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Re: [Phys-L] feeler-dealer, third law, et cetera



I suspect that the point that John D is getting at is related to the mistake one often sees in free body diagrams (particularly noticeable in constant circular motion situations) where students while drawing the forces acting on the body executing circular motion show all the usual forces that an expert does and then adds in one more arrow that they label (Mv^2)/r, "another force acting on the object".

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Thursday, December 12, 2013 6:13 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] feeler-dealer, third law, et cetera

On 12/11/2013 10:33 PM, Paul Lulai wrote:

Net force isnt *A* force it is a sum of forces.
An account balance is neither a debt nor a deposit.

If we adopt that approach, it means force is not a vector.

I say that because according to the definition of vector, the sum of two vectors must be *A* vector. This is called /closure/. This requirement is so fundamental that it sometimes goes without saying when people are listing the vector-space axioms:
http://en.wikipedia.org/wiki/Vector_space#Definition
but it is a requirement nevertheless:
http://en.wikipedia.org/wiki/Vector_space#Alternative_formulations_and_elementary_consequences

Going back to dealer/feeler notation...what is the dealer for the net force?

It looks like we have conflict between
a) the idea that every force should have a dealer and a feeler, and
b) the idea that force must be a vector.

We have to choose.
a) We have a physical intuition about forces.
b) We have a mathematical intuition about vectors.

That sounds like a tough choice, but not really, because
a) The notion of dealers and feelers is only /sometimes/ important.
b) The notion of closure is /always/ important.

It is common to start with a less-than-general example, and then extrapolate to the general case. The world will not end if we say that dealer-feeler forces are not the general case, just a starting point, just a foothold, just a springboard, just a subset of all forces.

As so often happens in pedagogy, and life in general, where you start out is not where you want to end up.

There is a built-in conflict between the dealer-feeler notion of force and the vector notion of force. I did not create this conflict; I just called attention to it.

Such conflicts are not particularly rare:
-- We have two very different notions of "energy" (the physics
energy and the DoE energy aka "available" energy)
-- There are at least two different notions of "conservation".
-- There are two different notions of "acceleration".
-- Within physics we have two different notions of "gravity".
-- There are two incompatible notions of "adiabatic".
-- There are at least four or five incompatible notions of "heat".
-- Even something as crucial and fundamental as the word "and"
has two strongly-conflicting meanings.
++ etc. etc. etc.
http://www.av8n.com/physics/weird-terminology.htm

Such conflicts are a serious impediment to making sense of the subject ... and not just for students. I've seen experts get seriously fooled.

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