25.4 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.
3Derivation 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
4Derivation 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)
5ExampleYou 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
6Conceptual 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
7Practice Problems See if you can speed your way around these! Total of 4 problems