Banked CurvesSection 5.4

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.

Derivation of Banked CurvesA car travels around a friction free banked curveNormal Force is perpendicular to roadx component (towards center of circle) gives centripetal force

y component (up) cancels the weight of the car

Derivation of Banked CurvesDivide the x by the y

Gives

Notice mass is not involved

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?

13.9

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 force

Practice ProblemsSee if you can speed your way around these!

142 P20 22, 24

Total of 4 problems

Insert Figure 5.11Ask what happens when go to fast? (slide up and over top of curve)Ask what happens when go to slow? (slide down curve)35 mph = 15.6 m/sTan = v2/rg tan = (15.6 m/s)2/((100m)(9.8 m/s2)) tan = .2483 = 13.9 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