A long, thin rod of length L and cross sectional area A and elastic (Young\'s mo

Question

A long, thin rod of length L and cross sectional area A and elastic (Young's modulus) E has mass M.

a) Think of the rid as being like a Hookes Law spring; it can be stretched by applying a force. What is the spring constant k for this spring?

b) By dimensional analysis, can you combine, L,A,E and M into a frequency? Do you have more than one choice? If so, which of the choices make most sense?

c) Look up the properties of femur bone and and compute frequency for the femur bone.

d) Repeat part (c) but replacing the mass M of the femur bone with the mass of the typical college-age human. Hold everything else constant. That is, think of this problem as being a human mass on a femur bone spring.

e) Compare the frequency you got in part C to the dimensional analysis frequency you can obtain by combining acceleration due to gravity g with L and M. what does frequency represent? Is it higher or lower? Does that jive with your intuition??

Please help me on this problem. I will award you lifesaver. THANK YOU

Explanation / Answer

By Hookes law of elasticity we have stress directly proportional to stralin. F= force Stress=F/A Strain=x/L (x= small displacement due to application of force) E=FL/Ax F=(AE/L)*x F=kx k=AE/L

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