A particularly instructive case of work is when it is equal to zero. This happens whenever the force is perpendicular to the displacement: the factor in the work formula vanishes and, however intense the force and however long the displacement, there is no energy transfer at all. Some forces are almost always in this condition.
Warning — When work is zero
The normal reaction and the tension of a string anchored to a fixed point are always perpendicular to the motion of the body: their work is zero. These forces do not transfer energy, but they deflect the trajectory.
If, however, the constraint or the anchor point moves, the force can have a component along the motion and do work. Example: a truck towing a car with a rope.
The lesson to draw is that “zero work” does not mean “useless force”. The normal reaction of a plane and the tension of a string holding a body in circular motion are decisive for the dynamics: they change the direction of the motion, curve the trajectory, prevent the body from sinking into the plane. They simply do not change its kinetic energy, because they have no component along the displacement.
The crucial caveat concerns the case in which the constraint itself moves. The perpendicularity that zeroes out the work applies relative to the motion of the point of application: if that point moves along the direction of the force — like the end of a rope pulled by an advancing truck — then the force gains a component along the motion and goes back to doing work, “passing” energy from one system to another. This is what allows the truck to drag the car along: the tension, no longer perpendicular to a stationary displacement, transfers energy from the towing vehicle to the towed one.
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Topics: Lavoro ed energia Concepts: Lavoro di una forza Skills: Impostazione simbolica
Related exercises: Problem — True or false on work and energy · Problem — Power of a lift · Problem — Work from a triangular force graph