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Mercury-compensated pendulum

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Mercury-compensated pendulum

    A small part of Nickel tube is fulfilled with mercury.

    (Alpha) Linear coefficient of expansion (Nickel)= 1x10^-5
    (Beta) Volumetric coefficient of expansion (Mercury)= 18X10^-5

    FIND: What part of tube should be fullfilled, that the period of the pendulum would not depend upon temperature. And there is two different cases:
    a) When centre of mass coincide with centre of Mercury in that tube.
    b) Include misalignment of centres...


    2. Relevant equations

    T=2pi(l/g)^1/2

    deltaV/V=Beta*deltaT

    deltaL/L=Alpha*deltaT

    L=L0(1+alpha*deltaT)
    V=V0(1+Beta*deltaT)

    Should be more but don't know. Maybe someone could help :-)
     
    Last edited: Apr 21, 2009
  2. jcsd
  3. Apr 24, 2009 #2

    djeitnstine

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    Hello simon. Would you happen to have any form of diagrams? I am having a difficult time imagining this. What is the tube connected to? Am I to assume the tube is the bob? some more details on the setup would be nice
     
  4. Apr 24, 2009 #3
    attachment.php?attachmentid=18596&stc=1&d=1240575450.jpg

    cases: a) the upper level of mercury should coincide with the mass centre of whole pendulum and b) it should not coincide.
     

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  5. Apr 26, 2009 #4

    Redbelly98

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    Hello SimonasV,

    Think about: what is "l" in the pendulum equation?
     
  6. Apr 27, 2009 #5
    l=L - length of pendulum
     
  7. Apr 27, 2009 #6

    Redbelly98

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    That's true if the pendulum mass is a point-mass.

    However, in this example the mass occupies a region of space. So how would we define l in this case? (Hint: it's the distance from the pivot point to ______?)
     
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