Question

The Achilles tendon connects the muscles in your calf to the back of your foot. When you are sprinting, your Achilles tendon alternately stretches, as you bring your weight down onto your forward foot, and contracts to push you off the ground. A 70 kg runner has an Achilles tendon that is 15 cm long with a typical 1.1×10−4m2 area. By how much will the runner's Achilles tendon stretch if theforce on it is 8.0 times his weight? Young's modulus for tendor is 0.15*1010N/m2.

Answer 1

Answer:

5 mm

Explanation:

Youngs's modulus (Y) is described by the following expression:

$Y=\frac{F*L}{\Delta L*A}$

Where F is the force exerted on the tendon, L is its length, A is its area and ΔL is its change in length (stretching).

The force in this case is 8 times the weight of the runner:

$F= 8*m*g\\F= 8*70*9.8\\F=5488 N$

Therefore, the change in length of the tendon is given by:

$\Delta L=\frac{F*L}{Y*A}\\\Delta L=\frac{5488*0.15}{0.15*10^{10}*1.1*10^{-4}}\\\Delta L= 0.004989 m$

the runner's Achilles tendon will stretch by 0.004989 m, which is roughly 5 mm.