Ed Schweber (edschweb@ix.netcom.com)
Physics Teacher at The Solomon Schechter Day School, West Orange, NJ
Hi:
John Mallinckrodt wrote:
>But students don't often grasp the important difference
>between writing "W = Fd" or "I = Ft" (which are *merely*
>definitions) and >writing "W = delta K" or "I = delta " (which
> are important expressions of physical relationships
>between separately >defined quantities). Students will be
> a step or two ahead if they >understand that they are not
>doing physics when they use the former equations.
John is certainly right when he says students confuse two versions of
equations that contain impulse and two versions of equations that contain
momentum.
But is it really clear which is the definition. Could we not define W =
delta K and work backwards to W = fd?
It seems that the real physics comes in when we make an interpretation
that goes beyond the manipulation of equations. For instance, when we
realize that under some circumstances work is path independent and invent
(notice I don't say discover) various forms of potential energy or when we
relate work done by a path dependent force (such as friction) to changes in
internal energy.
I would tentatively propose that real physics occurs when we make an
interpretive leap whose logic cannot be replayed backwards. We can interpret
Kelvin temperature as a quantity proportional to the average kinetic energy
per molecule by comparing the ideal gas law to calculations of gas molecules
colliding off the walls of a container. But we cannot derive I = delta P by
starting with the microscopic interpretation of temperature. It is
irreversible interpretations like these that constitute the real challenge
and meaning of physics.
BTW: two years ago I had a particularly bright AP class which was
disappointed that I didn't really prove that average KE per molecule was
proportional to Kelvin temperature and we had an extended and (I think)
productive discussion about how the microscopic and macroscopic
interpretations have an entirely different vocabulary that cannot be equated
through equations but only by interpretation. This is what physics is (at
least in my opinion).