Banked curves are curved paths, such as those found on roads or tracks, where the outer edge is elevated compared to the inner edge. This design helps vehicles negotiate curves at higher speeds by providing additional centripetal force through the component of normal force.
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Banked curves reduce reliance on friction to provide the necessary centripetal force for circular motion.
The angle of banking is calculated using the equation $\tan(\theta) = \frac{v^2}{rg}$, where $\theta$ is the banking angle, $v$ is velocity, $r$ is radius of curvature, and $g$ is acceleration due to gravity.
At a specific speed (the design speed), no frictional force is needed to maintain circular motion on a banked curve.
Centripetal force on a banked curve has two components: one from friction and one from the horizontal component of the normal force.
In real-world applications, road designers must consider factors like weather conditions and vehicle types when determining the appropriate banking angle.
Review Questions
How does a banked curve help in reducing reliance on friction?
What factors influence the calculation of the banking angle?
Why might real-world road designers need to adjust theoretical calculations for banked curves?
Related terms
Centripetal Force: The inward force required to keep an object moving in a circular path at constant speed.
Normal Force: The perpendicular contact force exerted by a surface on another object.
Friction: The resistive force that opposes relative motion between two surfaces in contact.