Banked highway curves and static friction

[joseg707]

Homework Statement

A 1200 kg car rounds a curve of radius 67 m banked at an angle of 12 degrees. If the car is traveling at 95 km/hr, will a friction force be required? If so how much and in what direction?

Homework Equations

F=ma
a=v²/r

The Attempt at a Solution

I don't know what I'm doing wrong with this problem. These are the two equations I have from them and when I try to solve I either get a huge number or a negative.

Ncos$$\theta$$-F_frsin$$\theta$$-mg=0

Nsin$$\theta$$+F_frcos$$\theta$$=ma

I'm positive that it needs friction force and I think it is in the direction of the center of curve, but I haven't figured out a way to solve. Can someone please help?

 

[Delphi51]

Banked curves are complicated. This site looks good:
http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Circular Motion/banked_no_friction.htm

 

[joseg707]

Hey thanks! I think I found out what I was doing wrong. I didn't really take notice that the force of friction was equal to the friction coefficient multiplied by the normal force. Thank you very much!

 

[davieddy]

Hey thanks! I think I found out what I was doing wrong. I didn't really take notice that the force of friction was equal to the friction coefficient multiplied by the normal force. Thank you very much!

I don't think you did.
Your equations were right but you need to solve for F by eliminating N.

By far the simplest way is to resolve || to the slope in the first place.