Re: [Phys-l] g...

[Hugh Haskell <hhaskell@mindspring.com>]

At 14:05  -0600 11/18/06, Cliff Parker wrote:
> I have a problem with g.  Despite my best efforts many of my 
> students still want to say that g is a force.  I can see where the 
> whole thing would be confusing for them.  Our first experience with 
> g is to call it the acceleration of gravity on Earth.  I stress over 
> and over that it is not "gravity", it is not "the force of gravity", 
> it is the acceleration that objects undergo as they fall to the 
> Earth.  However, bout the time I think that I have that idea pumped 
> into their heads we start using g to find weights w=mg.  Now the 
> object is not accelerating at all so what's g?  I usually only 
> address the idea that g is now being used as a constant that 
> represents the strength of the gravitational field if one of my 
> students brings it up, and that's not very often.  Maybe that's a 
> mistake.  Now g is appearing once again in Newton's Universal Law of 
> Gravity this time twice... Fg = G m1 m2 / d^2   I asked my students 
> to describe what g was on a quiz yesterday and got back answers that
>   were all over the map.  Any advice?
Cliff, you have caught exactly what I have felt for years is the 
problem of how we present g as a concept. If we forget the idea of g 
as an acceleration, and treat it as the gravitational field strength, 
which, because of the equivalence (apparent, but subject to 
experimental verification) of gravitational and inertial mass, 
happens to have the units of acceleration, and also happens to 
represent the acceleration of a freely falling object when not 
subject to any retarding forces, then we might be able to start 
making progress on what g means.

Too many texts present it as some sort of constant of nature, which, 
of course, it is not. And if we think of it as the gravitational 
field strength, then when we multiply it by the gravitational mass, 
we get a force, which some (but not me) call "weight" (I choose to 
call it "the force of gravity").

The parallel with electric force is then quite straightforward. If 
the force of gravity is the gravitational mass times the 
gravitational field strength, then the electric force is the 
electrical "mass" (AKA "charge") times the electric field strength.

Now, if either of these forces is a net force on a given object, and 
we divide that net force by the intertial mass, we get the 
acceleration of the object.

In the gravitational case, because of the equivalence of inertial and 
gravitational mass, the acceleration happens to be numerically equal 
to g, although it is a long way from being conceptually equal to g. 
On the other hand, there is no such conceptual disconnect in the 
electrical case, since everyone knows that electrical mass and 
inertial mass are not equivalent, and so the acceleration of an 
object under the net force of electricity in not equal to the 
electrical field.

So, as I see it, the issue is the historical precedent of calling g 
the acceleration of (or due to) gravity, which dates from an era when 
none of these niceties were thought of (although there is evidence 
that Newton had some concerns along these lines, but apparently no 
one else picked up on them for a long time).

So, I think that we would be better off all 'round if we dropped two 
phrases from our vocabularies: "acceleration due to gravity" (call it 
gravitational field strength), and "weight" (call it the force of 
gravity). Those two phrases seem to me to be the source of much of 
the confusion that students have (and I know I certainly had that 
confusion for a longer time than I like to admit).

Hugh
--

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

(919) 467-7610

When you are arguing with a stupid person, it is a good idea to make sure that
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					Anonymous