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Banked Curves

Banked Curves. Section 5.4. 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. Derivation of Banked Curves.

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Banked Curves

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  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

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

  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

  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

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

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