Tendons are strong elastic fibers that attach muscles to bones. To a reasonable

Question

Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hooke's law. In laboratory tests on a particular tendon, it was found that, when a 255 g object was hung from it, the tendon stretched 1.23 cm . A) Find the force constant of this tendon in N/m. B) Because of its thickness, the maximum tension this tendon can support without rupturing is 138 N . By how much can the tendon stretch without rupturing? C) How much energy is stored in it at that point?

Explanation / Answer

Load = mass*gravity = (255/1000)*9.81 = 2.443 N

Force constant = Load/extension = 2.443 / (1.22/100) = 200.22 N/m

Stretching in tendon is proportional to applied load.

Therefore, max. possible stretching = Max. load / Force constant = 138 / 200.22 = 0.674 m = 67.4 cm.

Energy stored = 1/2*Force constant*extension^2 = 1/2*200.22*0.674^2 = 45.48 J

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