Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Apparent weight



On Wed, 18 Feb 1998 Raacc@aol.com wrote:

First, I apologize to A. R. Marlow and the list for my last few posts. They
have been too cynical...

I'm sorry to say that I somehow misplaced your earlier post before
having a chance to respond, so I'll try to respond from memory. Cynical
or not, it seemed to make some good points. I don't have any problem with
teaching a Newtonian model of gravitational force -- it's a good model
as long as you can avoid the problems connected with instantaneous action
at a distance (conflict with special relativity, Etc.), and it gets us to
the moon and beyond. No place in it is there any need to introduce any
fictitious forces with no third law correspondents.

For the first half of a course in physics for nonphysicists I use it
totally. We go into some detail in discussing the fictitious nature of
the outward force people imagine acts on them when they are in circular
motion, such as in a centrifuge, and it is pointed out that IF such a
force really acted on the moon, counterbalancing the gravitational pull
inwards, then the moon would not be in orbit around earth, but would
instead sail off in rectilinear motion.

Thus prepared, the students can see one example where a "force" disappears
on careful analysis. Then, in the second half of the course, where we
want to lead them into some understanding of the advance to a better
theory of gravitation, we can point out how Einstein was able to replace
Newton's idea of gravitation as a force with gravitation as the effects
observable from living in curved spacetime. Then the weird aspects of
gravity as a force, the ones that so puzzled Einstein -- e. g., why does
it accelerate all masses equally -- immediately vanish. If gravity is
geometry then it SHOULD affect all masses in the same way.

The same approach, at a more advanced level, seems to work well with
physics majors also: teach them everything there is to know about
Newtonian gravitational force theory, including from time to time some
hints of the problems with it (instantaneous action at a distance, same
acceleration for large and small masses, unlike any other force, Etc.),
indicating that they will see the solutions to these problems in general
relativity. Then, say in the second semester of junior year mechanics,
toward the end, lead them into the better view of gravitation as geometric
curvature of space and time.

First, I'll assume that whatever Newtonian mechanics tells me concerning the
motion of a mass, GR will tell me the same thing at least within the scope
where Newtonian mechanics gives good results.

If I drop a ball, then I see it is accelerating with respect to my frame of
reference. To analyze this using Newtonian mechanics, I would say there is a
force acting down on the mass and describe this force as the weight. I'd
write (I'll assign up as my positive direction):

Fnet = ma
-W = ma
-mg = ma
a = -g

I would therefore conclude that the weight being the only force, the
acceleration would be g downward.

Now, Marlow states that W is a fictitious force, so I don't want to include it
on the Fnet side of the equation (where the real forces belong). Therefore, I
move it to the right side (as a frame of reference acceleration) and write:

Fnet = m(a+g)
0 = m(a+g)
a = -g

This says that when no force is acting on the mass, then it will have an
acceleration of g with respect to my frame of reference, the same result as
Newtonian mechanics.

Now, I stand on the floor and feel a force acting up on me. In Newtonian
mechanics I write:

N - W = ma
N - W = 0
N = W
N = mg

In GR I write:

N = m(a+g)
a = 0
N = mg

Now, I stand in an elevator that is accelerating. In Newtonian mechanics I
write:

N - W = ma
N = m(a+g)

In GR, N is the only real force and write:

N = m(a+g) directly.

How am I doing so far? Got to go to class.

Bob Carlson


Great. Keep going! To do Einsteinian gravitation instead of Newtonian
action-at-a-distance force gravitation, we have to recognize what Einstein
came to see: inertial frames must be freefalling and nonrotating.
Frames fixed to the earth's surface are neither. The earth's
surface pushes on us with a real force, making us deviate from our proper
inertial freefall motion in local spacetime, and that's the only force
acting on us. But we don't have to teach Einstein's gravitation from the
start; Newtonian theory can be a fine introduction, and many need never
move beyond that. But all of this is getting far afield from the question
of introducing fictitious forces into Newtonian theory.



A. R. Marlow E-MAIL: marlow@loyno.edu
Department of Physics, Box 124 PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453