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 11 times a person's weight. According to one set of experiments, the average area of the Achilles tendon is 78.7 mm2 , its average length is 27 cm, and its average Young's modulus is 1474 MPa

1) How much tensile stress is required to stretch this muscle by 5.4 % of its length?

2) If we model the tendon as a spring, what is its force constant?

3) If a 75 kg sprinter exerts a force of 11 times his weight on his Achilles tendon, by how much will it stretch?

Explanation / Answer

A) E = /
1474e6 Pa = / 0.054
= 2.72e10 Pa = 27 GPa = 27000 MPa

B) k = F / x
F = * A = 2.72e10Pa * 78.7mm² * (1m/1000mm)² = 2140640 N
x = 27cm * 0.054 = 1.5 cm = 0.015 m
k = 142709333.3 N/m

C) x = F / k = 11 * 75kg * 9.8m/s² /142709333.3N/m = 5.66e-5 m

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