Re: Swartz letter in AJP (work-energy theorem)

["Carl E. Mungan" <mungan@USNA.EDU>]

ALVIN BACHMAN wrote:

> If the widget only, then there is an energy transfer
> which we attribute to the work done by the force
> between the ice and the surface of the widget.

I don't necessarily disagree with the spirit of this idea. But I must
point out two features of this statement:

1. I don't have a good estimate for how much energy was *numerically*
transferred between the widget and the ice. Certainly I have no
reliable theory, and even experimentally, it seems a dicey
proposition to determine. There's no easy way to find out the thinly
spread gain of thermal energy by the ice and atmosphere along the
long track of the widget. I'll hope to see how well I can measure the
widget's loss and rely on energy conservation to tell me the answer.
But even measuring that isn't easy. I can measure its change in bulk
KE easily enough with a motion detector, but its change in thermal
energy is a lot harder. I'll need a sensitive thermometer and I'll
need to decide what I'm going to do about the fact that different
parts of the widget are at different temperatures. (I could wait for
it to thermalize, but in the meantime it would be losing some of the
thermal energy it gained by heat transfer to its environment.)

All of this is to say: I can *conceptually* agree with Alvin's
statement. But in practice I have no simple way to actually determine
the numerical values of the energy transfer and work done. There is
no empirically useful information in Alvin's statement. It's simply a
definition of abstract concepts.

2. I have a pretty good idea of how big the frictional force between
the ice and surface is. The model I use for this, f = u_k*m*g, is
approximate but let's agree it's a pretty fair estimate. I also have
a pretty good idea of how far (call it D) the widget travels before
coming to rest, or slowing down by some pre-agreed amount, assuming I
know its initial speed. I can now calculate f*D, but I think we all
see that that quantity has no relationship to the work defined by
Alvin.

Which is to say: I take it Alvin that you agree with Swartz that
there is no relationship between work and *bulk mechanical* energy
(as opposed to total energy including internal energy, be it
thermalized or not) that we should bother trying to teach our
students, *except* possibly for the rather trivial example of
"particles" (which don't actually exist in the real world). (And
should we bother teaching even that?)

If I have put words in your mouth, please feel free to differ. -Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
mailto:mungan@usna.edu       http://usna.edu/Users/physics/mungan/