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Linear expansion metal rod problem

  1. May 4, 2009 #1
    Metal rod A is 0.300 m long expands by 6.50x10^-4 m when its temperature is increased by 100 degrees Celsius. Another rod made of different metal B and of the same length expands by 3.50x10^-4 m for the same increase in temperature. A third rod C, also 0.300 m long, is made up of pieces of the first two metals placed end-to-end and expands 5.80x10^4 m for the same increase in temperature. Find the length of each portion of the third bar.

    i have no idea to solve this.. help..
     
  2. jcsd
  3. May 4, 2009 #2

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    From the first part of the question, you can get the coefficients of linear expansion of both materials α1 and α2. Now for the third rod C, let β be the fraction of 0.3 m which is made of material one. Then the fraction of 0.3 m made of material two will be (1 - β). The change in length of C is ∆L = ∆L1 + ∆L2, where ∆L1 is the change in the part made of material one and ∆L2 is the change in length of the part made of material two. Write out this equation and solve for β.
     
  4. May 4, 2009 #3
    do i have to use the 5.80x10^-4 m given?
     
  5. May 4, 2009 #4

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    Yes, ∆L = 5.80 x 10-4 m, the amount by which the length of C changes.
     
  6. May 4, 2009 #5
    how do i solve this part?
     
  7. May 4, 2009 #6

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    There's nothing to solve in that part. You're just saying that the fraction of 0.3 m that is made of material one is β. For example, if β = ½, then the length of material one in C will be ½ 0.3 = 0.15 m.

    β is a variable and you don't know what it is yet. That's what you have to find.

    Do this first: Expand out this equation: ∆L = ∆L1 + ∆L2 using the formula for linear expansion.

    Hint: ∆L1 = α1β(0.3)∆T.

    I have to go now so I may not reply for a while.
     
  8. May 4, 2009 #7
    ok i was just confused... my β is equal to 0.763

    i solve for the length of each material and the first part is 0.229 m while the second part is 0.071 m..

    is that correct?
     
  9. May 4, 2009 #8

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    Ya that looks correct. I got β = 0.766.
     
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