# Conservation of energy

1. Oct 31, 2004

### 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.

Last edited: Oct 31, 2004
2. Oct 31, 2004

### 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.

3. Oct 31, 2004

### Sirus

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