Question

4) [10 marks] A steel cable is being used to hoist a load of mass Mload 3.3 metric tons through a vertical height L. The steel cable has mass density p 7600kgm3 and tensile strength S-2.5 x 108 Pa. For safety reasons, the stress in the cable (that is the force per unit area) must not exceed Smax - 0.8S. In this question, the mass of the cable cannot be neglected . First assume that the cable has uniform cross-sectional area, A 2.2 cm2. What is the max- imum height to which the weight can be raised without exceeding the maximum permitted stress in the cable? » Next, suppose that it is desired to raise the load to the same height, but minimising the mass of cable used. Consider a cable whose cross sectional area varies such as to keep the stress just equal to Smax. By what factor is the mass of the cable reduced? Hint: to simplify the algebra, you m ay find it useful to define a dimensionless constant X = Mioadg/SmaxA, where g is the acceleration due to gravity.

Answer 1

32.3 XIO3 a.% The

32 3u1 2 062