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I'm so addicted to units that it took me a moment to realize that yes,
there is an alternative. The alternative to algebra is grade-school
arithmetic. Suppose you are in 4th grade. You know basic arithmetic,
but not algebra. You could represent force, mass, and acceleration by
/pure numbers/ devoid of units. In this scenario, to calculate the
force you might well need a fudge factor to make the answer come out
right, so it makes a certain amount of sense to write F = k m a, where
k depends on the choice of units.
At the start of this thread, on 07/26/2012 02:11 PM, Larry Smith wrote:
My engineering colleague says I should teach N2 as F = kma where k
can make it work in non-SI-unit systems. How do you respond to such
requests?
I answered this before, but I can give a more thoughtful answer
now:
Note the contrast:
-- For persons who can handle only arithmetic, not algebra, then
F = k m a makes a certain amount of sense.
-- However, any person who has advanced to the level of algebra
or beyond would be verrrry well advised to write F = m a (without
the k) and to consider the units as "baked in" to the definition
of F, m, a, and every other physical quantity.
Despite the Subject: line of this thread, the real issue has got
nothing to do with Newton's laws! To see what I mean, suppose you
measure length and width in feet, and multiply them together to get
area in acres. Then you have to write
area = k2 * length * width
where the fudge factor k2 depends on the choice of units.
That is to say, it makes no sense to pick on Newton's law, unless
you are going to inflict the same overcomplication on every other
equation known to man.