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Re: work done by friction



At 09:34 PM 10/27/99 -0800, John Mallinckrodt wrote:

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.

1) I have from time to time made mistakes.
2) When I make mistakes I am usually quick to admit them and apologize.

A search through my outbox for the word "sorry" provides proof of assertion
(1) and provides at least some support for assertion (2).

3) I don't see any significant mistake that I have made in this thread.

I wouldn't mind so much if that tactic didn't so
often end up muddying what ought to be exceedingly clear waters.

It seems to me I have made the same statements over and over again, in
particular the statement that friction does negative work on the sliding
block and zero work on the stationary table. I fail to see how I can be
accused of changing the terms of discussion.

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).

I stand by what I said. You call it an error, I still don't see any error
there. If I had to start over, I'd probably say the same thing again.

Explicitly here, you are speaking about the *total* energy of the block,
not merely its kinetic energy.

I explicitly discuss its total energy and also explicitly discuss its
kinetic energy. What's wrong with that?

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.

Yes, those are the implausible scenarios I had in mind. I still consider
it implausible to have a sliding block that produces heat which goes 100%
into the block and 0% into the table. But the gas example (below) is
plausible and indeed common.

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.

Actually, a more general argument could have been made. I didn't
heretofore make the general argument because I didn't need to make it. But
since you accuse me of ducking this issue, I will address it below.

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.

My inference is correct. The basis of the inference is not what you say.
With or *without* a change in total energy, a change in macroscopic energy
(kinetic energy in this case) obviously occurs. This change is properly
called work. The process responsible for this work is properly identified
as friction.

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.

I don't have a copy of your paper, so I cannot say for sure whether your
notion of frame-specific external work coincides with my definition of
work. I strongly doubt it, though. That is, I suspect you are leaping to
false assumptions about what I mean by work.

In any case I assert there is a standard, reasonable definition of work
under which my entire analysis is valid. In particular, "F dot dx" is what
I am talking about, where for the moment F is the force on the block and dx
is the distance moved by the block, in the specified reference frame.

This is the definition of work that would naturally apply in a typical
nondissipative situation, and I see no reason why I should be forced or
even tempted to adopt any other definition in this frictional situation.

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.

A consistent application of the standard, reasonable definition of work
leads inexorably to the application of the "F dot dx" formula, where in
this case F is the force on the table and dx is the distance moved by the
*table* -- which is zero.

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

Under a consistent application of the standard, reasonable definition of
work, they are not 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.

I stand by that statement.

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 specified in detail the quantity I call work. This may or may not
be the same as what you call pseudowork.

I have no quarrels with that
definition, I simply require you to recognize that it is a different
definition.

I do not recognize any inconsistency in my formulation of the problem. Nor
do I recognize any unphysical or implausible predictions resulting from my
formulation.

This is why I said and why I say again ...

Sorry, you can't have it both ways.

I am not trying to have it multiple ways. I used a consistent, standard,
reasonable, and useful definition of work. Under this definition, friction
does negative work on the sliding block and zero work on the stationary table.

This view of work is consistent with the statement that the block's
macroscopic kinetic energy is converted to heat and the heat is partitioned
between the block and the table. I consider this to be a very reasonable
way to describe the physics of the process.

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

Muddying the waters? I don't see how restating my position muddies the waters.

Dismiss your remarks? I have methodically explained why your attacks on my
analysis are groundless.

along the lines I see emerging in your most recent post
when you wrote things like:

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

I stand by that statement. I don't see how that muddies the waters. It is
perhaps not optimally explicit as to the sign of the work and heat, but a
charitable reader will interpret it in the context of N other statements
that friction does negative work on the block and imparts a positive amount
of heat to the block.

and, perhaps most enigmatically of all

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

I don't see how that is enigmatic. It says what it means and means what it
says.

My meaning is particularly clear if we consider a model system where the
frictional mechanism is embodied in a third substance (a "bearing" or a
"lubricant") between the block and the table, as I described in a previous
posting. Perhaps you missed that one.

Call this the reification of friction if you must. In this model system,
the block does work on the lubricant, and this work is equal and opposite
to the work the lubricant does on the block. Does that make you happy?
But (!) note that this work is *not* transmitted to the table. It is
dissipated as heat in the lubricant. From there the heat is typically
conducted into the table and the block according to some as-yet unspecified
partitioning scheme.

The definition of work that I use here corresponds exactly to the
definition that I would use if the block interacted with the table via a
spring rather than via friction. The spring would do negative work on the
block, and would do zero work on the table. Why is that hard to grasp?
Why is that not the first and only thing that comes to mind?

To move beyond this model system to the general case, we note that the
details of the lubricant are not important. The lubricant merely serves as
a placeholder for whatever frictional process or mechanism is actually
operating. This process, whatever it is, does negative work on the block
... and _ipso facto_ the block does positive work on the lubricant. It
turns this work into heat and partitions it between the table and the block.

... which is just what I've been saying all along ....

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

Let's now discuss the case of something doing work entirely on itself.
This corresponds to a frictional process that dumps 100% of its heat into
the block and 0% into the table. At this point the conceptual crutch of
the lubricant can be discarded; the frictional process can be considered
to be 100% internal to the block.

This case was carefully considered by James Prescott Joule, for the case
where the sliding block is replaced by a flowing gas.

You can refer to standard discussions of a gas expanding through an
orifice. The difference between expansion through an orifice and expansion
through a turbine is that in the latter case the gas does work on the
turbine, while in the former case the gas does work only against itself.
In the case of the orifice, the gas loses a certain amount of mechanical
energy (macroscopic kinetic energy, pressure, etc.) and 100% of that amount
is converted to heat. If we neglect the thermal conductivity of the
orifice and plumbing, 100% of that heat is carried in the outflowing gas.

This situation is properly described as "the gas doing work against its own
friction". This is the standard, reasonable terminology that you hear in
the research lab from people who know a very great deal about
thermodynamics. This terminology is a natural extension of other concepts
of work and heat.

You can invent new concepts and call them pseudo-work or voodoo-work or
whatever. I can't stop you. But you would be doing your students a favor
if you use the terminology that thoughtful experts use.

The analogy to the rest of this thread should be clear: If we imagine an
unusual extreme type of sliding friction, perhaps with a block having high
thermal conductivity and a table having low thermal conductivity, one can
imagine that the block does work almost 100% against its own friction. Its
total energy would be almost unchanged as it slides, but macroscopic
kinetic energy would be converted to heat.

Even in this extreme case, the change in the block's macroscopic energy is
properly called work. The process responsible for this work is properly
called friction. The same process of course produces heat. There is no
change in the macroscopic energy of the table, and therefore no work done
on it.

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