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Mechanics Question

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A particle slides under gravity along a smooth path in the x-z plane by z=b-(x^2/a).
    Show that the energy of this motion can be expressed as E=.5m*xdot^2*[1+(2x/a)^2] + mgb[1-(x^2/ab)]

    2. Relevant equations
    T(A)+V(A) = T(B)+V(B), where T is kinetic energy

    3. The attempt at a solution
    I understand how to get the potential energy term, but I am confused on how to calculate the kinetic term.
  2. jcsd
  3. Nov 21, 2007 #2
    [tex]v^2=\dot z^2+\dot x^2[/tex]

    [tex]\dot z=-\frac{2x\dot x}{a}[/tex]
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