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Re: Car acceleration



John D wrote:

I recognize that the result can be obtained using
pseudowork in fewer steps ...
but only because the problem was chosen to be
an exceptionally good match to the pseudowork
technique.

I claim (without having done a statistical analysis, I done) that a
substantial fraction of problems in standard texts in the so-called
work-energy chapter fall into this category. I further claim that if
you go through such chapters and systematically write things in terms
of pseudowork instead of work, the whole presentation will be more
streamlined, more coherent, and you will have eliminated a heck of a
lot of confusion on the parts of both students and instructors
dealing with topics like "frictional work" et al.

I am *not* saying proper work should not be taught at all. I am just
saying, we should choose the order of attack. Current texts are
written with mechanics first. Unless we have the liberty of switching
to an unusual text or of ignoring the text, we should carry the
program through. For the standard mechanics program, we don't need
work. Pseudowork is simpler, clearer, and is a solid foundation for
the *subsequent* energy (thermodynamics) program.

The following summary by John M is so elegant and compelling (in my
mind) that it boggles me that there is so much resistance to it. I
would call again on those who are against the concept of pseudowork:
At least learn what the concept is and how and when it applies. You
are not forced to teach it or even use it. But to not even be open to
educating yourself smacks of narrow-mindedness of the worst sort that
we (usually privately) rail about our students.

1. The static frictional force does "pseudowork" on the car.

(where "pseudowork" = external force dotted into the displacement
of the center of mass of system)

2. The pseudowork is equal to the change in the bulk translational
kinetic energy of the car.

(This is because static friction is the ONLY force that does
pseudowork on the car--neglecting any drag forces--and because net
pseudowork is ALWAYS equal to the change in the bulk translational
kinetic energy of a system.)

3. The static friction does no "real work" on the car

(where "real work" = external force dotted into the displacement
of the point of contact.

4. Thus, the total energy of the car does not change.

(Because NO "real work" is done on the car and the net real work
is ALWAYS equal to the change in *total* energy of a system as
long as there is no heat transfer to or from the system. This is,
however, a bit of a stretch in this case and, beyond neglecting
the drag forces, also requires us to pretend that the oxygen used
in the combustion processes as well as the exhaust products remain
part of the system. One could imagine a car that carries its own
oxygen tanks and diverts its exhaust into a big bag or something
like that! This statement is also contingent on the assumption
that we take into account "thermal energy" and that there are no
thermal losses from the radiator or any other source. The
pseudowork analysis is FAR simpler because it is subject to far
fewer caveats of this nature.)

John D further quipped:

Carpenters deal with wood.
Dairy farmers deal with milk.
Physicists deal with energy and momentum.

I agree! BUT!!!! Students are not physicists. Even physics majors in
their first physics course are not yet usually much further along the
learning curve than non-physics majors in their first physics course.

Do I want my students to eventually realize that symmetry and
conservation principles are what is really fundamental? Sure. Should
I come to class the first day, state this in words, write down N2 in
the form F=dp/dt and T1 in the form W+Q=delta(E_mech)+delta(E_int),
and tell them, "Next class, we'll have the final exam where I'll give
you a few problems to exercise these fundamental principles?"
<rhetorical answer deleted> Are there alternative texts that do a
better job at stressing these fundamentals? Sure again.

But meantime, with ordinary students and standard texts, we'll start
with kinematics and dynamics. No energy and momentum in sight. Then
we'll integrate the forces over time and space to get momentum and
mechanical energy (using pseudowork). Everyone will know about the
momentum and mechanical energy change of the car and relate it to the
forces. Then we'll take a closer look at the microscopics and their
momentum and mechanical energy. Finally we'll be able to talk about
energy from a fuller point of view and return to examples such as the
car.

You know all this. It's the standard program in the usual texts. Is
it the only program or the best program in town? Heck probably not,
but I'm too young to design a whole new curriculum from scratch or
get the department to sign on to one of the more innovative texts out
there, such as Matter & Interactions which is built around the
centrality of energy & momentum in every single chapter.
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/