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Young's modulus of a hanging wire

  1. Feb 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A hanging wire made of an alloy of titanium with diameter 0.5cm is initially 6m long. When a 60kg mass is hung from it, the wire stretches an amount 1.44cm. A mole of titanium has a mass of 48g, and its density is 4.54g[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngcm3. [Broken]

    Based on these experimental measurements, what is Young's modulus for this alloy of titanium?

    Y=


    As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.60×10-10m for titanium. The micro quantity ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi [Broken] (the stiffness of one interatomic bond) can be related to the macro property Y. Determine the interatomic spring stiffness:

    ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi [Broken]=

    2. Relevant equations


    Y=(FT/A) / (ΔL/L)


    3. The attempt at a solution

    A=pir^2
    A=pi(.25)^2
    Stress = (60)(9.8)/.1963
    Y= (588/.1963) / (600/1.44)

    I thought everything was set up right.. Need assistance on part 2 also, thanks.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 13, 2015 #2
    Watch those units. Also, arithmetic error.

    Chet
     
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