Re: superposition

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

On Wed, 15 Jan 1997, Martha Takats wrote:

> When I asked for examples of things (forces?) which don't obey the 
> superposition principle, I was hoping for examples which might be used 
> with an introductory course, when students first encounter electric 
> forces! All the examples which have come through seem too advanced to 
> be appropriate. I want something familiar...
> Martha Takats

I may have missed it, but I don't think anyone clearly stated what "The
superposition principle" is. First, it isn't a *physics* principle or law.
It is a mathematical relation. Is it any different than *additivity*?
Depends on who's talking about it. In typical college level books I see it
mentioned only as

a) the superposition principle of vectors.
b) the superposition principle for waves.

Some books have no entry for 'superposition' at all! And rightly so. The
word adds no insight, or understanding, or physical meaning to the
discussion. It is just a label. We don't need the word, or any concept
associated with it.

To make a comparison, how often do we in physics use the phrase
'transitive relation'? Don't we have transitive relations in physics? 
Sure; one important one is "If body A is in thermal equilibrium with B and
B is in thermal equilibrium with C, then A is in thermal equilibrium with
C." Some students say "that's obvious and trivial" thinking that it is a
tautology. But in fact it is the very important zeroth law of
thermodynamics which tells us that if we put a thermometer in A and it
comes to a reading R, then put it in C, and it comes to the same reading
R, then A and C are the same temperature. This gives meaning to
temperature, and you won't get far in thermo without it. Are all relations
transitive?  Certainly not. A homely example, If Andy loves Betty and
Betty loves Carl, it doesn't follow that Andy loves Carl. The relation
'love' isn't transitive. 

But does talk about transitive relations help understand the physics?
Probably not, for most students. Likewise talk of superposition doesn't
necessarily help either.

Anyway, here's a stab at stating the relation of superposition.

If cause A produces result A', and cause B produces result B', then the
two causes acting together will produce result A' + B'. When this is wo we
say that the cause and result obey a principle of superposition.

How many textbooks which talk about this bother to even try to define it?
No wonder physics books are hard to understand! Just stop to think how
many technical-sounding terms we toss around glibly yet never clearly
define. A bright student could easily give some teachers fits by insisting
on clear definitions of them, and then asking a follow-up "Why is it
important to know this?"

Ask the teacher to define:

Action.

Reaction.

Specific (as in specific gravity, specific mass, specific heat capacity).

Capacity (as in specific heat capacity, capacitance)
Where's the 'force' in 'electromotive force' (EMF)?
What's the motion implied by the 'motive' in electromotive force? (Doesn't
the 'seat of emf' stay put in one place, without moving?)

"Tends to"

"Per unit" (Must one have a whole unit of it, or would a fraction of one
unit be ok? Before you answer, does it make sense to say electric field is
force per unit charge in MKS where the unit of charge is a *huge* amount,
the Coulomb?) 

Rate of.


Any others?

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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