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short replies (not)




Here is the wording that led me to believe that you were talking about some
sort of PN version of Newtonian mechanics; I apologize if I misunderstood
that. I agree with the post from Espinosa who said that we oughtn't have to
bring GR into this discussion, so except in the example cited by Marlow
concerning force sensors and GR and the levitated cube example I'll stick to
Newton's three laws. The 3rd law limitations I'm referring to are simply
that it doesn't apply to magnetic forces. I'm not sure the 3rd is germane to
the discussion, but it may be in regard to how spring balances work.

(Note: Paul Camp, correctly pointed out in another post that we should
really say local free-fall frames; I references I make or made to free-fall
frames should be interpreted in that fashion.)

I should point out that free-fall frames are not inertial frames in
Newtonian physics.
...

They weren't able to be recognized as such by Newton, but they are
certainly
recognized as such in 20th century Newtonian physics. I use that term to
refer to the very accurate Newtonian approximatian to GR that works so well
in the weak field of the solar system.

I'm curious to learn how others on the list would answer the question
regarding how many force vectors you draw acting on a book sitting on a
table in a force diagram. I think Marlow more or less begged the question.
Comments please!!

...
I'm curious, how many force vectors does Marlow draw acting on the cube
(book) when he explains Newtonian mechanics to introductory students?
...

Regarding the charged cube levitating in the electric field. Marlow wrote:

Then attach the spring scale directly to the cube. It would still show
exactly the same thing -- attached to one side (what I called "up") the
scale would stretch, and you can see both the amount and the direction
of the force you have to apply to the cube to keep it from accelerating
relative to your lab. On the opposite side of the cube you would have to
push in the same direction by the same amount to do the same thing.

My experience with playing with springs tells me that the spring balance on
top of the cube won't stretch at all. Unless I actually pull up on the
spring, which is adding an additional force then the one I was trying to
measure in the first place.

Later he and I write:

jr>> ... (Note: a spring
jr>> balance works by measuring acceleration, we first measure the
acceleration
jr>> of the object relative to the spring, then take the reading;
...

am>Now I am truly and totally confused. If spring balances work by
measuring
am>acceleration, than I and every grocer in the world have been sadly
misusing
am>them and cheating the public. I thought we were supposed to wait until
am>any disturbing oscillations (accelerations) had died out before we took
am>a reading from the DISPLACEMENT of the scale.

I don't see why there is confusion, Marlow operational description of using
a spring balance is exactly what I indicated; in his description of the
operation of the balance: you first arrange things such that
"(accelerations) had died out"; namely you measure the acceleration to be
zero! then take the reading. If you don't arrange things first so that the
acceleration is zero you get spurious results.

In fact his grocer is going to say the spring balance read a force that
balances out gravity; just as in the rotating frame of reference the spring
balance attached to my left arm and the left door handle will measure a
non-zero force as I'm accelerating towards the right door handle.

We apparently disagree on the direction of the force that a spring balance
measures; Marlow says that it measures the direction of the force to be in
the direction of the force of the spring on the object. I think that in
practice we all use a spring balance to measure some other force and we
arrange things so the spring force balances that other force which we are
trying to measure. That is we use the third law in order to use the spring
balance to measure some other force pointing opposite to the direction of
the spring force on the object to which it is attached, which is the purpose
using the balance in the first place.
_____________

.... The integral to the centrifugal force dot dx will equal my
change in kinetic energy...

Not in any physics that I know, unless you put in "zero" as the
value of the centrifugal force, which of course will give you the
correct zero value of change in kinetic energy (as a dynamic quantity,
kinetic energy has a simple relation to acceleration or velocity ONLY
in inertial frames).

Yes it does, I measure my velocity at the beginning and end of a time
interval, before I contact the door handle; compute 1/2 mass vel_final^2
minus 1/2 mass vel_init^2 and find that it equals integral of
mass*const1*(const2 + dist from left door handle) X dr. Const1 and const2
can be determined solely from measurements in the non-inertial frame of
reference by doing the following:

put a spring scale between me and the right door handle. Repeat with a 10 cm
block of (sufficiently non-compressible) wood between the right handle and
the spring scale which is between me and the block of wood. We now have two
equations and two unkowns which is sufficient to find the two constants:
Namely

mass*const1*(const2 + dist 1) = first spring scale reading

note: dist 1 = left door handle to right door handle distance

and

mass*const1*(const2 + dist 2) = second spring scale reading

Note: dist 2 = left door handle to right door handle distance minus ten cm
(assuming a very thin spring balance; i.e. a pressure sensor)

Hence the work-energy thm applied.

