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Re: Car acceleration



John Mallinckrodt wrote:
...
Let's compare on this very simple problem.

A car of mass m starts from rest and accelerates due to a constant
static frictional force F on the tires. How fast is it going
after moving a distance d?

It's a semi-fair question. Let me try my hand at it.

m v = F t ==> v = F t / m
d = vbar t = .5 v t ==> t = 2 d / v
v = 2 F d / (v m) ==> v^2 = 2 F d / m
v = sqrt(2 F d / m)

There are two physics principles used here:
momentum, and distance=rate*time. The rest is
just a particularly easy instance of "two equations
in two unknowns".

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. If the givens had been slightly different,
or if the unknown had been slightly different,
the seeming advantage of pseudowork would vanish.
Specifically: suppose the acceleration was due
to the force of an on-board rocket engine, that
was decreasing in mass. An analysis in terms of
momentum would still be valid and informative.
A simple application of pseudowork would be
uninformative, and the attempt to repair it
would lose all semblance of simplicity.

This reminds me of various jokes about looking
under the lamp-post. Do we want to train our
students to do that? If the kindly professor
puts an easter-egg under the lamp-post, and tells
the kids to go look there, they can get a feeling
of accomplishment when they find something. But
it's not a real accomplishment. It's academic in
the worst sense of the word.

In the real world, very little of what you're looking
for is lying there under the lamp-post. Usually you
are struggling in the shadows, and that's when you
need tools and techniques that you can really trust.
-- Momentum is a concept that gets used in real
life over and over again.
-- Energy is a concept that gets used in real
life over and over again.

Students get confused in the car-acceleration
problem because they haven't learned to make a
clear distinction between momentum and energy.
That's a single distinction. If you foist on
them a third concept (by the addition of pseudo-
work) they suddenly have three times as many
distinctions to make. You haven't made it easier,
you've made it harder.

... especially when most texts would
work this problem exactly as I have and claim that they are using
*the* work-energy principle!

Don't stick that guilt-trip on me! I didn't
write those books. We can agree that there are
lots of amazingly bad books out there. But two
wrongs don't make a right. If you feed hay to
a dog and it looks malnourished, the solution is
not to feed it more hay. If the students are
spending waaay to much time worrying about
secondary things like work, to the exclusion of
deep physical principles like momentum and energy,
the solution is not to feed them more secondary
concepts.

BTW, as I reported previously, I've asked a number
of real live physics researchers if they could
define "pseudowork" for me. Precisely none of them
had ever heard the term (let alone used it).

And as you have also correctly pointed out on many occasions the
private wishes, desires, practices and biases of individuals, no
matter their credentials, are utterly irrelevant.

That's an overstatement. It depends.

Physics teaching involves more teaching than physics.
There are some things that are bizarre misnomers,
but we have to teach them because they are part of
the common conventional language. (How big is a
2-by-4 piece of lumber? It ain't 2" by 4". How much
Pb is there in a pencil-lead?) I included my little
survey to show that pseudowork cannot be justified
by a "required-for-communication" argument. This is
only tangentially related to the discussion of whether
it has intrinsic merit as a real-world general-purpose
calculational technique.