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Banked Curves Section 5.4

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

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

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Derivation of Banked Curves Divide the x by the y Divide the x by the y Gives Gives Notice mass is not involved Notice mass is not involved

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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? 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?

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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? 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 v = 43 m/s = 96 mph Cars go 195 mph around the curve. How? Cars go 195 mph around the curve. How? Friction provides the rest of the centripetal force Friction provides the rest of the centripetal force

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Practice Problems See if you can speed your way around these! See if you can speed your way around these! 142 P20 – 22, P20 – 22, 24 Total of 4 problems Total of 4 problems

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