May a more appropriate perspective as an educator:
I have another question along the lines of the recent discussion about
apples and oranges. People have provided some excellent insight into the
details of units as it pertains to their physical meaning and relationships.
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.
Alas, we have the fundamental meaning of education
(TIME)=(UNDERSTANDING)=($$). Which I refuse to elaborate upon the
dimensions and their appropriate meaning and interpretation, let alone
their mathematical relationship. ;)
Regards, Alan
Alan J. Scott
Department of Physics
University of Wisconsin-Stout
Menomonie, WI 54751
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E-Mail scotta@uwstout.edu
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