How Does Height Affect Weightlessness on a Frictionless Roller Coaster?

[DrunkApple]

Homework Statement

Consider a frictionless roller coaster such as
depicted below.
The acceleration of gravity is 9.8 m/s2.
Passenger cars start at point A with zero
initial speed, accelerate as they go down to
point B, swing around the circular vertical
loop B ! C ! B of radius 30 m, then go
on towards further adventures (not shown).
When a car goes through the top of the loop
(point C), the passengers feel weightless (for
just a moment).
What is the height hA of the starting
point A above the loop’s bottom B?
Answer in units of m

Homework Equations

KE = .5mv^2
PE = mgh

The Attempt at a Solution

I know that the system is conservative energy since there is no friction and whatnot, so mgh(a) is the total energy. But what I don't get is, how does weightlessness come into this?
If it's weightless, does that mean normal force doesn't exist?

 

[lightgrav]

did you forget ΣF = ma ? what about circular paths?

 

[DrunkApple]

then does gravity becomes the acceleration of centripetal force?

 

[lightgrav]

yes, to get the speed at the top ... Energy conservation then gets height at begining