## A cylindrically shaped piece of collagen (a substance found in the body in connective tissue) is being stretched by a force that increases f

Question

A cylindrically shaped piece of collagen (a substance found in the body in connective tissue) is being stretched by a force that increases from 0 to 3.06 10-2 N. The length and radius of the collagen are, respectively, 2.7 and 0.093 cm, and Young’s modulus is 3.10 106 N/m2.
(a) If the stretching obeys Hooke’s law, what is the spring constant k for collagen?
(b) How much work is done by the variable force that stretches the collagen?

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6 months 2021-08-31T05:17:39+00:00 1 Answers 0 views 0

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 