1. Banked Curves

2. Why Does Banking A Curve Help? Some centripetal force is created by a component of the normal force Normal Force is perpendicular to plane of motion FNFN FrFr

3. F r = F N sin θ mg = F N cos θ F N = mg/cos θ F r = mg ( sin θ/cos θ) F r = mg tan θ mv 2 /r = mg tan θ tan θ = v 2 /gr

4. Example What angle should a freeway off-ramp curve be banked? The radius of the curve is 50m and the average car travels at 50 km/h.

5. Example 2 A 1200 kg car rounds a curve of radius 70m with a banking of 12°. The car is traveling 90 km/h, will a frictional force be required? If so, how much?