Re: [Phys-l] Weight?

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

My take on weight is that it has been sufficiently confused that we should
possibly do away with the term in common physics usage.  The two definitions
that it is the "effective gravitational force" or just the gravitational
force are both used commonly in textbooks.  So in the two definitions the
term weightlessness in the space station is correct or incorrect depending
on the definition.  I would say generally stick to the term gravitational
force and avoid weight in most problems and examples.  Nobody has been able
to agree on the definition, and the texts are random.

And can the equation N=mg.  It is poor notation and incorrect in many cases.
If you lean against a wall the normal force F_N is NOT equal to mg.  The
notation of N, T... separate symbols for forces reinforces the idea that
each force is a different "thing".  But F_N (subscript N) reinforces the
idea that forces are the same thing, but involving different agents.  And of
course the following problem:  You have a 1kg mass on a table being pushed
down by a spring.  The spring has k=2N/cm and the spring is compressed 3cm.
What is the normal force exerted by the table on the mass.  If they learn
N=mg they will calculate the normal force as 9.81N.

If you must use weight as a term, I favor F_g=mg and is called the weight on
the surface of the Earth and is the gravitational force exerted by the Earth
on the object.  I also would always use the term "gravitational force" and
never the "force of gravity" because it implies "gravity" is the agent.  It
should be "force of the Earth on the object".  This seems nitpicky, but
students think of gravity as this mystical thing, and fail to associate it
with the Earth.  So if you ask them "What physics thing pulls you down",
they will say gravity, but it is not a physical thing.  Even after I say
that physical things are things you can taste, touch, see or feel, they
still say gravity.  So I ask them what is the color of gravity?  Actually
better notation would be F_(g, E on O) meaning the gravitation force of the
Earth on the Object, but that might be a wee too complex for many students.

I realize you said it can be "shown" that N=mg, but when students are given
that as an equation they memorize it and use it inappropriately, but F_g=mg
is just an empirical force formula, and they have to use it with other force
formulas to get answers.  The normal force has no formula and must be
decided by looking at other forces and the motion.  So sometimes F_N=F_g,
but in the problem I presented F_N=F_g+F_E (gravitational, elastic).  And
how you have them treat signs is another issue so I just presented it in
terms of the magnitudes.  I am convinced that rigid sign conventions remove
the thinking and become incantations, so I generally don't use them.

Trying to make weight an upward force may be a bit too foreign to students
because they KNOW that your weight pulls you down.  So associating it with
the gravitational force on the Earth may make much more sense to them.

In general extra equations should be avoided.  In other words only equations
that are necessary should be used.  The usual 4 SVT equations encourage
equation hunting, and derived equations such as N=mg then fall into that
category.  Students become very adept at just plugging into equations
without any thinking about why the equation is used and if it is
appropriate.  Unfortunately most of the texts sabotage you by giving all
kinds of handy equations which can then be used inappropriately.

This has been around the list many times, so you may have ignited another
firestorm.

John M. Clement
Houston, TX 

> What is weight?  Sometimes, when the origin of the lay word has not been
> technically defined (as is done in mathematics), it helps to find its
> etymology.  The etymology of "weight" goes back to "lift."  It, therefore,
> appears that the weight of a body has been considered an upward force.  I
> tell my students that weight is a force of support, pointing vertically
> upward.  From Newton's laws it follows that weight is equal and opposite
> to the force (pull) of gravity on the body.   It can then be shown that N
> = mg.  What I emphasize to the students is that mg (pull of gravity) is
> due to the whole Earth, including India, China, the Pacific Ocean, etc.;
> but N (the force of support is due only to the floor which is in contact
> with the soles of the shoes.  The agent of the force is completely
> different on the two sides of the equation.  I do not attempt to confuse
> the students with corrections that might exist from the Earth's rotation,
> Special Relativity, General Relativity, Quantum
>   Field Theory, String Theory, or any other such.