1. Banked Curves
Section 5.4

2. 5.4 Banked Curves
When a car travels around an unbanked curve, static friction provides the centripetal force.
By banking a curve, this reliance on friction can be eliminated for a given speed.

3. Derivation of Banked Curves
A car travels around a friction free banked curve
Normal Force is perpendicular to road
x component (towards center of circle) gives centripetal force
y component (up) cancels the weight of the car
Insert Figure 5.11

4. Derivation of Banked Curves
Divide the x by the y
Gives
Notice mass is not involved
Ask what happens when go to fast? (slide up and over top of curve)
Ask what happens when go to slow? (slide down curve)

5. Example
You are in charge of designing a highway cloverleaf exit ramp. What angle should you build it for speed of 35 mph and r = 100m?
13.9
35 mph = 15.6 m/s
Tan  = v2/rg  tan  = (15.6 m/s)2/((100m)(9.8 m/s2))  tan  =   = 13.9

6. Conceptual Problem
In the Daytona International Speedway, the corner is banked at 31 and r = 316 m. What is the speed that this corner was designed for?
v = 43 m/s = 96 mph
Cars go 195 mph around the curve. How?
Friction provides the rest of the centripetal force
tan  = v2/rg  tan 31 = v2/(316m)(9.8m/s2)  .6009(316m)(9.8m/s2) = v2  1861 (m/s)2 = v2  v = 43 m/s

7. Practice Problems See if you can speed your way around these!
Total of 4 problems