The interaction diagram is the most important tool for analysing a mechanics problem. It lets us identify all the forces present in a physical situation, without forgetting any and without inventing non-existent ones. It is the first step of any dynamics analysis: before writing a single equation, we draw who interacts with whom.
The underlying idea is simple but powerful. Every force arises from an interaction between two objects: there is no such thing as an isolated force, only ever a pair of bodies pushing or pulling on each other. Graphically representing these interactions forces us to make explicit every contact, every rope, every spring and — above all — the ever-present attraction to the Earth.
Principle — Rules for the interaction diagram
- Draw every object as a circle (or oval) with its name inside.
- The Earth is always present: weight is the interaction between every body and the Earth.
- Connect with a wavy line (squiggle) every pair of objects that interact with each other. Each squiggle represents one pair of twin forces (third law).
- Label each squiggle with the type of force: weight (body–Earth), constraint (surfaces in contact), tension (rope), elastic (spring), friction (surfaces that slide).
The squiggle is the heart of the method: a single wavy line between two circles reminds us that the interaction is mutual. By Newton’s third law, each squiggle encodes two equal and opposite forces, one on each of the two connected bodies. Labelling the squiggle with the force type (and perhaps with a colour) then helps avoid confusing a constraint reaction with a tension or with friction when we move on to the free-body diagram.
Note
Golden rule: Weight is always between the body and the Earth. If two bodies do not touch and are not connected by a rope or spring, there is no squiggle between them.
This golden rule sums up the most common mistakes: forgetting the weight (which acts even at a distance, so it requires no contact) and inventing interactions between bodies that in fact neither touch nor are connected. If these two checks are followed, the diagram will contain exactly the real forces of the problem, neither one too many nor one too few.
Links
Topics: Dinamica Concepts: Forza peso Skills: Diagramma di interazione Methods: Metodo del diagramma di interazione
Related exercises: Problema — Vero o falso su forze e moto · Vero o falso su leggi di Newton · Problema — Bilancia in ascensore