Observer 1 & 2 View Force on Subject A: Analysis & Resolution

[Andrew Mason]

To define a reference frame you don't need a mass that is at rest in that frame.

There doesn't have to be an actual mass at rest in that frame, let's call it frame RF. But it is difficult if not impossible to define it without reference to a body with mass. The coordinates of RF are identical to those of a system whose origin is fixed to a body with mass at rest at the origin of RF. If you disagree, tell us how you would define a reference frame.

To keep a mass at a fixed position (or in uniform motion) the net force must be zero.

Only in an IRF. Not in a NIRF. In a NIRF things accelerate relative to the NIRF if the net (real) force on a body is zero.

AM

 

[Doc Al]

In a NIRF things accelerate relative to the NIRF if the net (real) force on a body is zero.

Thus the need for a pseudo force. Are we finally done?

 

[Andrew Mason]

Thus the need for a pseudo force. Are we finally done?

??
You seem to be agreeing with me AT's statement "To keep a mass at a fixed position (or in uniform motion) the net force must be zero." applies only in an IRF. So that's progress.

I agree that demonstrates the need for a pseudo force to explain the motion of objects relative to a non-gravitationally free-falling NIRF (eg. one that is mechanically accelerated). One must apply a force to keep them from accelerating relative to the NIRF. So you can only treat the NIRF as an IRF if you posit the existence of a mysterious (pseudo) force that is making them accelerate. But in a gravitationally free-falling NIRF one does not have to apply a force to keep them from accelerating relative to the NIRF. It is always there (gravity). So where is the need for a pseudo force?

AM

 

[Dale]

But in a gravitationally free-falling NIRF one does not have to apply a force to keep them from accelerating relative to the NIRF. It is always there (gravity). So where is the need for a pseudo force?

In a free-falling NIRF (in a uniform gravitational field) a free-falling object has a=0. Therefore, by Newton's 2nd law the net force on the object must be 0. In Newtonian mechanics it is acted on only by a real gravitational force of -mg. Since -mg≠0, there must be another force +mg acting on the mass. This is the pseudo force. With the pseudo force the net force is mg-mg=0.

 

[A.T.]

To keep a mass at a fixed position (or in uniform motion) the net force must be zero.

Only in an IRF. Not in a NIRF.

The whole point of inertial forces is to extend that to NIRFs.

 

[Andrew Mason]

In a free-falling NIRF (in a uniform gravitational field) a free-falling object has a=0. Therefore, by Newton's 2nd law the net force on the object must be 0.

In other words, we are assuming that the NIRF is an IRF and we are trying to make Newton's 2nd law work.

In Newtonian mechanics it is acted on only by a real gravitational force of -mg.

This is where I see a problem. I don't see how you can detect that gravitational force except by reference to a genuine IRF. There is no way to detect it by reference only to the NIRF. In the free-falling NIRF a uniform gravitational field is undetectable.

If it is undetectable I am having difficulty understanding why you need a pseudo force to counter-act it or explain it. Otherwise, what you are saying is perfectly reasonable and rather obvious.

AM

 

[A.T.]

In other words, we are assuming that the NIRF is an IRF and we are trying to make Newton's 2nd law work.

I told you that in post #18

In the free-falling NIRF a uniform gravitational field is undetectable.

Gravity is still a real force that exits in every frame. That is a nice simple law, easy to remember. You don't have to worry about detectability.

If it is undetectable I am having difficulty understanding why you need a pseudo force to counter-act it or explain it.

Every accelerated frame has an inertial force -ma. That is a nice simple law, easy to remember. You don't have to worry about what real forces act.

If all legal laws were so simple without special cases, then lawyers would be superfluous.

 

[Dale]

In other words, we are assuming that the NIRF is an IRF and we are trying to make Newton's 2nd law work.

What we are trying to do is to correctly describe physics in the NIRF. This requires modifications to the equations from what you would have if the frame were inertial. Those modifications are the pseudo forces.

This is where I see a problem. I don't see how you can detect that gravitational force except by reference to a genuine IRF. There is no way to detect it by reference only to the NIRF. In the free-falling NIRF a uniform gravitational field is undetectable.

If it is undetectable I am having difficulty understanding why you need a pseudo force to counter-act it or explain it. Otherwise, what you are saying is perfectly reasonable and rather obvious.

I understand the distinction you are making. It isn't really a distinction between an IRF and a NIRF, but rather a distinction between the Newtonian and relativistic definition of "inertial". My comments above were in the context of the Newtonian definition of "inertial", but personally I agree with you in my preference for the relativistic definition.

 

[DrStupid]

In other words, we are assuming that the NIRF is an IRF and we are trying to make Newton's 2nd law work.

We are simply using Newton's 2nd law.

I don't see how you can detect that gravitational force

You only have to detect the bodies including their mass. Than the gravitational forces are given by Newton's Law of gravitation.

except by reference to a genuine IRF.

Of course this works too. Just choose a frame of reference where all forces cancel each other out. All remaining forces are also present in every other frame of reference.

 

[Zula110100100]

I think the problem is whether or not to "forget" that the NIRF is accelerating by a certain amount(g for free-fall) if you do not forget, then gravity is what keeps you in the frame, but I think as described in Newtonian physics, you do forget, so an anti-gravity is required to counteract the known gravity, also with the acceleration of the frame forgotten, a force is required to move the Earth up to meet me.

The question It seems is why can't I just remember I am using an accelerated frame K relative to an inertial frame k and add the requirement that to appear at rest in this frame there must be a real force giving acceleration equal to the acceleration of K?