I dont understand some part of work energy theorem

[madah12]

Homework Statement

$$\Sigma$$W = $$\Delta$$E
so if we have an elevator getting pulled by force equal to it's weight making it move with a constant velocity then the net force is equal to 0 so the sigma W is equal to zero but isn't there non zero change in potential energy ?

Homework Equations

The Attempt at a Solution

 

[vela]

If E is the total mechanical energy, you only need to account for the work done by the non-conservative forces. In this case, you have two forces on the elevator: the force of gravity, which is a conservative force, and the tension in the cable, which is non-conservative. The only work that you include on the lefthand side is the work done by the tension. The work done by gravity is already accounted for via the gravitational potential energy.

 

[madah12]

oh I see, would that said elevator have any power? because P=F*V=0*V=0
so then would it have 0 power but then it will have zero work or should we not take the net force?

 

[vela]

It depends what exactly the question is. If you're asking "What power is required to lift the elevator at a speed V?" you'd only consider the force doing the lifting, that is, the tension, and multiply it by the speed to find the power needed.