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Homework Help: Conservation of energy of three spring system.

  1. Apr 9, 2010 #1
    1. Find the equation for conservation of energy in system. System consists of three springs A,B and C with stiffness k, 2k and 0.5k respectively and natural lengths l, 0.5l and 2l respectively.



    2. Relevant equations
    Equation for conservation of energy [tex]E=K+U_{spring}+U_{gravity}[/tex]
    [tex]K=\frac{1}{2}mv^2[/tex]
    Datum taken at point A, [tex]U_{gravity}=-mgx[/tex]
    [tex]U_{spring}=\frac{1}{2}k(x-l_0)^2[/tex]
    Where [tex]K[/tex] is kinetic energy and [tex]k[/tex] is the spring stiffness and [tex]l_0[/tex] is the natural length.

    3. The attempt at a solution
    By analysing the diagam
    [tex]U_{springA}=\frac{1}{2}k(x-l_0)^2[/tex]
    [tex]U_{springB}=\frac{1}{2}*2k(x-\frac{1}{2}l_0-\frac{1}{2}l_0)^2=k(x-l_0)^2[/tex]
    [tex]U_{springC}=\frac{1}{2}*\frac{1}{2}k(4l_0-x-2l_0)^2=\frac{1}{4}k(2l_0-x)^2[/tex]
    [tex]K=\frac{1}{2}mv^2[/tex]
    [tex]U_{gravity}=-mgx[/tex]

    My question is, is the answer [tex]E=K+U_{gravity}+U_{springA}+U_{springB}+U_{springC}[/tex] and have I derived the individual energies correctly?
     
    Last edited: Jun 23, 2010
  2. jcsd
  3. Apr 16, 2010 #2
    Any ideas anyone?
     
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