Muscles are attached to bones by means of tendons. The maximum force that a musc

Question

Muscles are attached to bones by means of tendons. 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=A, where (sigma) is a proportionality constant. Surprisingly, is about the same for the muscles of all animals and has the numerical value of 3.0×105 in SI units. The gastrocnemius muscle, in the back of the leg, has two portions, known as the medial and lateral heads. Assume that they attach to the Achilles tendon as shown in the figure. The cross-sectional area of each of these two muscles is typically 26 cm2 for many adults. What is the maximum tension they can produce in the Achilles tendon?

Explanation / Answer

we can divide the figure, that has a 45 degree angle, into two triangles, with 22.5 as theta. we divide one triangle into its x and y components. since tension is downwards, we can disregard the x component and just work with the y. y=Fcos22.5.
For F, we use the given formula. sigma* 26cm^2.

F=3.0 x 10^5*26*10^-4 = 780 N
Now do Fcos22.5, and multiply by 2 (since we have two triangles),

we get 1441.25 N

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