# Conservation of energy related question

1. Feb 17, 2007

### endeavor

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 $$\theta$$ 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:
$$mg \cos \theta - N = \frac{mv^2}{r}$$
$$mg \cos \theta = \frac{mv^2}{r}$$
$$v^2 = rg \cos \theta$$
Then, taking the potential energy reference to be the height when the skier leaves the sphere,
$$E_i = E_f$$
$$K_i + U_i = K_f + U_f$$
$$0 + mg(r - r \cos \theta) = 1/2 m (rg \cos \theta) + 0$$
But this doesn't work if I try to solve for theta!

Last edited by a moderator: May 2, 2017