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A 13 cm long animal tendon was found to stretch 3.8 mm by a force of 13 N. The tendon was approximately round with an average diameter of 9.0 mm. Calculate the elastic modulus of this tendon.

  • URGENT -

    URGENT

  • Physics -

    *First, calculate the area:

    Area = (pi)r^2 = (π)4.5^2 = 63.6173 mm^2 = 0.0000636173 m^2

    *Now, use this equation to find E, the elastic modulus:

    E = (F/A) ÷ (ΔL/L0)

    *Convert all length measurements to m and then plug and chug:

    E = (13/0.0000636173) ÷ (0.0038/0.13) = 6 990 816.05 = 7.0 x 10^6

    *Elastic modulus is measured in N per m^2, so the final answer is 7.0 x 10^6 N/m^2

  • Physics -

    Further notes:

    *Found r by taking diameter and dividing by two

    *F = force = 13 N, listed in the problem

    *A = area, which was found above (to convert from mm to m, multiply the mm figure by 10^-3; to convert from mm^2 to m^2, multiply the mm^2 figure by 10^-6, or twice the exponent of the conversion from mm to m)

    *ΔL = 3.8 mm, listed in the problem

    *L0 (a.k.a. "L initial") = 13 cm, listed in the problem

  • Physics -

    Oh, and the equation for Young's modulus (the elastic modulus), E = (F/A) ÷ (ΔL/L0), is actually stress divided by strain:

    Stress = F/A
    Strain = ΔL/L0

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