Physics · LAWS OF MOTION

Refer to the given figure showing a car of mass \( m \) navigating a circular track of radius \( R \) banked at an angle \( \theta \). Under the maximum speed condition where static friction \( f \) acts down the incline, which pair of equilibrium equations correctly describes the force components along the vertical direction and horizontal centripetal direction?

1. Vertical: \( N = mg \cos\theta \); Horizontal: \( f = \frac{m v^2}{R} \)
2. Vertical: \( N \sin\theta = mg + f \cos\theta \); Horizontal: \( N \cos\theta + f \sin\theta = \frac{m v^2}{R} \)
3. Vertical: \( N \cos\theta + f \sin\theta = mg \); Horizontal: \( N \sin\theta - f \cos\theta = \frac{m v^2}{R} \)
4. Vertical: \( N \cos\theta = mg + f \sin\theta \); Horizontal: \( N \sin\theta + f \cos\theta = \frac{m v^2}{R} \)