Elevator Forces: Fupward vs Fnet vs a

[MIA6]

For elevator problem in Force, I have some confusions about basic concepts. Here give an example: an elevator is to be designed so that the maximum acceleration is 0.068g. Here why would the elevator's acceleration smaller than the gravity, then can it still pull the whole elevator up? Or whether it can pull elevator up depends on the upward force not acceleration? Fnet=Fupward-Fg(weight), Is a=0.068g here net acceleration? Fnet=0.068g*m? I think Fupward must be larger than the weight, but then the net force is smaller than the weight, does it matter? I mean if the net force is smaller than the weight, will the tension still be able to pull/lift the elevator up? Or we only look at Fupward to determine if it can lift the elevator. My confusions here are: a and Fnet vs Fupward.
THanks.

 

[rcgldr]

The force is controlled so that the maximum acceleration of the elevator and it's load are .068g.

 

[MIA6]

The force is controlled so that the maximum acceleration of the elevator and it's load are .068g.

sry, I don't quite understand what do you mean by the force is controlled?