Can the Law of Conservation of Energy Solve This Rolling Ball Problem?

[guru]

Need help with this problem

A 40 g ball is released from rest 2m above the bottom of a track. It rolls down a straight 30-degree segment, then back up a parabolic segment whose shape is given by y=(1/4)x^2, where x and y are in m. How high will the ball go on the right before reversing direction and rolling back down?

Have no clue how to start this problem.

 

[vsage]

how much potential energy does ball originally have? It can't lose any more energy going up the parabolic side than it gained from being dropped from 2m up.

 

[Sirus]

You can do this problem without any calculations. Apply the law of conservation of total mechanical energy:
$$E_{mechanical~initial}=E_{mechanical~final}$$
$$E_{potential~initial}+E_{kinetic~initial}=E_{potential~final}+E_{kinetic~final}$$