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

[John Denker <jsd@av8n.com>]

Michael Edmiston wrote:

> Can you draw a picture?

  http://www.av8n.com/physics/img48/f3a3.png

The rectangles represent the translation stages.  Each stage moves in the
direction given by the long axis of the rectangle.

The red stage moves relative to the green/striped stage.
The green/striped stage moves relative to the blue stage.
The blue stage moves relative to the table.

The particle of interest is shown as a gray disk.  It is not attached to
anything except the three springs.

The springs represent the three forces.  That is, by observing the elongation
of the springs, we can ascertain the forces being applied to the particle.

One spring is anchored to the red stage.  The other two springs are anchored
to posts attached to the table.  The other (non-anchored) end of each spring
attaches to the particle.

The springs produce three nonzero forces F1 F2 F3 that sum to zero.

The stages produce three nonzero accelerations a1 a2 a3 that sum to zero.

The particle is attached only indirectly to the top stage, but we can
observe that the particle does not move relative to the top stage, so
the acceleration (zero) of the top stage is also the acceleration of
the particle.  You can reach the same conclusion in several other ways,
including by using a verrrry stiff spring to connect the particle to
the top stage.

> He said to align the moving stages with F1, F2, and F3 respectively, and 
> adjust their operation so that they accelerate with a1 = F1/m, a2 = 
> F2/m, and a3 = F3/m.  Okay, but they could also be adjusted to F1/k, 
> F2/k, and F3/k where k is any number.

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 hate to sound like a stuck recording, but the point remains:
anything you can say about the force vectors I can say about the
acceleration vectors.  They're vectors.