Centripetal Force on a curved bank?

Question

Scenario: A car is going along a banked curved road.

Given:
The radius of that curved corner is 50 m
The car's velocity is 30 m/s
The angle of the curved road is 20 degrees

I'm asked to find:
-The normal force acting on the car
-The force of gravity on the car
-The coefficient of friction needed to keep the car from skidding

Here's a picture of the original question.
http://img158.imageshack.us/img158/1486/untitled1ld4.jpg

Answer 1

The forces acting on the car are:

Gravity pulling the car down the ramp

sin(20)*m*g

And gravity pressing the car into the ramp
cos(20)*m*g

And the Centripetal force pushing the car radially from the center of the curve, which has two components:

The part pressing the car into the ramp:
sin(20)*m*v^2/r

and the part pushing the car up the ramp

cos(20)*m*v^2/r

and friction if the forces parallel to the plane fo the curve don't balance and the car doesn't slide.

Normal force is the sum of the forces pressing the car into the ramp
cos(20)*m*g+sin(20)*m*v^2/r=N

The force of gravity is given above in two components

The coefficient of friction to keep the car from sliding
friction =N*u

And
cos(20)*m*v^2/r=
sin(20)*m*g+
u*(cos(20)*m*g+sin(20)*m*v^2/r)

The mass divides out

cos(20)*v^2/r=
sin(20)*g+
u*(cos(20)*g+sin(20)*v^2/r)

(cos(20)*v^2/r-sin(20)*g)/
(cos(20)*g+sin(20)*v^2/r)
=u
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