Young's modulus - 10 points first correct procedure!?

Question

Abductin is an elastic protein found in scallops, with a Young's modulus of Y=4.0x106 N/m2. It is used as an inner hinge ligament, with a cross-sectional area of A=0.78 mm2 and a relaxed length of L0=1.0 mm. When the muscles in the shell relax, the shell opens. This increases efficiency as the muscles do not need to exert any force to open the shell, only to close it. If the muscles must exert a force of 1.8 N to close the shell, by how much (in mm) is the abductin ligament compressed?

Answer 1

Ok, let's remember the definition of Young modulus :

Y = (F / A)/(dL / Lo)

Lo = initial lenght

dL = change of lenght

A = surface

F = force

4*10^6 = 1.8 / (0.78*10^-6) / dL / 10^-3

4*10^6 = 2.3*10^6*10^-3 / dL

dL = 0.575*10^-3 >>>> compress of the ligament

in mm :

dL = 0.575 mm

Hope that helped