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.
Where there is no displacement there is no work done.
The vast majority of cases of frictional forces given in textbooks
involve bodies losing kinetic energy as they slide along rough
surfaces. 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. 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.
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 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 - but this is a sliding not a dynamic
situation - and (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. It is not the situation dealt with in introductory textbooks.
You state "since the gain in thermal energy does not, except in
extraordinarily implausible scenarios, fully compensate for the loss
of kinetic energy". John, if you define the system appropriately
(both blocks) the the gain in thermal energy does fully compensate.
If you want to confine your system to the single block, 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. (BTW John does not
want to do any thing as silly as to conserve work, but I'll let him
speak for himself - he does it very well.)
As for your argument
"Work was done on the block, and the energy was converted to heat",
you are confusing thermal energy and heat but that, I guess, is
another story.
All in all, as I withdraw from this discussion, which is losing
pedagogical value, I thank Leigh for his contribution which really
cuts to the heart of the matter.
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!"