2 5.4 Banked CurvesWhen 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 curveNormal Force is perpendicular to roadx component (towards center of circle) gives centripetal forcey component (up) cancels the weight of the carInsert Figure 5.11
4 Derivation of Banked Curves Divide the x by the yGivesNotice mass is not involvedAsk what happens when go to fast? (slide up and over top of curve)Ask what happens when go to slow? (slide down curve)
5 ExampleYou are in charge of designing a highway cloverleaf exit ramp. What angle should you build it for speed of 35 mph and r = 100m?13.935 mph = 15.6 m/sTan = v2/rg tan = (15.6 m/s)2/((100m)(9.8 m/s2)) tan = = 13.9
6 Conceptual ProblemIn 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 mphCars go 195 mph around the curve. How?Friction provides the rest of the centripetal forcetan = 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