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Chapter 1: Q11-24E (page 1)

A relaxed biceps muscle requires a force of 25.0 N for an elongation of ; 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.

Short Answer

Expert verified

3.33×104Pa6.67×105Pa

Step by step solution

01

Given information:

ForceF=25N,ElongationΔl=3.0cm,lengthl0=0.2mandAreaA=50cm2

02

Concept/Formula used:

Y=l0FAΔl

Where, Y is Young’s modulus, I0 is length of muscle, F is muscle force, A is cross-sectional area and∆Iis elongation.

03

Young modulus for relaxed condition:

A=50cm2=50×10-4m2Y=0.2m25N50×10-4m23×10-2m=3.33×104Pa

04

Young modulus for maximum tension condition:

Y=0.2m500N50×10-4m23×10-2m=6.67×105Pa

Under maximum tension the muscle tissue is much more difficult to stretch.

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