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The tension in the cable is the net force by which it pulls the elevator. The result of the tension T in the cable to which an elevator is attached is the acceleration of the elevator in an upward direction. The force of gravity acting downwards accelerates the elevator by 9.8 m/s^2. If the net acceleration of the elevator due to the pull of the steel cable is 3 m/s^2 upwards, the actual acceleration towards the top is 3 + 9.81 = 12.81 m/s^2.
This implies a force equal to 2*10^5*12.81 acting on the elevator in the upwards direction. This force results in a tension equal to 2562 kN in the cable.
The required tension in the cable is 2562 kN.
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