An 8$\times$19(9/9/1) steel wire rope is used to lift a load of 20 kN from a depth of 1km. The maximum speed of rope is 2.5 ms–1 and the acceleration is 1.5 ms–2 when starting under no slack conditions. Determine the size of the rope required for a desired factor of safety of 4.5 Modified modulus of elasticity for rope is 68600 MPa.