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Homework Help: Linear expantion and elastic modulus- brass vs. glass

  1. Dec 20, 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

    Thank you mgb_phys for hint- it helped a lot:

    Qute: "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" (mgb_phys)

    So I calculated strain:
    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

    But now, I don't know how to combine brass and glass to find the final answer.
    I tried this, but I doubt is correct:

    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)?

    Any hints?
    Thank you for helping!
     
  2. jcsd
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