The cable supporting a 2130-kg elevator has a maximum strength of 2.18*104 n. what maximum upward acceleration can it give the elevator without breaking?

Answer;

=0.43 m/s²

Solution;

There will be the tension in the cable, T, upwards and the weight of the elevator, mg, downwards.

By Newton's second law, the sum of the forces will be equal to mass*acceleration.

Resultant force = m * a

Then T - mg = ma so the tension in the cable is

T = m (g+a)

The cable will break when T = 21,800 N

Solving for a, that happens when

a = 21800/2130 - g

= 10.23 - g (in m/s^2)

If you're using g = 9.8 m/s^2

Then the maximum acceleration allowed is 10.23-9.8 = 0.43 m/s^2