How did scientists arrive at the value or strength of the Strong Force?

Answer 1

Experimentation. This is a problem with the standard model of Physics - there is no theoretical support for the experimental constants of the universe.

String theory is an attempt to explain WHY forces and masses have the values they do.

Answer 2

Well, when the strong force causes a particle like an alpha particle to be ejected from a nucleus, its kinetic energy is the energy it got from being repelled by the other positive charges in the nucleus minus the energy needed to overcome the strong force holding it inside the nucleus. The maths of electrostatic repulsion is easy; it's a long-range force obeying an inverse square law. The strong force is mathematically a bit more complicated, but it's been worked out from this. The electrostatic repulsion between protons in a nucleus is very large; typically several newtons for each proton.

Answer 3

The strong force is the residual force left over from the unbalanced Chroma Force between Quarks. It tackled mathematically through Quantum Chromodynamics (QCD).
It is said that when Quarks separate, the force between them is so strong that it rips the fabric of space apart producing new Quarks and Antiquarks that they then re-bond with the free quarks producing jets of bosons and mesons.

These jets are seen in Cosmic Ray collisions with detectors and photo-films. The structure of the jets could not be explained before the QCD theory was proposed.

Using the QCD theory it is possible to assign a large coupling constant to the chroma force and this makes the solution of the equations by approximation (perturbation theory) very difficult.

SIMPLY:
The coupling constant is obtained from the measure of the nuclear forces present in high energy collisions which are the remnants of the unbalanced chroma forces between the constituent quarks.
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