Is the Normal Force in an Elevator Conservative?

[Caio Graco]

Homework Statement

Can normal force work? If so, is it a conservative force?

Relevant Equations

There is no equation for normal force.

Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent). My question is: since the total work on the closed path is zero, can we say that the normal force is conservative?

 

[kuruman]

Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent).

Simply not true. When accelerating down the elevator exerts a normal force that is still "up" (not negative) and large enough so that your acceleration matches the elevator's acceleration. If that were not the case, you would either hit the roof or, even worse, fall through the floor.

You need to think what the criterion for a conservative force is.

 

[jbriggs444]

Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent). My question is: since the total work on the closed path is zero, can we say that the normal force is conservative?

Suppose that you step into the elevator on the 2nd floor. The elevator is at rest. Your kinetic energy is zero.

You press the button labelled "3" and rise to the third floor. The elevator stops here. You press the button labelled "1" (or "G"). The elevator proceeds downward past the 2nd floor without stopping.

At the moment that the elevator passes the second floor is your kinetic energy greater than, less than or equal to what it was when you first pressed the "3" button? At this moment, is is the total work that has been done on you by the elevator positive, negative or zero?

 

[Caio Graco]

Suppose that you step into the elevator on the 2nd floor. The elevator is at rest. Your kinetic energy is zero.

You press the button labelled "3" and rise to the third floor. The elevator stops here. You press the button labelled "1" (or "G"). The elevator proceeds downward past the 2nd floor without stopping.

At the moment that the elevator passes the second floor is your kinetic energy greater than, less than or equal to what it was when you first pressed the "3" button? At this moment, is is the total work that has been done on you by the elevator positive, negative or zero?

By the time the elevator passes the second floor, my kinetic energy is greater than it was at the beginning. So the total work on me is positive. And I believe this shows that the normal force is not conservative because there is at least one case, like this, in which in a closed trajectory the total work is not zero. Is this friend?

 

[jbriggs444]

the normal force is not conservative because there is at least one case, like this, in which in a closed trajectory the total work is not zero

Yes.