A cable that is pulling an elevator should be able to withstand the maximum force that is exerted on it when the elevator is filled to its full capacity and its mass is at the maximum.
From the details provided in the problem, the maximum mass of the elevator can be 1080 kg. The cable supporting the elevator should be able to withstand the force exerted by this mass. This force is a constant; its value does not go up in the case of an accident. When the elevator is at its highest point, the force that is being exerted on the cable is equal to 1080*9.8 = 10584 N. This force remains the same irrespective of the height of the elevator.
The tensile strength of a material is given in terms of Pa, or force per unit area. For the same material a thicker cable can withstand a larger force without breaking. To determine the required tensile strength of the cable supporting the elevator, the diameter of the cable is required. A thinner cable would need a material with a higher tensile strength and vice versa.
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