Transcript Banked Curves

Banked Curves
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
FN
Fr
Fr = FN sin θ
mg = FN cos θ
FN = mg/cos θ
Fr = mg ( sin θ/cos θ)
Fr = mg tan θ
mv2/r = mg tan θ
tan θ = v2/gr
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.
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?