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Re: The sign of g



Mike Edmiston writes:

Robert Cohen asks if g can be a vector pointing downward. If we do t=
his, what does it represent? As others point out, g itself is not th=
e acceleration.

Hugh Haskell writes:
I forget who pointed out, that this is a good reason for not teaching
acceleration before teaching about forces, but I agree
whole-heartedly. I think a much more logical approach is to talk
first about constant velocity motion, then introduce the idea of
momentum, followed by force, which leads to Newton's laws and then
acceleration becomes a natural concept, which helps to give substance
to Newton's laws. Our school's introductory syllabus, with a few
minor modifications, is basically this sequence, at least in one of
the two introductory courses we teach.

I plan on using a sequence much like Hugh uses. I will use it to answer
Mike's question.

When I get to the gravitational force, I identify an empirical relationship
between the gravitational force, F (a vector that points downward), and an
object's mass (a scalar). We find that they are proportional to each other.
I then introduce g as the gravitational proportionality constant. However,
if we write F_g=gm, where g is a scalar, we have a problem. Therefore, I
write g as a vector with the same direction as the gravitational force,
i.e., downward. It happens to have a magnitude of 9.8 N/kg on earth.

Once I get to kinematics, I use F=ma to identify a, which is a vector. If
F=F_g then a=g. Both are vectors.

Later on, when we encounter a problem that requires a kinematic equation for
the vertical components, we must use the vertical component of a. Since
a=g, a is 9.8 m/s2 downward. If you prefer to use +/-, convert "downward"
into +/-, depending on whether downward is chosen to be positive or
negative.

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301