Re: why pseudowork (NOT)

[John Denker <jsd@MONMOUTH.COM>]

At 08:53 PM 10/28/99 -0800, John Mallinckrodt wrote:

> you seem here to be
> talking about a rigid block, one with no internal degrees of
> freedom.

No, I'm just recognizing the distinction between macroscopic and
microscopic degrees of freedom.

This is the distinction recognized by every physicist who ever described
the temperature of a baseball and then separately described its
center-of-mass motion without giving an ultramicroscopic description of the
thermal motions.

> This "rubbing of finger-tips" sounds like the beginning of an
> infinite regress to me,

No, not infinite, because it very soon gets down to the point where we have
a microphysical model of what's going on, i.e. to the point where we can
call it electrical fields and chemical bonds rather than calling it friction.

> but I'll grant you the likely unphysical
> nature of the model for the reasons you go on to note in the next
> paragraph.
>
> > I'll even make a stronger statement: until proven otherwise, I hold the
> > opinion that the ultramicroscopic forces (electrical fields, chemical
> > bonds, and all that) are of the sort that exert force while moving.  That
> > is, the stick/buzz model is not a sufficiently correct model of *any*
> > physical system that I know about to support the claim that the sliding
> > block and stationary table undergo equal and opposite work.

Does this mean you agree that it is unphysical to claim that the block and
the table undergo equal and opposite work?  Then we are basically in agreement.

Here's where things stand AFAICT:

1) For friction mediated by a lubricant, the claim that the block and the
table undergo equal and opposite work is indefensible.

2) For friction without lubricants, e.g. friction mediated by wiggly
asperities attached to the block and/or table, there are multiple viewpoints:
  a) According to one viewpoint, *all* the energy transferred to the table
is transferred by reversible conservative forces (and is therefore called
work) and is immediately thereafter thermalized.
  b) According to another viewpoint, some of the energy transferred to the
table is thermalized before transfer.  The transfer of thermal energy
should not be called work.
  c) According to yet another viewpoint, *all* of the energy that the table
gets is thermalized before it becomes part of "the table".

I assert that (2a) does not describe the typical sliding block and applies
only to an extreme limiting case.

I recognize that (2c) is also an extreme case.  It can be made less extreme
by revising it, such as:
  c') ... *all* of the energy that the main part of the table gets is
thermalized before it becomes part of "the main part of the table".

I choose to define things so that the wiggly asperities attached to the
tabletop do not belong to the *main* part of the table.  I define the
asperities to be part of the "frictional mechanism" in analogy to the
lubricant.  This definition is arbitrary but not unreasonable.

I recognize that this distinction between the frictional mechanism and the
rest of the table involves some approximations.  For example, real friction
includes processes such as the following:  Scraping radiates sound into the
main part of the table.  This is initially nonthermal.   After some time
(possibly a very long time by microscopic standards) it becomes
thermalized.  But this example is tangential to the present thread, because
sound doesn't do a lot of net "F dot dx" work.

If we are going to discuss processes that convert nonthermal energy to
thermal energy, we must somewhere draw the line between macroscopic and
microscopic.  The place I have drawn the line is arbitary but not
unreasonable.  It is in fact quite conventional, as evidenced by the
textbooks that handle these issues the same way.

=============

To summarize:
  --) The claim that the sliding block and the stationary table undergo
equal and opposite work is not true for the typical sliding block.
  --) The claim that friction does zero work on the table (while doing
negative work on the block) must be softened to something more like this:
Friction does zero work on the main part of the stationary table, while
doing negative work on the main part of the sliding block.

... where as always I take "work" to mean "net 'F dot dx' work" in problems
of this sort.


______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com