Re: Force or acceleration first (was The sign of g)

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 17:22 -0500 9/4/02, Tim Folkerts wrote:
> The discussion of "g" seems to me to be a bit like the chicken & egg
> question.  There are two intertwined ideas that can't really be separated.
> You either have to say "you will understand acceleration better after you
> understand force" or " you will understand force better after you
> understand acceleration".
Yes, they are intertwined, and you have to deal with some aspects of
these intertwined concepts before you are in a position to really
explain them regardless of where in the cycle you start. That's a
stipulation from the beginning.

Here's the way we do it. One of the first things we do is to have the
students measure the "weight" of some standard masses, using a spring
balance. they then graph weight vs. mass and, of course, get a slope
of approximately 10 N/kg. That is their introduction to the concept
of g--within two or three days after the start of classes. All they
know so far is that their familiar concept of weight is being
measured in an unfamiliar unit, the newton. But we tell them is could
as easily be measured in pounds, ounces, tons, stone, or whatever
they like. We are using newtons because that is the standard unit
used in science, and besides, it gives a nice value for the ratio of
weight to mass (they don't know what mass is yet--that has to come
later). So at this point, g is the conversion factor between weight
and mass.

Then after they learn a little about uniform motion, we get them into
momentum--experimentally, sort of. The approach is probably closest
to the idea of guided inquiry, although the guidance is probably a
little closer than McDermott's books call for. They also do a lab
exercise where they get a pretty good confirmation of momentum
conservation (lots of different types of collisions, elastic,
inelastic, partially elastic--all graphed as final momentum vs
initial momentum, and then the best straight line drawn through the
points, which gives a slope of pretty close to one). After several
years of frustration with most of the book experiments on momentum
conservation, Bob Morse told me about this one, and it works
beautifully.

With momentum, then they have to deal with changes in momentum. And
what causes momentum to change? Force. With the concept of impulse
introduced it is an easy step to Newton's laws. Acceleration still
has not been mentioned, only changing velocity, in a very vague way.
But once we get F = delta-p/delta-t, and they know p = mv, then m
delta-v/delta-t becomes almost obvious.

This alone, of course, doesn't give them an appreciation of
acceleration, but it get the seed firmly planted. Acceleration is
something useful, even needed if we are going to look at the details
of collisions. To get a "feel" for acceleration, we often do the
"reproduce the graph" experiment using motion sensors, as has been
repeatedly touted here by Jack Uretsky, and a couple of other lab
exercises which give them a bit more feel for the concept.

Only after they have seen force and then how it leads nicely to
acceleration, to they get to figure out that g is more than just the
weight-to-mass conversion factor. But with that idea and Newton's
laws, we now reveal g as the local gravitational field strength (the
fact that it is slightly reduced by the earth's rotation is saved for
later), and they learn the equivalence of gravitational and inertial
mass that leads to free-falling objects accelerating at an amount
equivalent to the value of g.

With luck, they will now understand why g has been called the
"acceleration due to gravity" or any other of a long list of
misnomers, that had me confused clear into grad school. We alert them
to the fact that they will see g misdesignated that in the future,
but they need to remember that the best designation is in terms of
the gravitational field. (We don't do GR in this course).

Even though I was trained as a theorist, I look at this as pretty
much an experiment-oriented approach. Not historical, but logical.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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