Besides the distinction between contact forces and action-at-a-distance forces, there is another, even deeper one, destined to become central when we tackle the energy method. Some forces have an associated potential energy — the weight force, the elastic force, and the electrostatic force — while others do not: friction, the tension in a rope, the constraint reaction. The former are called conservative, the latter are not. The difference is not a technicality: it concerns whether or not a force can store work in a reserve from which it can be returned in full.
The physical meaning is intuitive. The weight force and the elastic force depend only on the configuration of the system, that is, on the position of the body or the deformation of the spring, not on how it got there. When you lift an object, the work you do against gravity is not lost: it stays “deposited” in the potential energy of the position, ready to be returned in full if you let the body fall back. Likewise, the work spent compressing or stretching a spring is conserved in the deformation and is given back when the spring returns to rest. For these forces it is therefore possible to define a quantity — potential energy — that measures the stored work and depends only on the current state, not on the path taken.
Friction, by contrast, has no potential energy at all, because the work it does depends on the path and is not recoverable: it is dissipated as heat, that is, converted into thermal energy that does not spontaneously go back to moving the body. There is no “rest position” from which friction gives back what it took away. Similarly, tension and the constraint reaction have no potential energy of their own: they are forces whose work depends on the constraints and on the motion, and which typically just transmit or channel the action of other forces.
Note
This distinction between conservative and non-conservative forces is the cornerstone of the energy method, which we will develop in the chapter devoted to energy. There, the potential energy of weight and of springs will become an extremely powerful calculation tool, while the dissipative work of friction will appear as thermal energy produced. For now, it is enough to remember which forces store energy and which ones disperse it.
Links
Topics: Dynamics Concepts: Weight force · Elastic force and Hooke’s law
Related exercises: Problem — Spring with two hanging masses · Spring on an inclined plane · Worked exercise — two boxes with a spring and a pulley