The compressive strength of our bones is important in everyday life. Young’s modulus for bone is about 1.4 * 1010 Pa. Bone can take only abo

Question

The compressive strength of our bones is important in everyday life. Young’s modulus for bone is about 1.4 * 1010 Pa. Bone can take only about a 1.0% change in its length before fracturing. (a) What is the maximum force that can be applied to a bone whose minimum cross-sectional area is 3.0 cm2 ? (This is approximately the cross-sectional area of a tibia, or shin bone, at its narrowest point.) (b) Estimate the maximum height from which a 70 kg man could jump and not fracture his tibia. Take the time between when he first touches the floor and when he has stopped to be 0.030 s, and assume that the stress on his two legs is distributed equally.

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RI SƠ 6 months 2021-07-17T11:53:22+00:00 1 Answers 54 views 0

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  1. Ben
    0
    2021-07-17T11:55:13+00:00
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    Answer:

    Explanation:

    Young modulus ε = 1.4 × 10¹⁰ Pa

    ΔL = 1% of the original length = 0.01 x where x is the original length

    cross sectional area = 3.0 cm² =( 3 .0 / 10000) m²= 0.0003 m²

    ε = Stress / strain

    stress = ε × strain

    stress = F /A

    F force = ε × A × ( ΔL / L) =  1.4 × 10¹⁰ Pa × 0.0003 m² × 0.01 = 4.2 × 10⁴ N

    b) F net = F max – mg ( weight) = 84000 – ( 70 × 9.8 m/s² ) ( F is double since the stress on the two leg is equally distributed)

    f net = ma = 84000 – ( 70 × 9.8 m/s² )

    a =  (84000 – ( 70 × 9.8 m/s² )) = 1190.2 m/s²

    v = u + at

    where final velocity equal zero

    – u = -at since it coming downwards

    u = at = 1190.2 m/s² × 0.03s = 35.706 m/s

    using conservation of energy

    1/2 mv² = mgh

    1/2v²/ g = h

    h = 0.5 × (35.706 m/s )² / 9.8 = 65.04 m

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