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Suppose you take your new all-terrain vehicle (ATV) out for a spin, literally. Assume you are traveling at a constant speed v, and you take a sharp circular turn (either because it is fun or because you have to suddenly avoid an obstacle). Unfortunately, you take the turn too fast and roll over (a common problem).
a. Find the maximum speed that you can take a turn of radius of curvature Rc before rolling over (the inside wheels6 leaving the ground) in terms of L, the distance between the wheels, and d, the height above the ground of the vehicle’s center of mass. Assume that the ATV travels the turn without slipping; that is, the radius of curvature is constant.
b. Find the maximum speed for a typical ATV (with a wheelbase L of 3.5 ft and d of about 4 ft), assuming a sharp turn with radius of curvature of 5 ft.
c. What changes might you make to the ATV design to prevent rollover?

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