Re: The drag force -- a correction squared

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sun, 8 Oct 2000, Brian McInnes wrote:

> (4)if the idea of inserting m among the constants on the RHS is to
> eliminate the explicit appearance of mass in the differential equation
> of motion, it has the unfortunate consequence of implying that there
> is no such explicit dependence of the motion on mass.

Just so.  This, I suspect, is why the practice is generally
confined to texts for intermediate and advanced courses by which
time (we hope) the student knows better.

Another way of looking at it, however, is that *not* inserting m
among the constants on the RHS has the unfortunate consequence of
implying that the general solution of Justin's problem actually
depends *separately* on the specific values of *both* the drag
coefficient and the mass when, in fact, it only depends on one
parameter--the *ratio* of the drag coeffient to the mass.
Intermediate students should begin to understand and appreciate
devices like this that reveal a problem's minimal parameter set.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm