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 length 0.200 m and cross-sectional area 50.0cm^2.

Answer 1

`3.3*10^(4) Pa`

`6.67*10^(5) Pa`

Step-by-step explanation:

Complete statement of the question is

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 (Pa) for the muscle tissue under each of these conditions .The muscle is assumed to be a uniform cylinder with length 0.200 m and cross-sectional area 50.0 cm^2.

For relaxed muscle :

`F` = force required = 25 N

`L` = Normal length = 0.2 m = 20 cm

`\Delta L` = elongation in length = 3 cm

`A` = Area of cross-section = 50 cm² = 50 x 10⁻⁴ m²

`Y` = Young's modulus for the muscle

Young's modulus is given as

`Y = (FL)/(A \Delta L) \\Y =  ((25)(20))/((50*10^(-4)) (3)) \\Y = 3.3*10^(4) Pa`

Under maximum tension :

`F'` = force required = 500 N

`L` = Normal length = 0.2 m = 20 cm

`\Delta L` = elongation in length = 3 cm

`A` = Area of cross-section = 50 cm² = 50 x 10⁻⁴ m²

`Y` = Young's modulus for the muscle

Young's modulus is given as

`Y = (F'L)/(A \Delta L) \\Y =  ((500)(20))/((50*10^(-4)) (3)) \\Y = 6.67*10^(5) Pa`