal to the mass of "the object"
so we blur the distinction between mass and reduced mass;
-- the earth is the dominant contributor to creating the gravitational
field; and
-- we use "the object" as the eponym of the full two-body system.