Hooke’s Law for a Wire. A ? wire of length 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 = 1.297 mm) copper wire? See Table 11.1. (c) What would ?W h ? ave to be to stretch the wire in part (b) by 1.25 mm?
Solution 88P Step 1: Introduction In this question we have a wire, we need to find the force constant copper wire In the second part, we need to find weight by the wire can be stretched by 1.25 mm Data given Length of the wire l = 75 cm = 0.75 m 0 Diameter of the wire d = 1.297 mm radiusr = 0.6485 mm = 0.000648 m Amount stretched l = 1.25 mm = 0.000125 m 10 Young’s modulus Y = 11 × 10 Pa Step 2 : The force constant is given by The force constant is obtained using This can be written as F/A Y = l0l This is resolved to find force constant by F/l = Y (A/l 0 Here F/l = k = force constant Hence we have k = Y (A/l 0 We have the area of the wire using A = r 2 We get area as A = × (0.000648 m) 2 A = 1.319 × 10 m6 2 Using this we have force constant as 10 6 2 k = 11 × 10 Pa × (1.319 × 10 m /0.75 m) 5 k = 1.9 × 10 5 Hence we have force constant of the wire as 1.9 × 10