Re: N/kg versus m/s^2

["Moore, David" <DMoore@GDA.ORG>]

Title: RE: N/kg versus m/s^2

One person thus far (M. Edminston) in this discussion of the meaning of "g" has mentioned the view of General Relativity of the equivalence between the concepts of gravity and acceleration, but thus far I have not seen any mention of the difference between the inertial mass in F=ma and the gravitational mass in F=mg.  Perhaps since they are proportional in an inertial reference frame and can be considered to be identical in equations such f=ma and f=Gm1m2/r2 if the proper units are used, can help explain the "equivalence" of the m/s2 and N/kg units.

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                   David D, Moore: Physics Teacher 
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-----Original Message-----
From: John M. Clement [mailto:clement@HAL-PC.ORG]
Sent: Friday, January 26, 2001 7:22 AM
To: PHYS-L@lists.nau.edu
Subject: Re: N/kg versus m/s^2

Yes we all know that one may convert units and show the equivalence between
N/kg and m/s^2.  However, the central point is that using g=9.8m/s^2 is very
confusing to new physics students.  When they see F=mg and g is given as an
acceleration, it does not make sense to them.  A book on a table is not
accelerating, so using an acceleration to calculate the force is nonsensical
(from the student's point of view).  Telling them or trying to explain this
to them is useless, as the growing body of PER research has shown.  Going on
and appealing to fields is even worse.  No wonder most students just
memorize equations and consider physics to be incomprehensible!!!!!

I would not explain that gravitational mass and inertial mass are
equivalent, as that is a very subtle point which would confuse most of them
even more.

Now as to the objection to the word because.  Students see that g is
expressed as an acceleration, so they assume that the object is accelerating
when it is not, or that there is no/less/more gravitational force depending
on the motion.  Having taught it both ways, I can assure you that the
conventional treatment does not work well.  The overwheming majority do not
understand the conventional treatment of g.  The research shows that there
is a total disconnect between what most teachers try to tell their students,
and what the students actualy hear and percieve.

I used the words more rational, because it makes more sense from a
pedagogical point of view, and gives better results (student learning).  It
also is MUCH more rational to the students.  The more effective treatment
initially uses g as simply a parameter in an empirical force law F=mg.
Later on students can identify this with NTN's universal gravitational law.
This is not the only possible treatment, but it helps expose the connections
to the students in a manner that they can understand.  Students should be
able to get clues from the units, and they need help in making connections.
The other benefit of making g a proportional constant is that students can
discover g with a spring scale and balance.

Another part of the problem is because students do not generally think in
equations.  They tend to write F=10kg 9.8m/s^2 without first stating
F_gravitational=mg.  This looks like NTN's 2 law.  They pick up on this, and
then confusion reigns.

Formal arguments are totally lost on most beginning students.  Indeed the
range of thinking in many HS classes goes from middle concrete up to full
formal thinking.  A large number of HS seniors still do not understand
conservation of volume, which is supposed to click in at age 6.  As a result
there is a distinction between N/kg and m/s^2 in the minds of the students,
if they even notice the units.

Again, I would point out that the panel of physicists who reviewed HS texts
in TPT concluded that a more "useful" definition of g is derived from NTN's
gravitational law and should not be 9.8m/s^2 p299 (May 1999).  While this
review gave much good information, it made no attempt to evaluate texts on
their actual effectiveness.  They also did not mention any of the research
based curriculum material.  I suspect that none of the rated books actually
promote better understanding.

John M. Clement

>
> At 08:28 PM 1/25/01 -0600, John M. Clement wrote:
> >The equation F=mg is calculating the gravitational force on a
> given mass at
> >the surface of the earth,
>
> OK.
>
> >while F=ma is Ntn's 2 law.
>
> OK.
>
> >Unfortunately the majority of texts state that g is the gravitatonal
> >acceleration, while it is nothing of the kind.
>
> Huh?  Nothing of the kind?  It sure looks to me like something of
> that kind.
>
> >   g = G m_earth/r_earth^2 ignoring the complications of
> >the Earth's rotation.
>
> OK.
>
> >The first year physics student especially the HS student, does not
> >understand g in the standard text because obviously the object is not
> >accelerating.
>
> I'll agree with the main parts of that sentence _except_ the
> "because".  It
> may occur that some students don't understand g.  It may occur that some
> object is not accelerating.  The relationship between these two
> occurrences
> is vastly more complicated than a simple cause-and-effect relationship.
>
> >Under the more rational treatment g is then stated as being
> 9.8N/kg at the
> >surface of the earth, not 9.8m/s^2.
>
> According to physics as I understand it, 9.8N/kg is formally identical to
> 9.8m/s^2.  The foregoing attempts to create a distinction without a
> difference.  Calling it "the more rational approach" doesn't make it
> rational.
>
> I assume the idea is to focus attention on the force, so that we can add
> forces.  We may find there are forces, but no net force, which
> explains why
> the object mentioned above is not accelerating.  On the other hand, if we
> can add forces, pray tell why can we not add accelerations and come to the
> same conclusion (no _net_ acceleration)?
>
> >The gravitational acceleration is still 9.8m/s^2, but that is
> not the same
> >thing as g.
>
> This appears to be a restatement of the previous
> pseudo-distinction between
> 9.8m/s^2 and 9.8N/kg.  It remains inconsistent with the laws of
> physics.  Indeed one need not even apply any principles of physics;  just
> look up the definition of the symbol "N" and apply the laws of algebra.
>