How Much Should a Spring Be Compressed for a Roller Coaster to Complete a Loop?

[stella77]

Conservation of Energy please help!

Homework Statement

An 840 kg roller coaster car is launched from a giant spring of constant k=31kN/m into a frictionless loop-the-loop track of radius 6.2m, what is the minimum amount that the spring must be compressed if the car is to stay on the track?

Homework Equations

v=n+mg = (mv^2)/r
v= √(gr)

mgh=0.5mv^2

The Attempt at a Solution

mgh=0.5mv^2
mgh=0.5m √(gr)^2
mgh=0.5mgr
h = 0.5r
h= 3.1 m

and I am stuck after this... please help...

 

[Jebus_Chris]

Your velocity is correct.

It has initial energy which should be equal to the energy at the top point of the loop (what energies are present here?).
Find it's initial energy and set that equal to its final energy.

 

[stella77]

the initial energy is the potential energy right??

 

[Jebus_Chris]

Yes and then there are two energies present at the top of the loop.