Note: if I know about the fact that I'm in a rotating (non-inertial frame)
then I can interpret const1 and const2 in terms of the relative motion of
the frames of reference (but I don't have to do that in order to do the
physics and get correct predictions for the motion of the object (my poor
body being thrown about the inside of the car as I repeat experiments to
find my constants)

The interpretation, as everyone knows, is const1 = angular speed of one
frame relative to the other and const2 = the distance of the left door
handle to the center of rotation of the one frame relative to the other.
(Note: we're driving an American car and are turning CCW as the crow would
view it.)
________________
Later we have:
...
The problem with the above viewpoint is that it reduces dynamics to
kinematics; while OK mathematically and doesn't lose the self-consistency
of
the theory. (Marlow and I get the same numerical answers to problems)
....

As far as I can see, we don't at all get the same answers for any
dynamical quantities such as energy, work, momentum, mass.

I think we would get the same answers, because in the end we are solving the
same mathematical equations. The only way to know for sure is to have us
work the same problem. A partial attempt at that is in my above description
of the analysis of the change in the square of the velocity of my body as
determined solely by measurements in the non-inertial frame.
_____________
we also have:

... Once I'm in contact with the
door handle the none of the forces present are doing any mechanical work
as
my kinetic energy isn't changing (nor is my velocity vector changing
direction! in this frame of reference; ...

True, your velocity relative to the noninertial frame of the car is no
longer changing, but real work is being done, real bruises are being left,
and your kinetic energy is changing, and infrared detectors will detect
the dissipation that must accompany real physical processes.

I don't understand this, at the point in which my velocity relative to the
car is zero, even analyzed in the inertial frame we have no forces doing any
work; centripetal forces do no work. ( I think this is just a
misunderstanding as to what point of the process we are talking about)
_______________
If I follow Marlow's comments regarding confusion of dynamical and
kinematical quantities I arrive at the following:

Never ever, compute mass times velocity and call it momentum, 1/2 mass
times vel^2 and call it kinetic energy unless you are in an inertial frame
of reference etc. These dynamical words are reserved soley for calculations
done in inertial frames of reference. And only kinematical terms can be
used in non-inertial frames of reference; i.e. position, velocity and
acceleration.

This is a valid postion but can make working problems in non-inertial frames
of reference difficult (your always having to transform back and forth
between frames) and I assume is why the oceanographer guys don't do it this
way. (I'm not an oceanography, so if I'm mis-representing the community I
apologize; this is bases on my small knowledge of the field and what the one
person from the oceanographer community had posted)

BTW this means that almost all problems worked in introductory texts books
on the surface of the earth are wrong; because the moment they say that the
child sliding down an incline plane has a kinetic energy of 1/2 mass time
vel^2 they have incorrectly used a dynamical concept.

My viewpoint is: Newton's laws when transformed from an inertial frame of
reference to a non-inertial frame of reference are formally equivalent to
Newton's laws in an inertial frame if we call the "fictitious force" terms
forces. This is what I mean when I say I get correct answers by applying
Newton's laws in the non-inertial frame.

I recognize that these "fictitious" forces are not real, in sofar as they
are fundamentally different from "real" forces, namely they arise for purely
kinematical reasons and are therefore a kinematical effect (a real effect
non-the-less, nobody has ever suggested that the coriolus acceleration is
fictitious, which is my point). They also have other interesting properties,
namely they are always proportional to the mass of the object.

BTW thanks to Rick Tarara for actually having read all of these postings.

One last thought, What is Newtonian Mechanics?
My current answer (which may change after this thread finally dies) is:

Its a system for the prediction of motion of objects under the influence of
each other. It is done by taking Newton's three laws and experimental
determinations of forces, combining the two and turning the crank.

I say it is more than Newton's three laws for reasons I think Marlow would
agree with, i.e. If we take the 2nd law to define forces, we do reduce
dynamics to only being kinematics; and I don't want to do that, neither does
Marlow. (see the future part III posting)

Thanks as always to the patient.
Joel Rauber
rauberj@mg.sdstate.edu