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(Mathematical Physics) Mass on four elastic rods

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    In a gravitational detector we put a mass of 10^4 kg onto four rods, which are located at the angles of a square. The rods are 25 cm high with S = 3cm^2, two of them are made of copper, two of steele and they are situated on opposite sides. The top surfaces of rods are polished to the exactly the same height, the bottom side of the test mass is polished with same precision.
    A) For how much do the rods contract when we carefully place the test mass onto them, so that its center of mass is exactly above the center of the square?
    B) How does the height of rods depend on the temperature?
    How much does the temperature need to change so that only two rods would carry entire test mass?
    E(Cu)=8*10^10 N/m^2, E(steel)=2*10^11 N/m^2, the coefficients of linear thermal expansion are 17*10^(-6) K^(-1) for copper and 12*10^(-6) K^(-1) for steel.


    3. The attempt at a solution
    http://img638.imageshack.us/img638/8550/mafinaloga1.jpg [Broken]
    I think my attempt is not correct. I started by supposing that all rods contract to the same lenght.
    This is a problem from an old exam (Mathematical Physics) so I don't have the solution. Any help would be appreciated.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 11, 2012 #2
    It would seem the rods must contract the same amount (for the weight not the heat) since otherwise to rods carry all the weight thus the others don't contract thus they do carry weight which is a contradiction.
     
  4. Mar 12, 2012 #3
    Ok. How about the rest of my solution? (I'm sorry I had to post a picture, but I'm no good at typing equations and this was easier.)
     
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