Re: work done by friction

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Wed, 27 Oct 1999, John Denker wrote:

> At 07:04 AM 10/27/99 -0800, John Mallinckrodt wrote:
> > you can't have it both ways.  Either friction does work on
> > both the table and the block or it does no work at all.
>
> That's a joke, right?  Ha ha ha.

John D.,

You are a clever fellow from whom I have learned a few things, but, as has
been noted here before, you have a most annoying habit of changing the
terms of discussion in such a way as to avoid simply admitting when you
have made a mistake.  I wouldn't mind so much if that tactic didn't so
often end up muddying what ought to be exceedingly clear waters.

Allow me to remind you of what you wrote when I first addressed your
error:

> I reject for the Nth time that frictional forces don't do work.  They do
> work even in the case of a block sliding to rest on a stationary horizontal
> table.  At time T=0 the block has kinetic energy.  At a later time it has
> less kinetic energy, same potential energy, somewhat more thermal energy,
> and less total energy (since the gain in thermal energy does not, except in
> extraordinarily implausible scenarios, fully compensate for the loss of
> kinetic energy).

Explicitly here, you are speaking about the *total* energy of the block,
not merely its kinetic energy.  The "extraordinarily implausible
scenarios" that you are referring to are very clearly those in which all
of the lost kinetic energy winds up as internal energy in the block
itself.  Without that lost *total* energy you would *not* be able to go on
to say as you do:

> So where does the lost total energy go?  Something must have done negative
> work on the block.  That something is called friction.

Again, very clearly, you are using the fact that the *total* energy of the
block has been reduced to infer that "something must have done negative
work on the block" and you go further to identify the frictional
interaction as the agent of that work.  Although there are many different
useful work-energy relationships, the one you are clearly using (i.e.,
work on the system = change effected by a mechanical process in the total
energy of the system--the kind of work that Harvey Leff and I call
"frame-specific external work" in our paper "All About Work" referred to
earlier in the discussion) is one that is perfectly acceptable to me.  It
leads inexorably to the conclusion that the block has done positive work
on the table since the *same* frictional mechanism is responsible for the
increased total energy of the table.  This is certainly not a statement
that "work is conserved"--a bizarre notion if I ever heard one--but
*these* two works are indeed equal and opposite

Then you wrote:

> Of course the block did not to work on the table; nothing is going to do work
> on the table since it is assumed stationary.

Here you are using a *different* definition of work (i.e., work on the
system = change in kinetic energy of the system--the kind of work that we,
and many others, call "pseudowork").  I have no quarrels with that
definition, I simply require you to recognize that it is a different
definition.  This is why I said and why I say again ...

Sorry, you can't have it both ways.

I anticipate that you will respond to this message and I apologize to the
list in advance for offering my prediction that your response will serve
to dismiss my remarks without directly addressing them and/or further
muddy the waters along the lines I see emerging in your most recent post
when you wrote things like:

> That's a joke, right?  Ha ha ha.

and

> Actually the block gets both frictional work *and* frictional heating.

and, perhaps most enigmatically of all

> The mechanism in this case turns work into heat, and partitions the
> heat between the various participants.

In any event, I am done.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm