The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J . The cross sectional area of the wire is _____ mm 2 . (Given, Y = 2 . 0 × 10 11 N m – 2 )

Step-by-step solution

The formula to calculate the Young's modulus of the material is given by Y = stress strain = stress ∆ l L       . . . 1 The formula to calculate the potential energy U stored into the wire is given by U = 1 2 × stress × strain × volume = 1 2 × stress × ∆ l L × A × L =   1 2 × stress × A × ∆ l       . . . 2 From equation (1) and equation (2), it can be written that U = 1 2 × Y × ∆ l 2 L × A