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[Phys-L] Re: A Third law question



cliff wrote:

-- the bowstring suggested by David Willey


But why does the bow string resist? It is because of the inertia of the
bow. And why does the bow have inertia? Nobody knows. I think we miss the
issue at the heart of the students problem if we neglect this point.

There are several issues on the table, any or all of which may be at
the heart of the student's problem.

There have been a number of suggestions in this thread, and I now see
that they all have merit. To some extent we are all throwing out
hypotheses as to what "the" core problem(s) might be. These hypotheses
can be checked by running them past the student.

1a) Maybe "the" question is why do things have inertia at all. This
question is in some sense unanswerable. I don't know /why/ there is
inertia, and I especially don't know /how/ inertia occurs. Newton
responded "hypotheses non fingo" to a similar question, and for some
questions that is the best response.
1b) On the other hand, sometimes the student didn't mean to ask quite
such a deep question. We can discuss inertia at a less-deep level.
For instance, we could discuss what would happen if there were no
inertia, or very little inertia. To say the same thing more formally,
what would happen in a world where the Reynolds numbers were much
lower? Bacteria, for instance, live in such a world. Viscous forces
completely dominate inertial forces. They cannot "swim" the way
people swim, by throwing water backwards; instead the ones that
"swim" use flagella to corkscrew their way through the viscous
fluid, using viscous forces rather than inertial forces. The law
of motion in such a world is that objects at rest remain at rest,
and objects in motion quickly come to rest ... i.e. it is very
non-Newtonian. The details are far beyond the scope of what is
appropriate for a student who doesn't yet have the first clue about
what force is ... but I mention them to show that the student's
question is not trivial, not a dumb question at all.

2) If we assume that there will be some inertial force, maybe "the"
question is how does the material know to apply just the right
amount of force /at the point of contact/. The suggestions about
bowstrings, foam, optical levers on the wall, etc. all address
this point. I see much merit in in these suggestions, but we
should realize that they do not lessen the merit of the other
suggestions on the list.

3) There is also merit in shifting the whole discussion away from
force and reformulating it in terms of momentum.

Remember, we are collecting a toolbox full of good plausible hypotheses
as to what "the" problem is, and the more the merrier.

The best way to test these hypotheses is to interact with the student,
but in the absence of that, all we have to go on is the report that:

'Where does the disk get the
extra force when I push up with more force than its weight?' was her
repeated question.

This question can be interpreted in multiple ways, so there are multiple
possible answers.
1) The disk gets the extra force from inertia. We don't know why
inertia exists, but we know it does exist.
3) The disk doesn't need to get the force "from" anywhere, since force
is not a conserved quantity. Momentum is the corresponding conserved
quantity.
2) Forces can come and go at a moment's notice. The force is "steered"
to the point of contact by elastic effects. And using something
compliant like foam or bowstrings allows the force to be visualized.

============

What's easy for one student may be hard for another, and vice versa.

As for me personally, I figured out about momentum at an early age, based
on hijacking railroad cars and other experiences with things that had a
*lot* of momentum.
http://lists.nau.edu/cgi-bin/wa?A2=ind0109&L=phys-l&P=R34680

When I was eight years old, I'm not sure I could have explained what
"inertia" is, but I certainly understood what *momentum* is.

The interesting thing about pushing cars is that it takes just as
much pushing to get them stopped as it did to get them started.
After you've pushed a few cars, this idea becomes pretty clear.
But for a student who doesn't have much car-pushing experience,
this idea (conservation of momentum) can be pretty mysterious.
A lot of students seem to live in a pre-Newtonian world where
inertial forces are negligible compared to viscous forces, so that
an object at rest remains at rest and an object in motion quickly
comes to rest.

I suggest doing the car-pulling exercise, with a real car, with
students doing the pulling. I recommend pulling with ropes,
(as opposed to pushing) to increase safety; you don't want somebody
to slip and fall under a wheel.

There are various ways of arranging the details; one way is
to set it up as a tug-of-war game, with the car in the middle.
Unlike the usual tug-of-war situation, the two teams can take
turns: team "A" puts +X momentum into the car, and then team
"B" is required to get rid of that by pouring -X momentum into
the car.