A 85-kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee and hip joint – the femur. Assuming

Question

A 85-kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee and hip joint – the femur. Assuming the femur is 0.65 m long and has a radius of 2.00 cm, by how much will the bone be compressed (in meters)?

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Dulcie 3 days 2021-07-19T02:14:59+00:00 1 Answers 3 views 0

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    2021-07-19T02:16:03+00:00

    Answer:

    The bone is compressed to 4.213*10⁻⁶ m.

    Explanation:

    Given that ,

    Mass of the person M = 85 kg,

    Length of femur L =0.65 m

    Radius of femur r = 0.02 m

    To find,

    Compression of the bone l = ?

    The Young’s Modulus is given by Y= \frac{FL}{lA}

    Young’s modulus of human femur bone is Y = 9.4 *10⁹ Pa

    Rearranging formula ,

    l =\frac{FL}{YA}

    Weight supported by femur bone is 85 *0.9 =76.5 Kg

    Area = π r² =3.14* (0.02)² = 0.001256 m

    The length of compressed bone is  

    l =\frac{76.5*0.65}{9.4GPa*0.001256} =  \frac{49.725}{0.0118GPa} =4213.89 *10⁻⁹

    l = 4.213*10⁻⁶ m  

    The bone is compressed to 4.213*10⁻⁶ m.

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