Roller coaster in a circular loop problem

[razis_wwf13]

Homework Statement

A roller coaster car is on a track that forms a circular loop of radius R in the vertical plane.

(a) If the car is to maintain contact with the track at the top of the loop, what is the minimum speed v that the car must have at the bottom of the loop? Ignore air resistance and rolling friction.
(b) If the car has a speed 6v/5 at the bottom of the loop, then what will be force vector acting on the car by the track when it reaches the top of the loop? [v is the minimum speed calculated in (a).]
(c) If the car has a speed 4v/5 at the bottom of the loop, locate the point on the track where the car ceases to maintain contact with the track.

Homework Equations

0.5mv₁² + mg(2R) - 0.5mv₂² - mg(0) = 0.
F_c = N - mg

The Attempt at a Solution

For a), i just used the first eqn, sub in all the known datas, i got v = 2sqrt(gR) as the min speed needed.

For b), i assumed force vector needed is normal force. So at the top, i used the 2nd eqn, and i got N = F_c - mg = mv²/R - mg.

For c), i don't know how to attempt the qn. Hope you guys can help thx!

 

[Fightfish]

Your answer for (a) looks dubious; recheck your working.
For (c), consider how the centripetal force on the car varies with its position on the track (hint: use an angle approach). Then find the point where N = 0.