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Re: Meauring Volts?



Wes Davis wrote:

I find that most of my HS physics don't really UNDERSTAND the
difference between the quantity being measured and the UNIT for that
quantity. Has this possibility been discussed, and I missed it? Or is
the possibility too ludicrous to consider?

The distinction requested here is not ludicrous,
although the request is tricky and ambiguous.

Suppose a recipe calls for measuring out 500
grams of sugar.
-- The _substance_ being measured is sugar.
-- The _quantity_ being measured is 500 grams.
-- The _unit_ of measurement is 1 gram,
although other units could be used,
mutatis mutandis.

So I would say the the quantity being measured
is indeed different from the unit of measurement --
different by a factor of 500. I would expect
even the dimmest student to understand that
500 is not the same as 1.

On the other hand, this is a difference in
degree, not a difference in kind. From the
point of view of dimensional analysis, 500g
is the same kind of thing as 1g.

Is red cardboard the same as red paper, or is it
the same as blue cardboard? There are many
different equivalence relationships. Depending
on what purpose you have in mind, color may or
may not be a significant difference, and heft
may or may not be a significant difference. It's
not fair to ask students to read your mind and
know what sort of difference you consider
significant today.

Another variation revolves around the choice
of whether you say
-- the quantity being measured is 500 grams.
-- the quantity being measured is 500 grams of sugar.

Surely 500 grams of sugar is different from 500
grams of arsenic. But it remains totally ambiguous
what you mean if you ask "what is the quantity
being measured" without a lot of context.

The whole idea of mass is an abstraction, and a
kitchen scale is intended to measure mass independent
of chemical composition. (It generally does so
only approximately, because of buoyancy effects
et cetera.)

So we can define yet another equivalence class,
equating objects that have the same mass.
Determining the mass is only part of the more
complex task of determining mass and composition.

English is ambigous. Always has been. Always
will be. Don't expect students to give clear
answers to ambiguous questions.