Re: [Phys-l] A question about the Earth's gravity

["John Clement" <clement@hal-pc.org>]

> I agree that until you get to NLG, it can be tricky to use the word
> "Weight" and the equation W=mg.
However, F_g is a well defined term.  W=mg is not well defined because
different authors define weight differently.  The gravitational force in
Newtonian mechanics can be well defined.  Also to make the subject coherent
special symbols for the same concept should be avoided.  So F_g instead of
W,  F_n instead of N...  Similarly for gravitational acceleration you would
use a_g, and all acceleration would be labeled a with an optional subscript.

Actually, there is some research which shows that the order of material will
improve student understanding.  So interactions should be introduced before
Newton's second law.  If you do this, then the idea of gravitational force
should be introduced at the same time as all other "common" forces such as
normal, tension, frictional, buoyancy.  The term weight does not have to be
mentioned at this point and the equation for gravitational force has a
constant with the units N/kg.  The main advantage here is that Newton's
third law is actually introduced first, which improves understanding of it.
An even better approach is to use agent object notation such as F_g Eonb  or
gravitational force of Earth on the boy.

Then the second law can be introduced, and finally the first law.  But it is
never necessary to introduce the term weight, thus avoiding some problems.
If students start using the term weight, you can just say it is the
gravitational force, but it will not be allowed in explanations because it
has not been formally defined.  It is amazing that authors of texts seem to
think the laws have to be introduced in correct numerical order, while
research shows the reverse order is better.

The idea of introducing both the local and general gravitation at the same
time is reasonable, but not for most HS classes.

So initially the gravitational force is presented as decoupled from the
gravitational acceleration.  It is quite amazing how when students have to
do some simple calculations of falling bodies they do not notice that they
always get the same number for the acceleration as the constant in the
gravitational force equation.  But this still a good thing, because they are
forced to think first about the forces, and then to find acceleration rather
than taking shorcuts.  Later on they notice that the two numbers are the
same, and some even understand why.  They have actually memorized from a
previous physical science courses, the gravitational acceleration as 9.8,
but since they use g=10 N/kg which they found in a lab, they do not
associate the two numbers.

Of course this is because most HS physics students tend to range between
4/12 to 12/12 on the Lawson classroom test of scientific thinking skills
with an average around 6 or 7.  This means that the vast majority do not
have proportional reasoning, and have extreme difficulty with formal models.
Incidentally most intro college physics courses have similar students with
perhaps a higher cutoff at the bottom.  Scores of 1-4 are concrete
operational or pre age 10, 9-12 would be formal operational, and 10 appears
to be the threshold at which students can gain 100% on a conceptual physics
test.  This is for the published test in Lawson's book.  The multiple choice
version is slightly different.

Since most students lack proportional reasoning it is impossible for them to
understand why the gravitational acceleration and the field constant are the
same (neglecting small factors like buoyancy...).

John M. Clement
Houston, TX