1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
    http://img158.imageshack.us/img158/2091/chp8pro24pu5.png [Broken]

    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!
    Last edited by a moderator: May 2, 2017
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted