If a force is exerted on two ends of a Newt chromosome, it will stretch. The dat

Question

If a force is exerted on two ends of a Newt chromosome, it will stretch. The data here represent the applied force in nano-Newtons as a function of the change in length of the chromosome. The original, unstretched length of the chromosome represented in this graph is 13.6 ?m.

Presume that the chromosome shape can be approximated by a long cylinder with a diameter of 1.60 ?m. Throughout the problem be very careful with units and prefixes. If we model this chromosome as a spring, what is its spring constant?

What is the value of Young's Modulus for this given chromosome?

Explanation / Answer

Use the standard formula for an effective spring constant of a prismatic member:

k = E*A/L

where E is Young's modulus, A is cross sectional area, L is length.

You can derive this from stress, strain, and Young's modulus definitions.

A will equal Pi*d^2/4, if it is approximated as a cylinder.

Stress = E * Strain
F/A = E * ?L/L where L is unstretched length
E = FL/A?L
F = -k?L
E = (k?x)L/(A?L) = 4kL/(?d^2) since A = 1/4*?d^2

that should do it: E = 4kL/(?d^2)

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