Car on banked curve with Friction

[luckee]

Homework Statement

A car of mass 1200 kg enters a turn of radius 20 m traveling at 12 m/s. The curve is banked at an angle of 37°. What is the normal force on the car by the road? (Assume that there is friction, and use g=10 m/s².)

Homework Equations

F=ma_c
a_c=v²/r
f_s=$$\mu$$_sN

The Attempt at a Solution

I feel like this problem should be so easy, but for some reason I cannot come to the correct solution. There are 3 forces for this problem: mg, Normal and friction.

So far, what I got is this:

X-direction
ma_c=N sin $$\theta$$+$$\mu$$_s N cos$$\theta$$

Y-direction
0=N cos$$\theta$$-$$\mu$$_s N sin$$\theta$$-mg

Am I on the right path? and how do I solve this without given the mu s?

 

[jackqpublic]

mutiple the X-direction equation by [;\sin;][;\Theta;]
and the Y-direction equation by [;\cos;][;\Theta;]
then add them.

 

[tomcue]

Yes, you are on the right track. To solve for the normal force, you can use the equation for centripetal acceleration, ac=v^2/r, and substitute it into the x-direction equation. This will give you:
mac=N sin \theta+\mus N cos\theta
m(v^2/r)=N sin \theta+\mus N cos\theta
N(mg cos \theta - mv^2/r)=\mus N cos\theta

Then, you can solve for N by dividing both sides by (mg cos \theta - mv^2/r) and using the given values for mass, velocity, and radius. This will give you the normal force exerted on the car by the road.