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What is the maximum speed with which a car can move over a convex bridge? |
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Answer» SOLUTION :To move over a convex bridge, the car requires a centripetal FORCE. This centripetal force is provided by the weight of the car. Let us consider that when the car moves with a certain velocity v, the weight of the car is just sufficient to provide that necessary centripetal force, but if the car moves with a velocity greater than v, then car loses its contact with the bridge. Let the mass of the car be m and the radius of the circular path be R. So, the CONDITION for the car tonot lose contact with the surface of the bridge is `(mv^(2))/(r) le "mg" " "or, " " v le sqrt(GR)` So, a car can move with a maximum speed of `sqrt(gr)` over a convex bridge of radius of curvature r such that it does not lose contact with the bridge. |
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