The mass of an elevator is 500 kg. Calculate the tension in the cable when the elevator is (i) stationary, (ii) ascending with acceleration 2 m/s², (iii) descending with acceleration 2 m/s². Take g = 9.8 m/s².

Here are the calculations for the tension in the elevator cable under the given conditions.

Given:
Mass of elevator, $m = 500 \text{ Kg}$
Acceleration due to gravity, $g = 9.8 \text{ m/s}^2$
Acceleration of elevator, $a = 2 \text{ m/s}^2$

The forces acting on the elevator are the tension $T$ (upwards) and its weight $mg$ (downwards).
According to Newton's second law, the net force $\sum F = ma$.
Taking the upward direction as positive:

$$\sum F = T - mg$$

So, $T - mg = ma$.
Rearranging for tension:

$$T = mg + ma$$