Re: The drag force -- a correction squared

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sat, 7 Oct 2000, Ludwik Kowalski wrote:

> Jack should have said that "if everything else is the same"
> (air, shape and size of the object, same planet, etc.) then
> the drag force is proportional to the mass of the object.
> That how I interpreted his comment. But I agree with
> Brian that the statement is not valid in general.
> Ludwik Kowalski

Ludwik, I think, misses brian's point.  As far as all of this
goes, Jack was right; there is no need to add Ludwik's
restrictions.  It *is* a fact that, at their various terminal
velocities, the drag forces on *any* collection of objects will be
proportional to the masses of those objects (since they are
*equal* to the gravitational forces on those objects.)  This does
*not*, however, imply that drag forces are, in general,
"proportional to" the mass of the object to which they are
applied.  I'll go out on a limb (a short and sturdy one, I think)
and note that they don't even *depend* on the mass.  Drag forces
depend on the velocity, shape, size, surface characteristics, and
attitude of the object and also on properties of the medium
through which the object moves.  They never depend fundamentally
on the object's mass.

Notwithstanding all of the above, there is nothing "wrong" with
*expressing* a drag coefficient as the product of the object's
mass with another positive constant.  This is often done in
intermediate and advanced mechanics texts in order to eliminate
the explicit appearance of mass in the differential equation of
motion for objects subject only to gravity and drag.

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