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Conservation of energy related question

  1. Feb 17, 2007 #1
    1. The problem statement, all variables and given/known data
    A skier of mass m starts from test at the top of a solid sphere of radius r and slides down its frictionless surface. (a) At what angle [tex]\theta[/tex] will the skier leave the sphere? (b) If friction were present, would the skier fly off at a greater or lesser angle?
    [​IMG]

    2. Relevant equations
    Conservation of energy (because this problem is from that chapter)

    3. The attempt at a solution
    The skier will leave the sphere if the normal force becomes zero. So radially:
    [tex]mg \cos \theta - N = \frac{mv^2}{r}[/tex]
    [tex]mg \cos \theta = \frac{mv^2}{r}[/tex]
    [tex]v^2 = rg \cos \theta [/tex]
    Then, taking the potential energy reference to be the height when the skier leaves the sphere,
    [tex]E_i = E_f[/tex]
    [tex]K_i + U_i = K_f + U_f[/tex]
    [tex]0 + mg(r - r \cos \theta) = 1/2 m (rg \cos \theta) + 0[/tex]
    But this doesn't work if I try to solve for theta!
     
  2. jcsd
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