When relaxed, an elastic cord has length L, cross section area A, mass M, and Young modulus Y.

Question

An object of mass m is hung from the ceiling using the cord. The system reaches a steady state.
What is the longitudinal mass distribution lambda(z) of the stretched cord as a function of distance z from the object?
Hint: consider the stress-strain relation only for an infinitesimal segment of the cord. You may assume that the cross section remains A.
As usual, don't forget to explore the limits of your result.

Answer 1

Looks like a MIT 8:01 problem to me :)

It is too much for me at present but this link might help a little:

https://books.google.com/books?id=PTj2eEbT_jQC&pg=PA67&dq=elongation+of+long+hanging+rod+due+to+own+weight&hl=en&sa=X&ei=7TGfVI_7NcufgwSx-YKYCg&ved=0CGwQ6AEwCQ#v=onepage&q=elongation%20of%20long%20hanging%20rod%20due%20to%20own%20weight&f=false

Answer 2

try deleting the s on https
http://books.google.com/books?id=PTj2eEbT_jQC&pg=PA67&dq=elongation+of+long+hanging+rod+due+to+own+weight&hl=en&sa=X&ei=7TGfVI_7NcufgwSx-YKYCg&ved=0CGwQ6AEwCQ#v=onepage&q=elongation%20of%20long%20hanging%20rod%20due%20to%20own%20weight&f=false

Answer 3

Note equation 1.78 seems to be missing an = sign just left of the integral sign