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17 July, 18:50

Consider a steel guitar string of initial length L=1.00 meter and cross-sectional area A=0.500 square millimeters. The Young's modulus of the steel is Y=2.0*1011 pascals. How far (ΔL) would such a string stretch under a tension of 1500 newtons?

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  1. 17 July, 20:06
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    15mm

    Step-by-step explanation:

    we are looking for extension

    To get Extension you need the original length and the strain both of which you are given

    initial length L = 1.00m

    the area A = 0.5mm² = 0.5 mm² = 0.5 x 10⁻⁶ m² (we are changing to metres squared)

    E = 2.0 x 10¹¹ n/m², Young's modulus

    P = 1500N, the applied tension

    Now to Calculate the stress.

    σ = P/A (force/area) = (1500 N) / (0.5 x 10⁻⁶ m²) = 3 x 10⁹ N/m²

    Also, Let β = the stretch of the string.

    Then the strain is

    ε = β/L (extension / original length)

    By definition, the strain is ε = σ/E = (3 x 10⁹ N/m²) / (2 x 10¹¹ N/m²) = 0.015

    Therefore β / (1 m) = 0.015β = 0.015 m = 15 mm

    Answer: 15 mm
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