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 252 gobject was hung from it, the tendon stretched 1.25 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 137 N. By how much can the tendon stretch without rupturing?

c) How much energy is stored in it at that point?

Explanation / Answer

Part a) The force constant (usually called the "spring constant") is the amount of the hanging weight (mass × gravity) divided by the amount of the stretch.

kx = mg

K=0.252x9.8/1.25x10^-2

k=197.56N/m

Ans-Force constant is 197.56N/m

Part b)amount of stretch = weight / (spring constant). Use 137N for the weight, and use the spring constant you calculated in part (a).

Amount of stretch=137/197.56

=0.693 m

Ans- tendon can stretch upto 0.693 m

Part c)

The amount of stored energy is ½kx², where "k" is the spring constant and "x" is the amount of stretch. Another equivalent formula (gives the same answer) is: ½F²/k, where "F" is the applied force (137N)

U=1/2x197.56x(1.25x10^-2)^2

U=0.0154 J

Ans- Energy stored is 0.0154J

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