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Atwood machine probolem: Apply Lagrangian equations

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A uniform circular pulley of mass 2m can rotate freely about its axis of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by a massless string which passes over the pulley without slipping. The whole system undergoes planar motion with the masses moving vertically . Take the rotation angle of the pulley as generilesed coordinate and obtain Lagrange's equation for the mtoion. deduced upward acceleration.

    2. Relevant equations



    3. The attempt at a solution

    3Mdv/dt=3Mg-T

    Mdv/dt=T-Mg

    deltaH=a*delta(theta)

    v_c=v-a*omega

    Sigma=T*dr=0

    r x Mg(-y-hat)=0

    pulley is frictionless.

    Seems like the only thing I should do would be to find T which would help me find the acceletion for M.
     
  2. jcsd
  3. Feb 23, 2009 #2

    AEM

    User Avatar

    Shouldn't you be constructing the Lagrangian which is given by

    [tex] L = T - V [/tex]

    where T is the kinetic energy and V is the potential energy and from this you calculate the Euler-Lagrange equations?
     
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