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Linear expantion and elastic modulus- brass vs. glass

  1. Dec 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Onto a thick brass rod we attach equally long glass thread. At what temperature change will the glass thread break if the temperature coefficient of linear expansion for brass is
    α1= 20 x 10 ^-6 K^-1, and for glass is α2= 7 x 10^-6 K^-1? Young’s (elastic) modulus for glass is E1= 7 x 10^10 N/m², and shear modulus for glass is σ1= 7 x 10^7 N/m².

    2. Relevant equations

    Linear thermal expansion: α(L)= ΔL/ L(0)ΔT
    Young’s (elastic) modulus: E= FL(0)/ AΔL

    3. The attempt at a solution

    And from here I have no clue:confused: :redface:how to build a relationship between linear thermal expansion and elastic modulus and how to incorporate all the terms given to find the result.:uhh:
    Can someone please give me some hint?

    Thank you for helping!:smile:
     
  2. jcsd
  3. Dec 19, 2009 #2

    mgb_phys

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    Homework Helper

    You don't need a relation between them as such.
    You use the modulus for glass to work out at what strain the glass would break.

    Then you use the relative expansion of brass and glass to work out at what temperature the glass would have been stretched that amount.

    hint. remember the glass is also expanding as the brass does
     
  4. Dec 19, 2009 #3
    OK, I think I understood right:

    Strain: ε= ΔL/ L
    Stress: σ= F/A

    E= FL(0)/ AΔL → E= stress/strain= σ/ ε → ε= σ/ E

    ε = 7 x 10^7 N/m²/ 7 x 10^10 N/m²
    ε= 0.001

    α(L-glass)= [ΔL/ L(0)]/ ΔT= ε/ ΔT → ΔT= ε/ α(L-glass)
    ΔT= 0.001/ 7 x 10^-6 K^-1
    ΔT=0.14 x 10^3 K= 140 K

    Is this correct (big doubt?!, too low temperature)?
    Thank you for helping!
     
    Last edited: Dec 20, 2009
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