By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be

Question

By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2×10−4m2 and its Young’s modulus is 1.6×1010N/m2.

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Diễm Kiều 3 years 2021-09-05T02:28:55+00:00 1 Answers 74 views 0

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  1. RobertKer
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    2021-09-05T02:30:16+00:00
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    Answer:

    4.55×10^-5m

    Explanation:

    Young modulus of the material is equal to the ratio of the tensile stress to tensile strain of the elastic material.

    Young modulus = Tensile stress/Tensile strain

    Tensile stress = Force/cross sectional area

    Give mass = 73kg

    Force = mg = 73×10 = 730N

    Cross sectional area = 5.2×10^-4m²

    Tensile stress = 730/5.2×10^-4

    Tensile stress = 1.4×10^6N/m

    Strain = extension/original length

    Given original length = 52cm = 0.52m

    Tensile strain = extension(e)/0.52

    Substituting the values given into the young modulus formula we have;

    1.6×10^10 = 1.4×10^6/{e/0.52}

    1.6×10^10 = 1.4×10^6×0.52/e

    e = 1.4×10^6×0.52/1.6×10^10

    e = 7.28×10^5/1.6×10^10

    e = 4.55×10^-5m

    This shows that the femur compresses by 4.55×10^-5m

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