It is apparent from Table 12-2 that the tensile strength of most materials is two to three orders of magnitude smaller than Young?s modulus. Consequently, these materials, e.g., aluminum, will break before the strain exceeds even 1%. For nylon, however, the tensile strength and Young?s modulus are approximately equal. If a nylon line of unstretched length L₀ and cross section A₀ is subjected to a tension T, the cross section may be substantially less than A₀ before the line breaks. Under these conditions, the tensile stress T/A?may be significantly greater than T/A₀. Derive an expression that relates the area A?to the tension T, A₀, and Young?s modulus Y.

Table 12-2 Approximate Values of the Shear Modulus M, of Various Materials M, GN/m2 Material Aluminum 30 Brass 36 Copper 42 Iron 70 Lead 5.6 Steel 84 Tungsten 150