Constraint forces

Constraint forces — the tension of a rope, the normal reaction between surfaces — make up the second family. Unlike conservative forces, they do not admit potential energy: they don’t “store” energy in a reservoir, but transfer it directly from one body to another. In the bubble diagram they therefore give rise to no $E_\text{pot}$ bubble, only to an arrow connecting the kinetic energies of two distinct bodies.

Principle — Rule for constraint forces

The work of a constraint force connects the $E_\text{cin}$ bubble of one body with the $E_\text{cin}$ bubble of the other body. No potential-energy bubble appears.

The constraint force does positive work on the body the arrow enters and negative work on the body it leaves. The two works are opposite.

Constraint forces (rope, normal reaction): they transfer kinetic energy directly from one body to another. No $E_\text{pot}$ bubble.

Since the two works are equal and opposite, their sum is zero: the constraint force merely redistributes kinetic energy between the two bodies, without creating or destroying any. But there’s an even simpler case, and a very frequent one in problems: that of the fixed constraint.

Principle — When the work of a constraint force is zero

If the constraint is fixed, the work is zero.

• If one end of the rope is anchored to a stationary wall, the tension at that end does no work (the point of application doesn’t move).
• If the surface the body rests on is stationary, the constraint reaction does no work (the reaction is perpendicular to the relative motion and the constraint is stationary).

If instead the constraint moves (sliding surface, rope pulled by a lorry), the force can have a component along the motion and do work: it “passes” energy from one system to another.

The plane's reaction is $\perp$ to the motion of the body sliding on it $\Rightarrow L=0$. In a moving lift, however, it can have a component along the motion!

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Topics: Lavoro ed energia Concepts: Lavoro di una forza Methods: Diagramma a bolle di scambio energetico

Related exercises: Problema — Vero o falso su lavoro ed energia · Problema — Potenza di un ascensore · Problema — Lavoro da grafico forza triangolare