Re: [Phys-l] Equations (causal relationship)

["Michael Edmiston" <edmiston@bluffton.edu>]

The picture is great.  Now I understand the previous description.

As for the following...

> Yeah, so what?
>
> The decomposition of zero net acceleration can be done many ways;  my
> chosen values a1 a2 a3 are not unique ... but in the same breath I
> point out that the decomposition of zero net force can be done in many
> ways;  the values F1 F2 F3 are not unique.

I thought we were trying to demonstrate that the accelerations and 
forces had to be connected by m, not just any number.  Yes, F1 F2 F3 are 
not unique, but once the forces are chosen I thought the goal was to 
show that the accelerations are then determined by F = ma.  I now see 
that F(net) = 0 is a special case for which this can't be done.  Duh!

Thinking out loud here... If your drawing is used for a case in which 
F(net) is not zero, then your red, green, blue stages cannot have 
arbitrary accelerations, but must have the F = ma relationship if the 
red stage and particle are to have the same acceleration.

So... if the red stage is moving relative to the particle, we adjust all 
the stages as necessary to stop the relative motion.  No wait.  Relative 
motion is okay if constant velocity.  Rephrase... if the red stage is 
accelerating relative to the particle we adjust the accelerations of all 
the stages until the red stage is not accelerating relative to the 
particle.

But if the accelerations are matched and the velocities are not, the 
springs will stretch.  So it seems your apparatus requires that the 
stages be adjusted so that the red stage has the same velocity as well 
as the same acceleration as the particle.  We should be able to measure 
the accelerations even if the particle and our measuring device are 
moving in different inertial frames?

I guess it is the connection between the red stage and the particle 
(through the spring) that is the problem.  Don't we just want to have 
your stages near enough to the particle (but not connected) so that we 
can observe when the red stage is not accelerating relative to the 
particle.  Assuming we have the same number of stages as forces, and 
each is aligned with one of the forces, then by adjusting the stages 
until the accelerations are matched, we have measured the individual 
component accelerations.  I see the light.


Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu