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March 29, 2017

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A high-speed test track for cars has a curved section — an arc of a circle of radius R = 3000 m. The curved section is banked at angle θ = 7 . 94 ◦ from the horizontal to help the cars to stay in the road while moving at high speeds. The acceleration of gravity is 9 . 8 m / s 2 One day, oil spills on the track making a few meters of the curved section frictionless. Calculate the speed v of a car which can cross the oil spill of the curve without slipping side- ways. Answer in units of m / s

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