Static friction, uniform circular motion problem

[thepatient]

So I've been pondering on this question for quite a while and I'm a little stumped. It's not a homework problem; just a problem I came across yahoo answers a week ago. Basically it's a true or false question:

Homework Statement

If a highway curve is properly banked and posted at 45 mph, it is a good idea to drive somewhat below this speed if your tires are bald or if the road is icy?

Homework Equations

a(rad) = v^2/R
F(net) = ma
F (static friction force) is less than or equal to Force of normal times coefficient of static friction.

The Attempt at a Solution

So basically, I first assumed it's true, because the reduced friction between the road and tires at a higher speed would probably make you skid off the road. Others said false because it's undergoing uniform circular motion through the curve. Which would also make sense too.

What do you guys think? Am I right or wrong? XD I tried solving but there are too many unknowns and the force of static friction would have an x and y component if I choose a standard axis, which makes it very messy. I tried a tilted axis, but then I get an x and y component of acceleration, which is just as bad. XD

 

[thepatient]

I think I obtained the general formula for the minimum velocity in order to take the turn. I used forces and x and y components of acceleration and obtained v =[ (gtan(theta) + zg)/(1+ztan(theta)/R) ]^1/2
g = gravity (about 9.8 m/s^2)
theta being the angle that the banked curve makes on the x axis
z being the coefficient of static friction
R being the radius of the curve

I'm not sure if I did the right approach by using components of acceleration and letting the magnitude of the acceleration in the x-axis be v^2/r cos(theta) and y-axis acceleration v^2/r sin(theta)

http://i272.photobucket.com/albums/jj198/1000_2008/IMG_0485.jpg?t=1290936317//Min or max velocity... darn and I thought I was doing good in physics. :(

 

[S.Mukherjee]

hi,
the statement is false because if the road is banked for a speed of 45 mph then it means that at 45 mph, there is no friction acting on the tyres in the radial direction because centripetal forces are provided by normal reactions solely.So, friction only acts in the direction tangential to the vehicle . So if the tyres are worn out, then one must drive at 45 mph and not less than that because driving at less 45 mph will generate a friction in radial direction opposite to centre of revolution.This will create chances of slipping if these frictional forces are not high enough which is quite possible if tyres are bald or road is icy.