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Re: adding apples and oranges, a different perspective



We often find it useful to express a quantity as the sum of two values,
each in different units (same dimensions). Eg. I might report my height
either as 5.75ft or - more commonly - as 5 ft 9 inches. Mixing units of
the same dimensions is not only allowed - it is useful, so long as it is
clear.

Apples and oranges are not different units of fruit (as would be pounds
or baskets), they are different kinds of fruit. I guess I would have to
say they are different sub-dimensions under the mother-dimension "fruit".

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Alan J. Scott <scotta@UWSTOUT.EDU>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Tuesday, October 27, 1998 2:14 PM
Subject: adding apples and oranges, a different perspective


. .
But there needs to be an "economy of explanation" principle applied
here.
A good, scientific interpretation of using units might not serve a
struggling introductory physics student very well. The student probably
doesn't have the capacity to appreciate the subleties and higher levels
of
thought needed to critically evaluate the intricacies of dimensional
analysis.

Case in point:

It was stated that 3 apples + 2 oranges = 5 pieces of fruit, thus,
different units can be added.

This will lead the student to conclude that 4 Newtons + 5 Dynes = 9
units
of force. Or worse yet, 2 grams times 5 km/hr^2 = 10 units of force.

I would encourage the more advanced students to examine the theoretical
underpinnings of dimensional analysis, while telling the less advanced
students that "3 apples + 2 oranges" cannot be added! For a student
that
is struggling with algebra and adds 2 kg + 4 N = 6 (whatever units),
going
into a detailed explanation of unit analysis might be a rather
inefficient
and ineffective use of time.
. . .