Re: work done by friction

[John Denker <jsd@MONMOUTH.COM>]

At 06:21 AM 10/29/99 +1000, Brian McInnes wrote:

[addressing me, I suppose?]

> John, I'm making one last (possibly misguided) effort to lay out where
> you and I differ.
> Primarily it is on the ground that work, as defined in terms of forces
> acting on PARTICLES is given by the line integral of that force over
> its displacement.

We don't differ on that!

> Where there is no displacement there is no work done.

That's one of the things I've been saying.  We agree.

> The vast majority of cases of frictional forces given in textbooks
> involve bodies losing kinetic energy as they slide along rough
> surfaces.

OK.  Fine.  That case is covered by the analysis I've been doing.

> In these cases (of dynamic friction) the mechanism is such
> that the frictional forces are localized, that is, there is no
> displacement of the points of application and NO work is done by the
> frictional force.

I have said over and over again that no work is done on the table because
it undergoes no displacement.  It appears we agree on that.

So here is perhaps where we diverge:  The block obviously does undergo
displacement!  How can anybody deny that?  The block feels a force and
undergoes a displacement, and therefore work (negative work in this case)
is done on it.

> Textbooks generally assume a single frictional
> force over the whole of the two "surface" in contact and, on the
> grounds that the point of application of this force (supposedly around
> the centre of the surface), claim that negative work is done on the
> sliding body.

So the textbooks agree with me.  I'm not surprised by that!  I don't know
what the "center" of the surface has got to do with it, but the rest sounds
right.  The "single" force is merely a summarization of lesser forces,
which seems like a harmless simplification.

> Sherwood and Bernard in the reference I cited yesterday (AJP, 52,
> 1001-1007) draw attention to the paradox this creates in interpreting
> the energy situation "Where is the energy term representing the
> increased internal energy of the block?"  Sherwood and Bernard not
> only explain the situation much better than I do but take 7 pages to
> do so. If you are really interested in looking at an alternate way of
> understanding other than the one that you have I recommend that you
> read and think about this paper.

I don't have a problem with the idea that energy disappears from the
organized macroscopic degrees of freedom and reappears in the disorganized
microscopic degrees of freedom.  I can't imagine why S&B or anyone else
would consider this a paradox.  I haven't read the S&B paper, and nothing
said in this thread gives me the slightest discomfort with the analysis
I've been doing.

> I have considered your points and agree that (1) if there is
> non-sliding (static) friction involved as, for example, in
> accelerating vehicles or accelerating conveyer belts, then those
> frictional forces do work

We agree that to focus on static friction would be a change of topic.  My
analysis has concentrated on dynamic friction at your request.

> (2) in situations where objects are dropped on to
> belts that, for a very short interval of time, sliding friction forces
> do do work and the microscopic friction model not only allows this but
> requires it - this is a transient situation but, I admit, it does
> exist.

So we agree.

>  It is not the situation dealt with in introductory textbooks.

I don't see the difference.  You said the textbooks considered the case of
a sliding body.  This phase you call "transient" is precisely the phase
where sliding occurs.  That is the phase I've been analyzing all along.

> You state "since the gain in thermal energy does not, except in
> extraordinarily implausible scenarios, fully compensate for the loss
> of kinetic energy".

OK, you got me there.  I'm sorry I wrote that sentence.
  1) In particular the word "since" suggests that my conclusions rest on
the subsequent observation, which they do not.
  2) Also it appears I should have specified "the gain in the block's
thermal energy does not fully compensate the block for its loss in kinetic
energy".  I thought this second point was obvious from context but I guess
not obvious enough.

By calling attention to the total energy (rather than the macroscopic
energy) I was doing the less-than-general case.  I hoped this
less-than-general case would be more easy to see.  But apparently my hopes
were misplaced, and this just caused a distraction.  I'm sorry for the
distraction.

But a correct conclusion supported by a less-than-general argument is still
a correct conclusion.  Using work in the ordinary, standard, reasonable way
to denote F dot dx, I reiterate the assertion that friction does negative
work on the sliding block and zero work on the stationary table.

>  John, if you define the system appropriately
> (both blocks) the the gain in thermal energy does fully compensate.

I agree.  I never meant to say otherwise.  I'm astonished that anybody
would think I'm stupid enough to say otherwise.

> If you want to confine your system to the single block,

I do not want to pretend that the single block constitutes the entire
system.  That would not conserve momentum, and would in ordinary cases not
conserve energy either.  Yuck.

> things are
> messy and you are right in the middle of the paradox that Sherwood and
> Bernard drew attention to and that John Mallinckrodt drew your
> attention to in a couple of very recent posts.

I am nowhere near making that mistake.  I renew my assertion that friction
does negative work on the sliding block and does zero work on the
stationary table.  You have been gracious enough to state that you agree
that it is true "sometimes" and in "transient" situations.

I guess the only place where we differ is that I assert that this continues
to happen throughout the time the block is sliding on the table.

> I am very happy to accept his proposition that "We have a word,
> "work", which refers to a quantity we can't define uniquely, and for
> which definitions giving conflicting results are known, and we ask the
> question "Can friction do work?" Ridiculous!"

But there seems to be reasonably wide consensus that "F dot dx" is the
right sort of work to be using here.  I don't see anything ridiculous here.
 I don't see any reasonable grounds for non-consensus here.

If the block and the table were interacting via a spring, everybody would
agree (I hope) that F dot dx is the right sort of work to use.  Everybody
would agree (I hope) that the spring does negative work on the sliding
block and zero work on the stationary table.

I am just completely baffled as to why people would be unable to see the
parallel between the spring forces and the frictional forces.  I can even
underline the parallelism by separating the "work" phase from the "heating"
phase, as follows:
  a) bringing a frictionless block to rest using the spring, thereby
storing energy in the spring;
  b) disconnecting the spring from the system, and while disconnected,
allowing it to convert its internal organized potential energy to heat or
thermal energy or whatever you want to call it; and
  c) reconnecting the now limp but warm spring to the rest of the system
and allowing it to exchange thermal energy or heat or whatever you want to
call it with the block and table.

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