Banking angle for highway curve at 93 km/h with 210 m radius

[Gattz]

Homework Statement

A circular curve of highway is designed for traffic moving at 93 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 210 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 93 km/h?

Homework Equations

a=v²/r

The Attempt at a Solution

I found acceleration to be 3.177 m/s². Then I tried setting ma to F_nradial, which I got to be mgcostheta * mgsintheta. But there are two thetas.

 

[defunc]

Wheres the cosine coming from? I think the correct equation should be ma=mgsin(theta)

 

[planck42]

Before trying to directly calculate centripetal acceleration, ask yourself about the forces that act on a car in motion on a banked curve.