Re: Nitpicking: gravity is not a force???

[Hugh Haskell <hhaskell@mindspring.com>]

Ai Phing Wrote:
> My students tend to think of g as the force.  And I have to keep
> correcting them that it's acceleration, not force.  I use the words
> "gravitationl pull" or "weight" for force though.  I never thought of
> gravity as a field.  That really clears things up.  (Understanding comes
> really late in life....)
[snip]

Be very careful how you use the language when talking about "g." Students
hve more trouble with this concept than almost anything else in mechanics.
Clearly "g" is not the force of gravity. That is "mg." But neither is "g"
an acceleration, and this is one of the problems that students have. "g" is
properly the strength of the local gravitational field (corrected for the
rotation of the earth), and it should not be confused with an acceleration.
The fact that a freely falling object (in a vacuum) near the earth's
surface falls with an acceleration numerically equal to "g" is due to the
fact that what we call "inertial mass" and "gravitational mass" appear to
be the same thing (this is the first step towards Eintein's general theory
of relativity), and so we can cancel the "m"-term out of the second law
equation mg=ma. I know that I am fighting a losing battle in trying to get
textbook to stop using the phrase "acceleration due to gravity" as the
definition of "g" but I think this is why so many students are confused on
this point (as I was at that stage as well). It is important to be aware
that the equation w=mg is *not* a statement of Newton's second law, but
rather a rule for calculating the force due to the action of the
gravitational field on an object of gravitational mass m. On the other
hand, the equation F=ma, is not a rule for caclulating forces, but a
statement of what happens when a force F is applied to an object of
inerttial mass m. In other words it is properly a statement of "cause and
effect."--a dynamical statment about how matter behaves under the influence
of forces. Thus, although w=mg and F=ma look similar to the beginning
student, they are really very different entities.

This idea becomes really important when you get to circular motion, and
students try to create a "centripetal force" as a separately applied force
on an object, rather than treating it as the resultant of the other applied
forces that are making the object travel in a circle. When we write
F=mv^2/r we are really saying that the sum of all the applied forces on an
object of inertial mass m are such that it travels in a circle with
centripetal acceleration v^2/r, and the applied forces are such things as
tension in a string or rod (spokes of a wheel, etc), normal forces of the
rails (i.e. roller-coaster, etc.), the friction force on the wheels of a
car in a curve,  or the force due to the gravitational interaction of the
earth and moon, or the electrical interaction of the proton and electron,
or the magnetic force on a moving electron, and so forth. In other words,
there is no "centripetal force" in its own right, but we know that an
object moving in a circle at constant speed must be subject to a net force
which gives it an acceleration directed toward the center of the circle and
is of magnitude v^2/r. I have observed teachers try to apply a "centripetal
force" to an object moving in a circle, and then get really confused when
things don't work out the way they know they should, and it almost alwyas
arises because they forgoet (or never realized) that the centripetal force
appeared only as the resultant of other forces and not as a separate force.

There is a great deal more that could be said about this, but I'm sure you
get my point, so I'll stop before I overdo it, if I haven't already.

Hugh


Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
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