A piano wire of length 1.2m and area of cross section 4 x 10^–7 m² is under tension of 80N. Find the extension in the wire and potential energy stored in the wire. The Young's modulus of the material of wire is 2.1x10¹¹N/m².

Solution

Length of the wire, l = 1.2 m
Area of cross-section, A = 4 x 10^–7 m2
Tension, T = 80 N
Young's modulus of the wire, Y = 2.1

\times

10¹¹N/m²
Now, using the formula,

Young's modulus is given by

Y = \frac{FL}{A ∆ L}

Extension in the piano wire is given by,

∆ L = \frac{TL}{AY} = \frac{80 \times 1.2}{2.1 \times 10^{11} \times 4 \times 10^{- 7}} = 11.43 \times 10^{- 4} m

Potential Energy stored in the wire is,

U = \frac{1}{2} \frac{YA (∆ L)^{2}}{L} = \frac{1}{2} \times \frac{2.1 \times 10^{11} \times 4 \times 10^{- 7} \times (11.43 \times 10^{- 4})^{2}}{1.2} = 0.0457 J

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