Show work **Highway Design and Safety Considerations**A highway travels along the side of a mountain at a constant elevation, navigating around spurs and into draws. An engineer, in an effort to minimize costs related to drainage, has designed the highway to slope away from the mountain at an angle of 5° below the horizontal. While this design is effective for drainage, it creates challenges on sharp turns, which have a minimum radius of 100 meters and a posted speed limit of 15 meters per second.**Problem Statement:**a. **Static Friction Calculation:** Determine the minimum coefficient of static friction between the tires and the road required to allow a car to safely maintain the speed limit while navigating a tight draw.b. **Maximum Speed and Spur Radius:** Using this coefficient of friction, calculate the maximum speed a car can safely travel around a tight spur with a 100-meter radius. Additionally, determine the minimum radius a spur should be constructed with to ensure vehicles can maintain the speed limit.**Visual Aids:**- **View from Above Diagram:** This diagram presents an aerial view of the highway's path relative to the mountain side. The road curves around mountainous features like draws and spurs. - **Free Body Diagrams:** These diagrams show a rear view of a vehicle navigating the road. The mountain side is depicted on the left, illustrating forces acting on the vehicle due to the sloped road and curvature.The text encourages understanding of how road design impacts vehicle safety, particularly on curved and inclined sections. It emphasizes calculating necessary conditions for maintaining speed limits under various geometric road conditions.

the free body diagram as follows When the vehicle moving in a circular path, then frictional force is equivalent to centripetal force to maintain the vehicle in equilibrium. To find the static friction coefficient, consider the frictional force fk=μsN=FcWhere N=mgcosθand Fc=mv2rμs=mv2rmg×cosθμs=v2cosθrg=152×cos5100×9.8μs=0.229 The static friction coefficient is 0.229. The minimum speed the car can go in a tight spur is calculated by equation the centripetal force to the horizontal component of the normal reaction. Fc=Nsinθmv2r=Nsinθ, where N=mgcosθv=rgtanθv=100×9.8×tan5v=9.26 m/s The maximum speed of the car in the spur is 9.26 m/s. To maintain the minimum speed the radius of the spur : v2rg=tanθr=v2gtanθr=1529.8×tan5r=262.42 m The maximum radius of the spur is 262.42 m.

Answered: A highway traverses the side of a…

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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**Highway Design and Safety Considerations**

A highway travels along the side of a mountain at a constant elevation, navigating around spurs and into draws. An engineer, in an effort to minimize costs related to drainage, has designed the highway to slope away from the mountain at an angle of 5° below the horizontal. While this design is effective for drainage, it creates challenges on sharp turns, which have a minimum radius of 100 meters and a posted speed limit of 15 meters per second.

**Problem Statement:**

a. **Static Friction Calculation:** Determine the minimum coefficient of static friction between the tires and the road required to allow a car to safely maintain the speed limit while navigating a tight draw.

b. **Maximum Speed and Spur Radius:** Using this coefficient of friction, calculate the maximum speed a car can safely travel around a tight spur with a 100-meter radius. Additionally, determine the minimum radius a spur should be constructed with to ensure vehicles can maintain the speed limit.

**Visual Aids:**

- **View from Above Diagram:** This diagram presents an aerial view of the highway's path relative to the mountain side. The road curves around mountainous features like draws and spurs.

- **Free Body Diagrams:** These diagrams show a rear view of a vehicle navigating the road. The mountain side is depicted on the left, illustrating forces acting on the vehicle due to the sloped road and curvature.

The text encourages understanding of how road design impacts vehicle safety, particularly on curved and inclined sections. It emphasizes calculating necessary conditions for maintaining speed limits under various geometric road conditions.

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