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6 July, 21:15

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 * 1011 Pa. The mass of the load is closest to

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  1. 7 July, 00:59
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    The mass, m, of the load = 11.3 Kg

    Explanation:

    Young's Modulus = Stress / Strain

    Stress = Force / Area

    Force = mass, m * acceleration due to gravity, g

    assuming g = 10ms⁻²

    therefore, Force = 10m

    m is mass of the load in kilograms

    Area of steel wire = π * r^2, where π = 3.14, r = 1.2/2 = 0.6mm or 6.0 * 10^-4m

    = 3.14 * (6.0 * 10⁻⁴m) ^2 = 1.13*10⁻⁶m²

    Stress = 10m / 1.13*10⁻⁶m²

    Strain = extension / original length

    = (new length - original length) / original length

    = (3.2016 - 3.2000) / 3.2000

    Strain = 0.0005

    Using Young's Modulus = Stress / Strain

    Note: 1Pa = 1N/m²; Young's modulus for steel is 2.0 * 10¹¹ Pa or N/m²

    2.0*10¹¹ N/m² = Stress / Strain

    2.0*10¹¹ = (10m / 1.13*10⁻⁶) / 0.0005

    0.0005 * 2.0*10¹¹ = 10m/1.13*10⁻⁶

    10m = 1.13*10⁻⁶ * 0.0005*2*10¹¹

    10m = 113

    m = 11.3 kg

    Therefore, the mass, m, of the load = 11.3 Kg
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