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

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

> Carl, in the original post it was a _cold_ widget to obviate the
> complication of having thermal work done on the widget.

Sorry Jim, it just doesn't work that way, if you'll excuse the pun.

I am rubbing the widget across the ice. The widget *will* therefore warm up.

I *agree* with you however that minimal thermal work (I take it this
is a code phrase to avoid having to say "heating") was done. (But see
my postscript A below for qualifications.)

One might be tempted to describe this as warming by work, in the
style of Joule's paddle wheel. BUT there is a crucial difference: In
the paddle wheel experiment, my arm or falling weights or something
is doing work on the wheel to turn it and warm up the water.

But in the present example, no external agent is pushing the widget
along. It's just sliding along and slowing down.

So let's summarize the situation:

1. widget slows down (loses KE)
2. widget warms up (gains internal energy)
3. net energy change of widget = gain in internal - loss in KE = some
negative amount

Why does this happen? Explanation: friction does *two* things here.
It does positive work (see my postscript B below for explanation) on
the ice and atmosphere, causing them to gain internal energy and the
widget to lose PART 1 of its KE. But it *also* converts some of the
widget's bulk KE into internal energy *of the widget* causing the
widget to lose PART 2 of its KE. So in our summary:

1. widget loses KE1 + KE2
2. widget gains internal energy equal to KE2
3. net energy change of widget = KE2 - (KE1 + KE2) = -KE1 (which went
to the environment)

Carl

ps A: While I'll allow the heating may be minimal, it's not strictly
zero. You necessarily have a widget at one temperature in contact
with ice and air at other temperatures. (Keep in mind the widget's
surface temperature is changing as it slides.) In fact, the surface
temperature of the widget isn't even uniform in general. And of
course the answer depends on part on the timescale of the experiment.
Yuck, so I'm only willing to go with "minimal" not "zero".

ps B: Some may object, how can the widget do work on the stationary
ice? The answer depends partly on your definition of work, but if we
go with the standard thermodynamic definition, you necessarily must
conclude that the ice is *not* stationary but that little bits on its
surface get jiggled by the widget, causing those bits to warm up.
This is *inherent* in the nature of sliding friction. You can't
simultaneously say that sliding friction occurs AND that no
thermodynamic work is done on the surface. Take your choice of one,
barring such "rigged" examples as one object symmetrically sliding
across an identical object in deep space.
--
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/