Is Work Path Dependent with a Zero Total Displacement?

[fiziksfun]

Is work done if the total displacement is 0?

It doesn't matter what path the object took to get from A back to A, right? As long as it ends at A, then its zero work, correct?

So work IS NOT path dependent, it's a state function, like energy, right ?

 

[Hootenanny]

Is work done if the total displacement is 0?

In general, yes.

It doesn't matter what path the object took to get from A back to A, right? As long as it ends at A, then its zero work, correct?

No. In general even if the displacement is zero when a force acts on a moving object, work is done.

So work IS NOT path dependent, it's a state function, like energy, right ?

Nope, work is path dependent.

For example, consider dragging a block across a rough surface for a distance of ten meters and then dragging it back to the same place you started. Did you do work on that block?

 

[thomate1]

I can confirm that work is a state function and is not path dependent. This means that the amount of work done does not depend on the path taken, but only on the initial and final states of the object. Therefore, if the total displacement of the object is 0, the work done will also be 0 regardless of the path taken. This concept is known as the principle of conservation of energy, where the total work done on an object is equal to the change in its kinetic and potential energy. So, if the object ends at the same point where it started, there is no change in its energy and thus no work is done.