# Banked Curve

**1. The problem statement, all variables and given/known data**

A curve with a 140m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction between tires and road needed to prevent skidding?

**2. Relevant equations**

F_fr = MkN

N = mgcosθ

∑F = ma

∑F_net-x = mv^2/r = Nsinθ

**3. The attempt at a solution**

I have drawn my xy coordinate system so that the x component is parallel to the curve, and , and found that the normal force is mgcosθ. However, I don’t know how to combine my equations together to find an angle theta. Is finding an angle here even the proper approach if the problem does not ask for it? Should I be doing something else instead?

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