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Re: the energy



Hugh Logan wrote:

> I wonder if it would be possible to visualize the flow
of energy using the classical or everyday picture of space and time.
Could one make a video of work done on spring showing some kind of fluid
flowing into the spring system corresponding to its increase in
potential energy?

Yes, I visualize the energy flow as being closely analogous
to fluid flow. As Feynman said, "the same equations have the
same solutions". Of course this requires imagining some ideal
incompressible indestructible fluid; energy is much more
strictly conserved than any real fluid is.

Establishing a super-detailed connection between the motion
of the spring and the motion of the E-fluid might be hard.
I've never really tried, but I suspect it wouldn't be worth
the trouble.

> Perhaps more difficult, could one make a video showing
the flow of energy as a fluid in an isolated system of charged particles
(including their electric field) from the electrostatic field into the
kinetic energy of the released particles?

Most people (of all ages, not just students) have a hard
time visualizing anything in D=3. Therefore a detailed
accounting of the energy in a complicated arrangement of
charges will probably be very hard to visualize.

I don't see anything in the
modeling materials that actually permits one to visualize the flow of of
a substance-like fluid in energy transfer.

It depends on what level of detail you require. At some level
it suffices to have two beakers, one labeled Left and one labeled
Right, and you pour some juice from one to the other and back
again, repeatedly, while pattering about the left and right ends
of a teeter-totter.

The point is that a decrease in one region is accompanied by
a simultaneous equal-magnitude increase in adjacent region,
which is my working definition of conservative flow.

....

When a baseball is thrown, it is
difficult for me to think of something like a fluid corresponding to the
baseball's energy flowing.

That's a good point. That situation doesn't really correspond
to a flow of energy from region A to region B ... the energy is
just transformed in place, transformed from KE to PE and back
again. Since there's no spatial separation, flow images don't
really apply ... and I'm not sure what images should apply.
Maybe red fluid turning into blue fluid and back again?? I like
Bob's suggestion of pennies flipping heads <--> tails ... I
wonder if we could somehow refine it to give some control of
the PE/KE ratio.

The change of PE <--> KE *within* a closed region is conceptually
simpler than the more general situation where energy is flowing
across the boundary of a non-closed region.

> In particular, "The wind streaming against
his face and chest is what carries away the waste heat." I suppose one
can think of energy flowing along with the wind if the system is
enlarged to include the air. But does one visualize (or feel) the flow
of air or of energy?"

I visualize it that way.

This view is pretty nearly mandatory when you do fluid dynamics.
There you don't have a simple two-way distinction of "the system"
versus "the environment".
Instead you have jillions of little regions, all peers, and you
need to express the conservation law so that it applies to each
region. If you have a region where hot air is flowing in while
cold air is flowing out, that makes a positive contribution to
increasing the energy of that region.

I'm not suggesting that we teach fluid dynamics in the first weeks
of intro-level physics class. But we can use what we know about
fluid dynamics, relativity, and everything else in order to build
confidence in what the laws of physics really say. It's nice to
know that talking about *flow* of energy cannot possibly get you
into trouble, even if you can't (yet) tell the kids what makes
you so sure.