Understanding the relationship between Force, Energy and Fields.
Although the different laws of Mechanics have been taught for more than two centuries, it seems that physicists still confuse the notions of force, work of force and potential energy. The used formulization has prevented physicists to understand the essential role of space medium that occurs through physical fields.
Yet another time, mathematical formulas are correct but their expression and interpretation mislead everyone.
According
our previous demonstration potential energy is a specific property of space field and its gradient generates field's force according the conservative law: dp/dt + gradE_{field }=0.
Forces and Forces learn to tell them apart
However, when an object is constrained by an external force that is not derivative of a field's energy, the general equation of dynamics: dp/dt=F_{cons }remains applicable.
Note that this kind of external forces, named constraint forces to be told apart, differs from field forces. They don't operate everywhere in space but:

They only apply on material contact

They only propagate through material supports, such as ropes or levers

They influence the free motion of an object in space by providing or by removing kinetic energy not by carrying on potential energy

As shown through the two examples above, superposing constraint forces and fields leads to a more general expression (1) which integration leads to the well known energy conservative law (2).

dp/dt + gradE_{field } = F_{cons } (1)

ΔE_{kinetik } + ΔE_{field } = W_{cons } (2)
In order to preserve the energy balance the term W_{cons } has been introduced. It represents the work of a constraint force. It is equal to the constraint force time the distance along which it applies.
The work and the nature of a force
Note first that the notion of work is useless when only fields operate; it is to say that only constraint forces work.
Although mathematically correct, applying a work to a field force is a physical nonsense because field force is itself the derivative of energy. This kind of formalization has really hidden the real nature of a field: a space property that carries energy.
Second, the idea to unify every nature of forces in only one expression is a very bad one. According the point of view that takes into account the energy balance, we can classify them into several natures:

The field's force which is the derivative of a space field energy (gravity, electric and magnetic forces)

The constraint force that carries on a work through material contacts (pulling, pushing, rubbing)

The reaction force that prevents an object to pass through one another or an object to be broken off. These forces are only passive, they can't interfere in no way with energy balance (bearing, retaining)

The coherence force that keeps the stability of matter up to a certain level of energy. When a threshold of stress is reached, it suddenly frees or captures an amount of energy (weak and strong interactions, chemical links between atoms)
According Synergetics model, each of these natures has a physical meaning:

The field's force is the derivative of fields' space energy according specific rules for each of the three cases  Gravitation, Electrostatics, Magnetostatics

The constraint force is a macroscopic force that takes source from a material apparatus: muscles, engines, shocks

The reaction force comes from the coherence force that holds atom together

The coherence force corresponds to the wave resonance of energy. A resonant state maintains its energy up to a level where external stress is too strong. Inversely, a resonant state can suddenly occur when surrounding conditions allow it.