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Re: [Phys-l] Force proportional to v



"Anyway ... I'm not suggesting that anybody explore the world of
"F ∝ v" in introductory physics classes, but I am suggesting that
it should not be pooh-poohed too vehemently. It's nice to know
where the students are coming from, and to realize that they're
not completely crazy."


but isn't that the common experience? If it weren't wouldn't Aristotle have formulated V and sometime A is proportional to F?

Au contraire; I suggest an exploration of the bacterium's world first might be useful, e.g. marbles falling in oil, blocks pulled by weights on sandpaper, etc. Then watch feathers in evacuated tubes, Behr free fall, Atwood's machine, negligible friction carts and air tracks, etc.

Besides don't many of you use sonic rangers and coffee filters in concept. Physics courses?

bc, all for showing Aristotle was just incomplete.

p.s. just for fun last week I found the drag coefficient for 1 => 5 stacked coffee filters: 1.0 +/- 0.1 And R = 1 => 2 E+4



John Denker wrote:

On two recent occasions, Tim F. has decried the tendency for some
students to believe that force is proportional to velocity.

I don't want to put too fine a point on it, but it is amusing
to note that that's not wrong physics ... it's just different
physics.

Imagine a bacterium happily living in a bowl of broth, or any
other situation with a very low Reynolds number. As a practical
matter, the first two laws that describe such a situation are:

I) Objects at rest remain at rest. Objects in motion
come to rest.

II) The velocity of an object is proportional to the
applied force, inversely proportional to the size
of the object, and inversely proportional to the
viscosity of the medium.

Reference: Stokes' Law:
http://scienceworld.wolfram.com/physics/StokesFlowSphere.html

The Reynolds number is a useful concept because it tells you the
importance of inertial effects relative to viscous effects. At
low Reynolds number, mass is irrelevant and viscosity is everything.

In contrast, the physics of Galileo and Newton is the physics
of high Reynolds numbers. It is the physics of the industrial
revolution: things that are big and fast and massive, such
that viscosity is a small correction term, or can be neglected
entirely.

Looking at things from a bacterium's point of view is both interesting
and challenging. For example, bacteria do not -- and cannot --
swim the way we do. If they were to put their arms forward and
bring their arms back, they would end up where they started. They
need a completely different stroke. Corkscrew motions are one
solution.

Anyway ... I'm not suggesting that anybody explore the world of
"F ∝ v" in introductory physics classes, but I am suggesting that
it should not be pooh-poohed too vehemently. It's nice to know
where the students are coming from, and to realize that they're
not completely crazy.

"There is a world where viscosity is dominant and inertia is
negligible, but that is outside the scope of this course.
You can worry about that when you are a junior or senior in
college. In the meantime, we are going to start by exploring
the world where inertia is dominant, and viscosity is small
or perhaps completely negligible. Four hundred years of
experience have taught us that this is the right place to
start. It is easier to understand viscosity in terms of
F=ma than the other way around."

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