Centripetal Force: Banked Curve

[badsniper]

Homework Statement

A 1200 kg car travels around a curve banked at 42.5 degrees in a circular path of radius = 150m, but the ramp is only 55m long. The force of friction on the car is 9000N, calculate the speed of the car.

So:

radius = 150 m
θ (angle the incline makes with the horizontal) = 42.5
mass = 1200 kg
Friction = 9000 N

Homework Equations

F_c= F_Nx + F_Fx

F_c= mv² / r

The Attempt at a Solution

The car does not move in the y-plane, therefore:

F_f + F_g + F_N = 0

F_N = (mg + F_fsinθ)/cosθ

Solve for F_N and I got 24213.83512 N

Then I used the value of F_N to find F_Nx and added F_Fx to it.

Then I multiplied by the radius, divided by the mass and took the square root leaving me with 54m/s.

However, when I use the formula found on this page http://en.wikipedia.org/wiki/Banked_turn" I got 67 m/s.

Which one is right? And If I'm wrong, where did I go wrong?

 

[LawrenceC]

How did you apply the 9000N to the equations on the Wiki site?