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Chapter 1: Q24 E (page 1)

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鈥檚 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 50.0cm2.

Short Answer

Expert verified

3.33脳104Pa6.67脳105Pa

Step by step solution

01

Given information:

Force: F = 25 N,

Elongation: 鈭�l=30.0cm,

length: l0=0.2mand

Area:A=50cm2.

02

Concept/Formula used:

Y=l0F鈭�l

Where, Y is Young鈥檚 modulus,l0is length of muscle, F is muscle force, A is cross-sectional area and 鈭�l is elongation.

03

(a) Young modulus for relaxed condition:

A=50cm2=50脳10-4m2

role="math" localid="1664362495934" Y=(0.2m)(25N)(50脳10-4m2)(3脳10-2m)=3.33脳104Pa

04

(b) Young modulus for maximum tension condition:

Y=(0.2m)(500N)(50脳10-4m2)(3脳10-2m)=6.67脳105Pa

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

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