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Thermal Elongation of 2 different rods

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data
    A metal rod of length 30 cm elongates 0.075 cm when heated from 00C to 1000C. a second rod of the same length but from an other metal elongates, at the same temperature difference, 0.045 cm.
    A third rod is made of 2 pieces from the 2 previous ones and of the same length elongates, at the same temperature difference, 0.06 cm. what are the length of the 2 pieces the rod is made of.

    2. Relevant equations
    $$L=L_0(1+\alpha\Delta t)$$

    3. The attempt at a solution
    Finding ##\alpha## of the rods:
    $$30.075=30(1+100\alpha_1)\rightarrow\alpha_1=25E-6$$
    $$30.045=30(1+100\alpha_2)\rightarrow\alpha_2=15E-6$$
    The combined rod:
    $$30.06=L_1(1+100\alpha_1)+(30-L_1)(1+100\alpha_2)$$
    $$0.06=L_1(25-15)E-4+30\cdot 15E-4$$
    $$0.06=L_1\cdot 10E-4+0.045\rightarrow L_1=15$$
    The answer should be 10 cm and 20 cm
     
  2. jcsd
  3. Sep 24, 2014 #2
    I think your answer is correct. But you can always check which one provides the correct elongation.
     
  4. Sep 24, 2014 #3
    I get 15 also.

    Chet
     
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