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A banked curve of radius R in a new highway designed so that a car traveling at speed v0 can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly then it will slip toward the center of the circle. If it travels too fast, it will slip away from the center of the circle. If the coefficient of static friction increases, it becomes possible for a car to stay on the road while traveling at a speed within a range from vmin to vmax. Derive formulas for vmin and vmax as functions of μs, v0, and R.
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