Work problem, involving a circle and velocity

[vande060]

Homework Statement

An amusement park roller-coaster of
height h has a loop-the-loop of radius R. A
frictionless car starts at the top. Find its speed
at each of the points a, b, c. Find the normal
force (vector) exerted on it at points a and b.
Find the minimal h-to-R ratio that will enable
the car to negotiate the loop without losing
contact at point b.


link to picture:
http://s861.photobucket.com/albums/ab174/alkaline262/?action=view&current=untitled-1.jpg

Homework Equations

(1/2mv^2 + V)final - (1/2mv^2 + V)initial = sum of forces non conservative forces

The Attempt at a Solution

i was going to try and find the velocity just as the car reaches the loop, then use that velocity in the above formula, but with new parameters for the circle

so here is what i tried to do to find the velocity at that point

(1/2mv^2 + mg(0)final - (1/2m(O^2) + mgh)initial = 0

^ i thought this equation should be equal to zero, because there i don't think there area any non conservative forces.

solving for v final = (2gh)^1/2, not so sure about this though

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like i said before i want to parametrize this circle now, first with regards to point a

x = Rcos((pi/2)*t)
y= Rsin((pi/2)*t)

r vector = Rcos((pi/2)*t) , Rsin((pi/2)*t)
v vector = -(pi/2)Rsin((pi/2)*t) , R(pi/2)cos((pi/2)*t)



im not really sure where I am going with this second part, any suggestions?

 

[Quinzio]

A point running in circle experiences an acceleration.
do you know what is it ?

 

[vande060]

A point running in circle experiences an acceleration.
do you know what is it ?

i remember centripetal acceleration from class, ac = ω2R =
v2/R, I am not sure how to work that into the formula above, or how it would fit into any other formula, except maybe f=ma?

 

[Quinzio]

At the top of the loop, the car will not fall down but it will remain "glued" to the track. Why ?

 

[vande060]

At the top of the loop, the car will not fall down but it will remain "glued" to the track. Why ?

the centripetal force must be greater than the force of gravity, is that right?