On 11/18/2003 09:09 PM, Ludwik Kowalski wrote:
> 1) What is gained by replacing the concept of static
> force (see my original message below) by the
> concept of "flow of momentum?"
Answer:
a) We gain some clarity. In particular it is hard
to speak about "the" force at a given location in
space, because for instance at the boundary between
A and B there will necessarily be _two_ forces, one
associated with the A side of the A/B boundary and
one (equal and opposite) associated with the B side.
Which is "the" force at that location?
In contrast, we can happily speak about momentum flowing
from A to B across the A/B boundary. The meaning of
that is unambiguous. We have a definite flow at a
definite location.
b) We also gain some generality. The momentum
formalism generalizes to cases where momentum crosses
the boundary of a region without a force on the
boundary, for instance the rain falling into the
railcar. Also the momentum formalism generalizes
nicely to special relativity and general relativity.
Momentum is a conserved quantity, which is a big deal.
> 2) What is lost by replacing the concept of force by
> the concept of "flow of momentum?" Clarity.
I find it more clear and less laborious.
The main conceptual hurdle comes from the fact that
a vector quantity is flowing. Students need to first
learn about flowing scalar quantities (milk, electric
charge, energy) and then advance to flowing vector
quantities.
> a) Momentum is m*v; in a static situation each
> part of a system is at rest (yes, in the lab frame,
> and macroscopically).
Yes. So? Is that meant to suggest there's a problem?
I don't see a problem. The momentum just flows around
in cycles.
In an electrical circuit (in the limit where Kirchhoff's
apply) there is no charge accumulating (or accumulated)
anywhere, yet a current flows.
> b) Fluids can flow. What does the "flow of
> momentum" mean in the context of an
> introductory physics course?
> c) Why should a static force experienced by a
> person on a floor (it has the same magnitude
> as m*g) be replaced by the "flow of momentum."
> Is this concept less mysterious that the concept of
> force? In which direction is the momentum flowing?
Contact contributes a flow of upward momentum across
the floor/person boundary into the person. That is,
we have +Z flow of +Z momentum. This is of course
trivially equal to -Z flow of -Z momentum.
Meanwhile gravitation contributes a +Z flow of -Z
momentum. I don't associate this with the
floor/person boundary; rather it flows into each
molecule of the person independently.