Work. Positive, Negative, or Zero

[Llacrossedude]

1. The Problem:
An elevator is hoisted by its cables at a constant speed is the total work zero, negative, or positive?
2. Homework Equations :
g= -9.81m/s²
3. The Attempt at a Solution
I'm thinking that since the weight of the elevator is in downward direction along with the acceleration of gravity also in the downward direction, that the tension in the cables and the displacement of the elevator should even out and. Thus the answer is zero though I'm not sure.

 

[faymalaka]

your lucky you stated g is negative. Therefore work is postitive as it goes in the direction of the force applied.

 

[Llacrossedude]

Ohh since the tension and the displacement are in the positive direction, that makes the work done positive because they are opposing the natural acceleration of gravity?

 

[faymalaka]

the tension is the force in this situation, and the displacement is the distance moved. The direction of the displacement does not effect the direction of the momentum, Momentum always follows the force. This is because sometimes you may have a non straight line direction and you need to find the components. The only reason the tenstion is considered the postive direction is because you stated that gravity is -9.81 and tension opposes it. By saying gravity is negative, you set up a coordinate system.

 

[PhanthomJay]

To be clear, the question asks for the total work (work done by all forces), which is zero. The tension force in the cable, acting up, is equal to the weight (gravity) force, acting down, in accordance with Newton's first law. The tension force does positive work (force and displacement are in same direction), and the gravity force does negative work (force and displacement are in opposite direction). Since the magnitude of the forces and displacement are the same, the work done by the tension force plus the work done by gravity equals 0.