For small stretches, the Achilles tendon can be modeled as an ideal spring. Experiments using a particular tendon showed that it stretched 2.66 mm when a 125-kg mass was hung from it. (a) Find the spring constant of this tendon. (b) How much would it have to stretch to store 50.0 J of energy

(a) Spring constant K = 460526.316 N/m

(b) Spring is stretched by 14.73 mm

Explanation:

We have given mass m = 125 kg

Acceleration due to gravity

Spring is stretched to x = 2.66 m = 0.00266 m

(a) Force on spring is equal to F = Kx

And force due to gravity is F = mg

These two forces will be equal

So mg = Kx

So

K = 460526.316 N/m

(b) Energy stored is given as E = 50 J

Energy stored in spring is equal to

So

x = 14.73 mm