A conservative force has the property that the work done in moving a particle between two points is independent of the path taken. It implies that the force is dependent only on the position of the particle. Now we can use this idea to define a function called the potential energy.
It is a conservative force that gives rise to the concept of potential energy and not the other way round. If the force were non conservative, the force would not be dependent on position only and thus we could not have defined a potential energy function.
A simpler way to find out whether a force is conservative or not is to find out the closed line integral of force, i.e $\oint dr F$ and convert it into the area integral of the curl of the force by using Green's theorem, i.e
$$ \oint F dr = \int_A (\nabla \times F) da$$. Thus if the curl of the force is zero, it automatically means that the force is zero. It is now trivial to see that the gravitational as well as the spring force are conservative as the curl of both forces vanish.
A better way to look at your equation, in my opinion, is
$$\Delta PE = -W_{\mathrm{cons}}.$$
That's closer to a definition of potential energy. But, in either order, another concept is that you can substitute a change in potential energy for the work by a conservative force when you analyze the motion of a system. In other words, you use either the work done by a conservative force or the potential energy contributions of that conservative interaction, but not both.
For example, in a system involving gravity and air resistance one could write (using $K$ for kinetic energy, $W$ for work, $U$ for potential energy)
$$K_{\mathrm{initial}}+W_{\mathrm{grav}}+W_{\mathrm{air}}=K_{\mathrm{final}}$$ using the work-energy principle, $$\Delta K = \Sigma_{\mathrm{all}} W.$$
Or$$K_{\mathrm{initial}}+U_{\mathrm{g,initial}}+W_{\mathrm{air}}=K_{\mathrm{final}}+U_{\mathrm{g,final}}.$$
You can see these are equivalent by subtracting $U_{\mathrm{g,final}}$ from both sides of the last equation and applying $\Delta U_{\mathrm{grav}}=-W_{\mathrm{grav}}$.
So the answer to your "or" question is neither of those is correct:
- Conservative forces can change kinetic energy and can be accounted either by the work they do or the change in potential energy of the system, and
- Non-conservative forces can change kinetic energy and must be accounted by the work they do. There isn't a potential energy function which helps us.
Best Answer
Relation between Forces and Potential Energy
In order to examine the relation between two terms we must consider the definitions of each term:
a) forces:
b) Potential Energy
Mechanical energy (ME) is the ability of a body to do [mechanical work]. A body has ME because of:
Potential energy is associated only with elastic, conservative forces, that act on a body in a way that depends only on the body's position in space. These forces can be represented by a vector at every point in space forming what is known as a vector field or force field
An elastic force is conservative because it conserves the KE it subtracts to a body as potential energy. In the bottom sketch when body B is shot up in the air, it has PE = 0 and KE (mgh) = 10 (mg) * h, when it reaches h/2 has KE = 5 * h and PE = 5 *h, and at height h has KE = 0 and PE = 10 * h: ME is costant = mgh.
This you have learned in another answer. You ask now: