The work of friction

Friction is a force that always does negative work: it slows bodies down, converting kinetic energy into thermal energy. This is not a “loss” of energy but an irreversible transformation: the body and the surface heat up. Unlike what happens with gravity or a spring, the heat produced cannot be fully recovered and returned to the motion: once energy has dispersed into the disordered agitation of particles, it doesn’t spontaneously reorganise back into ordered macroscopic movement.

Principle — Work of friction

The kinetic friction force $\vv{F}_a$ does negative work: $L_{\text{attr}} = -|\vv{F}_a| \cdot |\Delta\vv{s}|$ The thermal energy of the system increases by $|L_{\text{attr}}|$.

The negative sign isn’t a formal detail: it says that, whatever the direction of motion, the friction force is always oriented opposite to the displacement. The scalar product between force and displacement is therefore negative at every instant along the path, and the magnitude of the displacement $|\Delta\vv{s}|$ is the distance actually covered while sliding, not the net displacement between start and finish. This radically distinguishes friction from conservative forces, whose work depends only on the endpoints of the path.

In the bubble diagram friction appears as an arrow from $E_\text{cin}$ to $E_\text{term}$: it has no bubble of its own because it doesn’t admit potential energy. Conservative forces deserve a bubble, a reservoir where energy can be stored and later drawn back out; friction does not, because its effect is one-way. The arrow pointing towards $E_\text{term}$ never has a companion pointing the other way: it’s the graphical signature of irreversibility.

Bubble diagram with friction: elastic energy turns into kinetic, which in turn becomes gravitational potential and (partly) thermal. Friction is an “arrow” towards $E_\text{term}$, not a bubble.

Links

Topics: Lavoro ed energia Concepts: Energia termica da attrito · Attrito dinamico · Lavoro di una forza Skills: Bilancio energetico a bolle Methods: Diagramma a bolle di scambio energetico Objects: Blocco

Related exercises: Problema — Spingere una cassa in moto · Problema — Lavoro contro l’attrito · Problema — Blocco spinto con attrito