A relaxed biceps muscle requires a force of 25.4 N for an elongation of 3.20 cm; under maximum tension, the same muscle requires a force of 500 N for the same elongation. Find Young's modulus for the muscle tissue under each of these conditions if the muscle can be modeled as a uniform cylinder with an initial length of 0.220 m and a cross-sectional area of 50.3 cm2.

Question

Engineering

Agustin Lawson

7 June, 23:27

A relaxed biceps muscle requires a force of 25.4 N for an elongation of 3.20 cm; under maximum tension, the same muscle requires a force of 500 N for the same elongation. Find Young's modulus for the muscle tissue under each of these conditions if the muscle can be modeled as a uniform cylinder with an initial length of 0.220 m and a cross-sectional area of 50.3 cm2.

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Gunner Pearson · Answer 1

First condition

Young's modulus = 34716.7N/m^2

Second condition

Young's modulus = 994035.8N/m^2

Explanation:

Young's modulus = Force*length/area*extension

Length = 0.220m, area = 50.3cm^2 = 50.3cm^2 * 1m^2/10000cm^2 = 0.005034m^2, extension = 3.20cm = 3.20/100 = 0.032m

First condition: Force = 25.4N

Young's modulus = 25.4*0.22/0.00503*0.032 = 34716.7N/m^2

Second condition: Force = 500N

Young's modulus = 500*0.22/0.0050.3*0.032 = 994035.8N/m^2