Question

1. A uniform steel wire of length 3 m and area of cross section 2 mm² is extended through 3 mm. Calculate the energy stored in the wire, if the elastic limit is not exceeded. ( $Y_{steel}$ = 20 x 10¹⁰ N / m²) (Ans 0.6 J)

Answer 1

Given :

L = 3 m,  

A = 2 mm² = 2 × 10⁻⁶ m² ,

l = 3 mm = 3 × 10⁻³ m,  

Ysteel = 20 × 10¹⁰ N/m

W =( 1/ 2) × F × l

Young’s modulus, Y = FL /Al

∴ F = YA l/L

W = 1 /2 × F × l

∴ W =( 1 /2)(YA l/L)l

=YAl²/2L

=20x10¹⁰x2x10⁻⁶x(3x10⁻³)²/2x3

W=0.6J

∴the energy stored in the wire is 0.6J

Answer 2

Explanation:

A uniform steel wire of length 3 m and area of cross section 2 mm² is extended through 3 mm. Calculate the energy stored in the wire, if the elastic limit is not exceeded. ( = 20 x 10¹⁰ N / m²) (Ans 0.6 J)