The cable supporting a 1950 kg elevator has a maximum strength
of21920 n. what maximum upwardacceleration can it give the elevator
without breaking?

1.43 m/s^2

Explanation:

Each time you see mass and force, you will probably be going to need to use Newton's second Law. This law basically shows the relationship between the force being applied on an object and its mass and acceleration:

Now, the force that the cable exerts on the elevator, not only has to accelarate it, but it also has to counter gravity. The maximum tension of the cable minus the weigth of the elevator would give us the net force being applied on the elevator:

3.2x10^7