A wire of length I₀and cross-sectional area A supports a hanging weight W.

(a) Show that if the wire obeys Eq. (11.7), it behaves like a spring of force constant AY/I₀, where Y is Young€™s modulus for the material of which the wire is made. 

(b) What would the force constant be for a 75.0-cm length of 16-gauge (diameter = 1.291 mm) copper wire? See Table 11.1.

(c) What would W have to be to stretch the wire in part (b) by 1.25 mm?

Table 11.1: Approximate Elastic Moduli

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Material Young's Modulus, Y (Pa) Bulk Modulus, B (Pa) Shear Modulus, S (Pa) Aluminum 7.0 x 1010 7.5 x 1010 2.5 x 1010 Brass 9.0 x 1010 6.0 x 1010 3.5 x 1010 Copper Il x 1010 14 x 1010 4.4 x 1010 Crown glass 6.0 x 1010 5.0 x 1010 2.5 x 1010 Iron 21 x 1010 16 x 1010 7.7 x 1010 Lead 1.6 x 1010 4.1 x 1010 0.6 x 1010 Nickel 21 x 1010 17 x 1010 7.8 x 1010 Steel 20 x 1010 16 x 1010 7.5 x 1010