Identifying Forces

Identify real forces and avoid invented forces in a physical system. Theory, formulas, worked examples and interactive graphs.

Conceptual context

This page answers a question that comes before any calculation: which real forces act on a system, and how do we establish that each one has a concrete physical agent that exerts it? Before adding vectors or applying the second law, it is necessary to decide which forces exist and which would be inventions.

The forces this page organises are the weight $P$, the normal force $N$, friction $f$ (with its limit $f_s$), the tension $T$ and the applied force $F_{ext}$. Each one has its own criterion of existence: the weight exists whenever there is mass and a gravitational field; the normal force and friction exist only if there is active contact ($c$ = 1); the tension exists only if the rope is taut; the applied force exists only if the agent that exerts it can be named.

The difference between this page and "free-body diagrams" is intentional: here the central task is to decide the physical existence of each force by its agent, not only to represent it as a vector. If there is no identifiable agent, the force is not drawn.

🟢 Essential level

The essential intuition can be summed up in one question to ask force by force: who exerts this on the body? The weight is exerted by the Earth, always present if there is mass. The normal force $N$ is exerted by the contact surface, and exists only while the contact is real. Friction $f$ is also exerted by the surface, but only if there is a tendency or tangential relative motion. The tension $T$ is exerted by a rope or cable, and only if it is taut, never slack. The applied force $F_{ext}$ is exerted by an identifiable external agent, such as a hand, a motor or a push.

One error at this level is drawing a force "because it seems it should be there" without being able to name its agent. If you cannot say which concrete object exerts it, it is probably a phantom force, not a real force.

Another error is keeping contact forces after the contact has disappeared: if a block lifts off a surface, both $N$ and $f$ must disappear from the diagram at that same instant, not remain "out of habit".

🔵 Formal level

Basic formulas

The weight is calculated by multiplying the mass $m$ of the body by the local gravity:

Definition of weight

This relation is valid in practically constant gravitational fields, such as the Earth's surface, and it is the only force in this list that never depends on whether there is contact or a rope.

Static friction does not have a fixed value: it adjusts itself up to a maximum determined by the coefficient $\mu_s$ and the normal force $N$:

Real student questions

How do I know whether a force is real or invented? Ask yourself which concrete physical agent exerts it. If you cannot name it, do not draw it.

Is the normal force always equal to the weight? No. They coincide only in vertical equilibrium with no other vertical forces; with an inclined rope or a vertical applied force, the normal force changes.

Can I draw friction even if the body does not move? Yes. Static friction $f_s$ exists whenever there is a tendency to slide, even if the body remains at rest.

Causal audit protocol by agent

A distinctive contribution of this page is the causal audit protocol by agent. It is not a matter of "doing more calculations", but of checking that each declared force passes four operational filters:

1. Source filter: the external body interacting with the system can be named.
2. State filter: the interaction is active at the instant analysed ($c$ = 1 for contact forces).
3. Direction filter: the chosen sense is consistent with opposition (friction) or physical support (normal force, tension).
4. Consistency filter: the declared force does not contradict $c$ or the regime of $f_s$.

If a force fails a filter, it is classified as a phantom force and removed from the model. This language of "phantom force" is useful because it forces the separation of visual intuition from verifiable physical causality. In professional practice, that filter prevents a diagram that looks flawless from leading to wrong safety or maintenance decisions.

The protocol also improves traceability: when two analysts disagree, they do not argue only about numerical results; they discuss which filter failed and why. That change of conversation speeds up technical consensus and reduces repeated errors in team training.

Final synthesis

Identifying forces correctly means associating each one with a verifiable physical agent and an active state of interaction, never with habit or with the symmetry of the drawing. The weight $P$ is always present; the normal force $N$ and friction $f$ depend on contact being active; the tension $T$ depends on the rope being taut; the applied force $F_{ext}$ depends on an identifiable agent.

Once this criterion is firm, the rest of dynamics is built on correct diagrams from the first step, avoiding errors that no amount of later algebra can correct.