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A highway traverses the side of a mountain at constant elevation, around View from above: spurs and into draws. A "clever" engineer, trying to cut out the cost of a drainage system, has designed it to slope away from the mountain at 5° below the horizontal. While this solution works fine for drainage, there are some unintended consequences near the sharp turns, which have a minimum radius of 100m and a posted speed limit of 15 m/s. Draw road a. What minimum coefficient of static friction between tires and road will allow a car to maintain the speed limit as it goes around a tight draw? Spur Free Body Diagram rear view, mountain at left b. With this coefficient of friction, what marimum speed can the same car go around a tight (100m radius) spur? What minimum radius spur should be constructed so that the speed limit can be maintained? Free Body Diagram rear view, mountain at left Mountain Side Valley Side

A highway traverses the side of a mountain at constant elevation, around View from above: spurs and into draws. A "clever" engineer, trying to cut out the cost of a drainage system, has designed it to slope away from the mountain at 5° below the horizontal. While this solution works fine for drainage, there are some unintended consequences near the sharp turns, which have a minimum radius of 100m and a posted speed limit of 15 m/s. Draw road a. What minimum coefficient of static friction between tires and road will allow a car to maintain the speed limit as it goes around a tight draw? Spur Free Body Diagram rear view, mountain at left b. With this coefficient of friction, what marimum speed can the same car go around a tight (100m radius) spur? What minimum radius spur should be constructed so that the speed limit can be maintained? Free Body Diagram rear view, mountain at left Mountain Side Valley Side

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A highway traverses the side of a mountain at constant elevation, around spurs and into draws. A "clever" engineer, trying to cut out the cost of a drainage system, has designed it to slope away from the mountain at 5° below the horizontal. While this solution works fine for drainage, there are some unintended consequences near the sharp turns, which have a minimum radius of 100m and a posted speed limit of 15 m/s. View from above: Draw a. What minimum coefficient of static friction between tires and road will allow a car to maintain the speed limit as it goes around a tight draw? Spur Free Body Diagram rear view, mountain at left b. With this coefficient of friction, what maximum speed can the same car go around a tight (100m radius) spur? What minimum radius spur should be constructed so that the speed limit can be maintained? Free Body Diagram rear view, mountain at left Umax = Rmin = Mountain Side Valley Side
Transcribed Image Text:A highway traverses the side of a mountain at constant elevation, around spurs and into draws. A "clever" engineer, trying to cut out the cost of a drainage system, has designed it to slope away from the mountain at 5° below the horizontal. While this solution works fine for drainage, there are some unintended consequences near the sharp turns, which have a minimum radius of 100m and a posted speed limit of 15 m/s. View from above: Draw a. What minimum coefficient of static friction between tires and road will allow a car to maintain the speed limit as it goes around a tight draw? Spur Free Body Diagram rear view, mountain at left b. With this coefficient of friction, what maximum speed can the same car go around a tight (100m radius) spur? What minimum radius spur should be constructed so that the speed limit can be maintained? Free Body Diagram rear view, mountain at left Umax = Rmin = Mountain Side Valley Side
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