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Re: [Phys-L] form of Newtons 2nd and 3rd laws



On 07/26/2012 05:29 PM, Chuck Britton wrote:

I've had engineers insist that it should be presented as:

a = F/m

(Some Engineers are very good at insisting)

Gaaack. We have seen physicists insist on the same thing, in this
very forum. It's related to not understanding the difference between
equation and causation.
http://www.av8n.com/physics/causation.htm

However, I'm hoping we do not need to go there again. By all that's holy,
a = F/m means *exactly* the same thing as F = m a, for all nonzero m.
The axioms of algebra demand it. This seems so important and so obvious
that it's hard even to have a rational conversation about it. Which part
of "axiom" did those folks not understand?

My favorite form of N2 goes something like:

F = delta p / delta t

This is closer to what Newton wrote (IIRC) and we've already covered
momentum and collisions before needing Force and acceleration.

Amen, brother.

In complicated situations, such as fluid dynamics, trying to keep
track of the forces is not worth the trouble. Every sane person I
know keeps track of the momentum instead. Once upon a time, I spent
a day trying to re-express the fluid equations in terms of forces.
I didn't finish the job. I convinced myself it was possible in
principle ... just really really not worth the trouble.

Closer to the charter of this list: Think about the FCI. On this
test, six of the 30 questions deal directly with the third law.
(I'm talking about questions 4, 15, 16, 17, 25, and 28.)
I find this emphasis to be quite remarkable. The physics of force is
a vast subject, so lots of important stuff had to be left out to make
room for these questions. In particular, we learn something from the
fact that even though I see these questions as grossly repetitions,
the test-takers evidently do not. Often a given student will get
some of them right and some of them wrong, which means that particular
student has not grasped the underlying concept at all.

My first point is this: If you rephrase the third law in terms of conservation
of momentum, these problems go from being messy and confusing to being so
simple they practically answer themselves:
Is the momentum that the car gives to the truck the same as the
momentum that the truck receives from the car?


It really bugs me when "conceptual" becomes a euphemism for "dim-witted".
Until I started reading "conceptual physics" books I thought physics
concepts were good things.

Here's a specific constructive suggestion: Let's teach some important
concepts, starting with conservation. This can be revisited again and
again: conservation of energy, conservation of momentum, conservation
of electrical charge, It can be extended to things that are "almost"
conserved, such as the entropy of an almost-reversible interaction, or
the near-conservation of mass during ordinary chemical and mechanical
interactions.

Specifically, this means teaching the third law in by emphasizing
conservation of momentum (with little or no emphasis on action and
reaction). I look at those FCI questions and just shudder. Why would
anybody in the real world asksuch a question? The whole situation
strikes me as academic in the worse sense of the word. That is, you
have to learn a "concept" so that you can answer a question that is
simultaneously oversimplified yet messy and unrealistic and /contrived/
to illustrate the "concept". In the real world, when a car pushes on
a truck, there is no such thing as "the force". There are all sorts
of forces, changing from place to place and changing from time to time.
The system /as shown in the diagram/ is ill-adapted to measuring the
forces. You could redesign the system to make it more amenable to
measurement, but now we are going far beyond the question, far outside
the rules of the game. In the system as shown, it would be nearly
impossible even to /diagram/ the various real-world forces.

If somebody had assigned me this test, I would have considered it a
big demotivator. Why should I take a class that makes things more
complicated than they need to be, for no good reason? I want to
learn ideas that make my life better, not worse.

I would like to live in a world where it was /not necessary/ to ask
the same question six different ways (except maybe on the rarest
of occasions, as a calibration). The idea is that anybody who
understood the concept would automatically and instantly get all
such questions right.

As applied to ultra-simple point-particle interactions, speaking in
terms of action and reaction is equivalent to conservation of momentum
... no harder, no easier. HOWEVER ... when applied to mess real-world
situations, action/reaction gets less and less useful, while conservation
of momentum rises to the occasion.

============

Note that I have not said anything about the /order/ in which things
are taught. All evidence available to me suggests that you can start
almost anywhere. The only approach that makes any sense to me is the
spiral approach, where each idea is revisited so many times that nobody
even remembers (let alone cares) what the initial presentation was like.

I'm opinionated about what the final result should be (not about the
path taken to get there).