Question

A relaxed biceps muscle requires a force of 25.0 N for an elongation of 3.0 cm; the same muscle under maximum tension requires a force of 500 N for the same elongation. The muscle is assumed to be a uniform cylinder with a length of 0.200 m and a cross-sectional area of 50.0 cm��. Find Young's modulus for the relaxed muscle.

Answer 1

The Young's modulus for the relaxed muscle is 33.33 N/cm².

Step-by-step explanation:

The Young's modulus for the relaxed muscle can be calculated using the formula:

Young's modulus (E) = stress / strain

In this case, we can calculate the stress and strain values using the given information:

Stress = Force / Area

The force required for elongation in the relaxed muscle is 25.0 N, and the cross-sectional area is 50.0 cm². Therefore, the stress is:

Stress = 25.0 N / 50.0 cm² = 0.5 N/cm²

The strain can be calculated as the elongation divided by the length:

Strain = Elongation / Length

Thus, the strain can be calculated as:

Strain = 3.0 cm / 0.200 m = 0.015

Substituting these values into the formula for Young's modulus:

E = 0.5 N/cm² / 0.015 = 33.33 N/cm²

Therefore, the Young's modulus for the relaxed muscle is 33.33 N/cm².