BIO Biceps Muscle. 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. Find Young’s modulus for the muscle tissue under each of these conditions if the muscle is assumed to be a uniform cylinder with length 0.200 m and cross-sectional area 50.0 cm2.
Solution 24E Step 1: We have to calculate the Young’s modulus when it is in relaxed condition. Force on the muscle during relaxed condition, F relaxed25 N Cross sectional area of the muscle, A = 50 cm 2 2 2 Converting cm to m So, 1 cm = 10 m4 2 -4 2 Therefore, A = 50 × 10 m Length of the muscle, L = 0.2 m Elongation of the muscle, L = 3 cm = 0.03 m Therefore, equation for the Young’s modulus, Y = linear stres= F/A linear strain L/L FL 25 N×0.200 m That is, Y = A L = 50×10 m ×0.03 m 4 Young’s modulus of the muscle tissue in relaxed state, Y = 3.333 × 10 Pa