Answer:
Part(a): The value of the spring constant is
.
Part(b): The work done by the variable force that stretches the collagen is
.
Explanation:
Part(a):
If '
' be the force constant and if due the application of a force '
' on the collagen '
' be it's increase in length, then from Hook's law

Also, Young's modulus of a material is given by

where '
' is the area of the material and '
' is the length.
Comparing equation (
) and (
) we can write

Here, we have to consider only the circular surface of the collagen as force is applied only perpendicular to this surface.
Substituting the given values in equation (
), we have

Part(b):
We know the amount of work done (
) on the collagen is stored as a potential energy (
) within it. Now, the amount of work done by the variable force that stretches the collagen can be written as

Substituting all the values, we can write

Explanation:
we can use the formula F = ma
hence,
500 = 75a
a = 6.666 m/s² or 6(2/3) m/s²
hope this helps.
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