The maximum force that a muscle can exert is directly proportional to its cross-

Question

The maximum force that a muscle can exert is directly proportional to its cross-sectional area A at the widest point. We can express this relationship mathematically as Fmax = sigmaA, where (sigma) is a proportionality constant. Sigma has the numerical value of 3.0 x 10^5 in SI units.
In one set of experiments, the average maximum force that the gastrocnemius muscle in the back of the lower leg could exert was measured to be 740 N. What does this result tell us was the average cross-sectional area, in cm^2, of that muscle for the people in the study? So, A =?cm^2?

Explanation / Answer

Given F max = 740 N We know F max = A From this average cross sectional area A = F max /                                                                 = 740 N / ( 3 x 10 5 )                                                                 = 24.666 x 10 -4 m 2                                                                 = 24.666 cm 2

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