Spring compression to complete a loop (energy)

[etothey]

Homework Statement

An 840kg 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

Wspring=0.5kx^2
Wkinetic = 0.5mv^2
Wpotential = mgh

The Attempt at a Solution

I have an attempt but it is not correct and I would be thankful if someone could tell me why.
0.5kx^2=0.5mv^2=mgh
Thus x=(mgh*2/k)^0.5
x=(840*9.8*12.4*2/31000)^0.5
x=2.57m.
The answer should be 2.87m.
Thankful for any help.

 

[supratim1]

do some calculation using conservation of energy. you will find, minimum initial velocity required to complete a loop of radius R is

v = sqrt(5gR).

so 1/2 mv^2 = 1/2kx^2.

solve.

 

[supratim1]

and Welcome to Physics Forums etothey!

 

[etothey]

do some calculation using conservation of energy. you will find, minimum initial velocity required to complete a loop of radius R is

v = sqrt(5gR).

so 1/2 mv^2 = 1/2kx^2.

solve.

Thank you very much!

 

[supratim1]

you are welcome.