Why does a car engine not do work if the wheels don't slip?

Question

I saw this mind boggling result that if the tires don't slip then the work done by an engine to move a car is zero. Why is this true? Moreover, what does this truly mean? **Update:** Sorry about not being clear, but I was talking about an idealised case where air resistance is negligible and the tires are perfectly rigid and there is no internal friction at play.

Answer 1

There are several ways to approach this question. The one I will choose is a bit of a technicality. When the engine is operating, it executes torque on the tires (this means it is actually doing rotational work on the tires, but that is a different topic).

If the tires were free to rotate under this torque, they would. However, frictional contact with the surface causes them not to spin. What happens instead is that the tires exert a frictional force on the ground, and the ground (by Newton's 3rd law) exerts a frictional force back on the tire. This reaction force of the ground on the tire (through frictional contact) is what gets the car rolling and moving forward.

So, technically, the force caused by the engine acts on the ground. But work, in the physics definition, requires displacement. Work can be defined in words, in a mechanics context, as a quantity measuring the effectiveness of a force in causing displacement. So, to do work in physics terms, something has to move.

However, the force the engine exerts through the tires acts on the ground, which does not move. The reaction force this causes from the ground is what moves the car. We can demonstrate this by seeing what happens if the car is on slippery ice or no with negligible frictional contact. Even though the engine still does the same thing, the car does not move. It is the reaction force from the ground which is needed to move the car forward.

Usually, we simplify this by just saying the engine's work is driving the car forward (since it is the final cause of the force which moves the car forward). But it is technically the ground doing the work through frictional contact.

Let me know if you have any other questions. Thanks!