Analysing a Circular Highway Curve: Angle, Friction & Speed

[chiurox]

Homework Statement

A circular highway curve with a radius of 200m is banked at an angle such that a car traveling 45km/h can just make it around the curve if the highway surface is frictionless.
a. what is the angle between the highway surface and the horizontal?
b. if a car travels at 40km/h around the curve, what is the centripetal force acting on the car?
c. What is the minimum value of the coefficient of friction between the tires and the highway surface necessary to prevent the car in (b) from skidding?
d. If the angle of the highway curve is as in (a), but the radius of the curve is increased to 300m, what is the speed a car must be going in order to negotiate a curve without skidding?

Homework Equations

tan(theta) = v^2/gr

The Attempt at a Solution

45km/h would be 12.5m/s
a. tan(theta) = (12.5m/s)^2 / 9.8*200
theta = 4.6degrees
b. I know that F_n sin(theta) = mv^2/r
but I'm confused how to solve this one.
c. I'll leave this blank since I haven't solved (b)
d. sqrt{tan(4.6)(9.8)(300)} = v = 15.4m/s correct?

 

[chiurox]

For part C, I have F_f = u_s F_n
v^2 = u_s gr
1600 = u_s(9.8)(200)
u_s = 0.816 right?

For part D, I have sqrt(tan(4.5)(9.8)(300)) = v = 15.2 m/s is that right?