Roller Coaster Physics in a Gravity-Less Park?

[murrskeez]

Homework Statement

A roller coaster is designed in an area of the park that is gravity-less. The roller coaster will accelerate a cart with a total mass of 10kg, from the initial position as shown in the figure to point A. After passing through point A, the cart will no longer speed up and have constant speed as it goes around the loop with radius R.
a) Draw the free body diagrams for the cart at point A, B, and C.
b) What is the force the track exerts on the cart at points A, B, and C given the velocity of the cart as it goes around the loop, v = 35m/s?
c) What is the acceleration between the initial position and point A, given the velocity at point A needs to be 35m/s.
d) What is the net work done on the cart as it goes from point A to the top of the loop at point C?
e)Now considering gravity, at point B, the cart will slow down with a rate of 10m/s2. If the velocity at point A is 35m/s, then what is the magnitude of acceleration at this point?

Homework Equations

w = sfcosθ
vx² = v0x² +2a(x-x₀)

The Attempt at a Solution

For parts a and b, I'm confused about the park being gravity-less...wouldn't that mean there would be no gravitational force on the cart and thus no normal force? I don't see how the track could exert a force on the cart if it isn't affected by gravity. Why would the cart even remain on the track?
c) 6.13m/s2
d) how could work be done without the force of gravity?
e) I don't even know where to begin.

I'm very confused, any feedback would be greatly appreciated.

 

[PhanthomJay]

That's a weird park for sure. But why can't you have a normal force without gravity?
The normal force is a contact force that in this case provides the inward centripetal acceleration. And surely work can be done without gravity, as in pushing an object in gravity-less space. But use the work-energy theorem to see if work is done in this example without gravity. You can also use the theorem for the gravity condition.