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A cylindrically shaped piece of collagen (a substance found in the body in connective tissue) is being stretched by a force that increases f
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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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2021-08-31T05:17:39+00:00
2021-08-31T05:17:39+00:00 1 Answers
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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