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



Edmiston, Mike wrote:
Why don't we just agree as follows:
a) Sometimes ma is calculated from F and sometimes vice versa;
b) The equation F=ma covers both cases.


Absolutely. I've never had a problem with that.

We should probably just leave it at that.

==================

But being a glutton for punishment today:

I can imagine a particle having its net acceleration resolved into a 3D
coordinate system. I personally wouldn't say that a(x), a(y), and a(z)
are three simultaneous accelerations; rather, I would say they are
components of the one acceleration. Then, when a(net) is zero, I would
say all the components are zero.

Assuming x y and z are orthogonal, the only way the vector a(net)
can be zero is for each of its components to be zero. I didn't
think that issue was in dispute. I thought the topic of recent
discussion was three nonzero linearly-dependent accelerations that
added to zero.

Where I have difficulty is imagining three simultaneous nonzero
accelerations that add to zero. The only observable result is a(net)
equals zero. I cannot oberve the individual nonzero accelerations. I
don't think it is a failure of my imagination or my experimental skill
that I can't figure out a way to measure them, I think they cannot be
measured in principle.

I think they can ... in principle and in practice.

Here's how I visualize it:

Imagine three uniaxial translation stages, of the kind you see all
over the place on optical tables. Stack three of them together,
one atop the other. The particle of interest is attached to the
top of the stack.

Arrange that the first stage has its axis aligned with force F1, the
second one aligned with force F2, and the third one aligned with
force F3.

Arrange that the first one accelerates at the rate F1/m, the second
one at the rate F2/m, and the third one at the rate F3/m.

The three accelerations are nonzero. They add to zero. You can
see the stages moving, even though the particle does not move.

This is not the only combination of accelerations that adds up
to zero ... but F1+F2+F3 is not the only combination of forces
that results in equilibrium.

Anything you can say about force vectors I can say about acceleration
vectors. They're vectors; they add tip-to-tail.