Neither the force nor the acceleration is more 'fundamental' or the principal phenomenon. If a = b x c, then it states a relationship that is simply true - one does not have to first have c, and then when it is applied to b, yields a.
If you have measured m and a, then it predicts F.
If you have F and m it predicts the acceleration, and so on.
As I understood your interpretation F=ma is that this expression JOINS UNKNOWN quantities F, m and a together. It is not fruitful at all. I ask you for the following. How do you measure F or m? Please give the examples!!:)
You do not clarify your independent methods to measure m and F. I do it as I understood. Please fix my text if you thought about the other ways.
1. Your independent measurement of inertial mass m. This method is suitable to measure mass of planets. It is not suitable at all to measure a mass of stuff at our Earth.:)! Furthermore besides the 1st and 2nd Newton`s laws your method is based on the other two statements:
a) the Einstein`s equivalence principle: inertial mass=gravitational mass.
b) the law of gravity, Fg=GmM/r^2
Your method is as follows. You measure the orbital period T of a satellite around unknown mass M. Then equating ma=Fg (m - satellite mass) you find the expression for unknown mass M as a function of T, r (orbital radius).
2. Your independent measurement of force. Why do you decide that there is a force between conductors carrying electric current??:) I do not understand you!
My conclusion is as follows. Your method of determination of m is NOT INDEPENDENT as it uses 2nd Newton`s laws . Moreover it uses additional statements (see items a and b).
> It is not suitable at all to measure a mass of stuff at our Earth.:)
Why not?
It's not terribly accurate for small objects, but whether I am determining the mass of a planet, or a teacup, the method is the same.
>your method is based on the other two statements:
Naturally.
At no time did I say that the methods were somehow independent. You merely asked how I might measure F or m.
I quote, "How do you measure F or m?"
I have told you.
Of course there is a need to first make an objective statement as to what 1 Newton causes - as a change in a physical system, such as an acceleration, or a displacement of a sprung system.
At no time did I say otherwise.
> I do not understand you!
Yes you do. You are building a strawman - of course there has to be an ab-initio definition of what a mass or a force is. F=ma simply relates all three properties together *once* one has made a determination of two of the variable, the third is predictable.
This, I suggest, is not a real avenue of research and I will refrain from commenting further on the topic.
I do not understand how do you INDEPENDENTLY measure F or m.
I know that fundamental fluid mechanics equations are based for the 2nd Newton`s law for the system of points (it is Navier-Stokes equation), conservation of mass (continuity equation), heat balance equation (energy equation). The first and later laws are based on the 2nd Newton`s law.