Re: Work done by Friction

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Tue, 21 Jul 1998, Tim Burgess wrote:

> Hi!
> 	I'm with a group of high school physics teachers. We are in disarray.
>
> 	Textbooks that we use commonly refer to the "work done by friction"
> in  slowing the speed of objects.  There are some who think this approach
> is flawed.  Others indicate that the right answer is commonly obtained
> by treating such friction as work.

I always tell my students that getting the "right" answer isn't enough. 
One must use valid methods. 

> 	Some would just ignore the textbook treatment and indicate that
> "work done by friction" is not the way to address the energy "dissipated".
Arnold Arons' excellent book "A Guide to Introductory Physics Teaching"
has a treatment of this in section 5.10 "Work and Heat in the Presence
of Sliding Friction." He considers the case of a block of mass m sliding
on a horizontal surface under application of an external horizontal force
F. The friction force is f. Arons says:

	The block alone is not an appropriate system for [applying the
conservation of energy equation]... What happens at the interface is a
very complicated mess: we have abrasion, bending of "asperities," welding
and unwelding of regions of "contact" as well as shear stresses and
strains in both the block and the floor. The work done on the block at the
interface is _not_ simply [friction times displacement of center of mass],
and we are unable to deal fully with the quantity W [the work done by
external forces on the block].

	In this circumstance, we can take advantage of the possibility
frequently available in application of the conservation laws: that of
sweeping an area of ignorance under the rug by judicious choice of system.
The system to choose in this instance is the _combination_ of block and
floor.

	...[then] we no longer have to worry about the intractable
situation at the interface since the frictional forces are now internal
and no work is exchanged with the surroundings...

	...[this] yields the following insights: (1) The increase of
thermal internal energy of the floor-block system is directly equal to that
part of the work done by force F that does not go into the form of kinetic
energy of the bloc, providing no heat is transferred to the surrounding
air. (2) This work, which is said to be "dissipated", is directly
transformed into thermal internal energy; the increase in thermal internal
energy does _not_ result from a transfer of heat to the system.

	...F delta-x_cm is the real work done on the block-floor system,
while f(delta-x_cm) is the pseudowork done on the block.

Also see Aron's section 5.7 "Real work and pseudowork" He speaks of deeply
rooted preconceptions students have, based on everyday experience, to
which standard texts add a burden of additional misconceptions, all of
which become hard to eradicate in later study.

	The principal misconception planted in introductory physics is
that the "work" quantity (force times center of mass displacement)
appearing in the "work-kinetic energy theorem", obtained by integration of
Newton's Second Law, is identical with the "work" appearing in the general
law of conservation of energy, namely the First Law of Thermodynamics.

The first, F(delta-x_cm), he calls pseudowork (following Penchina's
suggestion). The term work is reserved for that in the First Law of
Thermo, which is the integration of the work done all across the boundary
of the chosen body.

Arons references:

Penchina, C. M. "Pseudowork-Energy Principle," AJP, 46, 295 (1978)

Sherwood, B. A. and Bernard, W.  "Work and Heat Transfer in the Presence
of Sliding Friction," AJP 52, 1001 (1983) 

Erlichson, H. "Work and Kinetic Energy for an Automobile Coming to a
Stop," AJP, 45, 769 (1977).

Any good library should have back issues of AJP.

> 	There are strong opinions present here.  What is the thoughts of 
> those of you on this list?
>
> Tim

I agree with Arons. The problem situations in elementary texts can be
recast in the form he suggests. Do not take the sliding body as the
system, but take the system as the body *and* the surface it slides on.
For most students, the mere requirement that they clearly specify a system
in which to do the problem is a big step forward in understanding.

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Professor of Physics                                FAX: 717-893-2048
Lock Haven University of Pennsylvania, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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