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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. 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 Normal Force is perpendicular to road x component (towards center of circle) gives centripetal force y component (up) cancels the weight of the car Insert Figure 5.11

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**Derivation of Banked Curves**

Divide the x by the y Gives Notice mass is not involved Ask what happens when go to fast? (slide up and over top of curve) Ask what happens when go to slow? (slide down curve)

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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? 13.9 35 mph = 15.6 m/s Tan = v2/rg tan = (15.6 m/s)2/((100m)(9.8 m/s2)) tan = = 13.9

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

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**Practice Problems See if you can speed your way around these!**

Total of 4 problems

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