The Achilles tendon, which connects the calf muscles to the heel, is the thickes

Question

The Achilles tendon, which connects the calf muscles to the heel, is the thickest and strongest tendon in the body. In extreme activities, such as sprinting, it can be subjected to forces as high as 15.0 times a person's weight. According to one set of experiments, the average area of the Achilles tendon is 78.6mm2 , its average length is 30cm , and its average Young's modulus is 1474MPa. Part A How much tensile stress is required to stretch this muscle by 5.0% of its length? Express your answer using two significant figures. Part B If we model the tendon as a spring, what is its force constant? Express your answer using two significant figures. Part C If a 75kg sprinter exerts a force of 15.0 times his weight on his Achilles tendon, by how much will it stretch? Express answer in two significant figures

Explanation / Answer

first do some conversions: 30cm = .30m*.05 = .0150m (5% stretch) 78.6mm^2 = 7.86x10^-5 m^2 A) d = SL/E ----> S = dE/L (d = stretch, S = stress, L = initial length, E = young's mod) (0.015m x 1474x10^6 Pa) / 0.30m = 7.37x10^7 Pa B) F = SA (F = force, A = area) 7.37x10^7 Pa * 7.86x10^-5 m^2 = 5792.82N then F = kx ----> k = F/x (k = spring constant, x = displacement) 5792.82N / 0.015m = 386188 N/m C) 75kg * 9.8m/s^2 * 15 = 11025N d = FL/EA (11025N * 0.30m) / (1474x10^6 Pa * 7.86x10^-5m^2) = 0.0285m

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