How Is the Elevator's Acceleration Calculated Using Newton's Second Law?

[cheerspens]

Homework Statement

A 1000 kg elevator is held up by two cables. If each able exerts a force of 6000N upwards upon the elevator, find the elevator's acceleration.

Homework Equations

F_g=mg

F_NET=ma

The Attempt at a Solution

I started with a force diagram to help me and then I think I'm supposed to use the F_NET=ma formula. So I plugged in the variables as follows: (6000+6000)-F_ge=1000a
How do you solve for acceleration in this problem when I also need to find the Force that gravity exerts on the elevator (F_ge)?

Would the answer be 2.2m/s^2?

 

[rock.freak667]

F_ge would simply be the weight, mg, of the elevator.