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1.A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.08, a car at rest must not slide into the ditch and a car traveling less than 60 km/h must not skid to the outside of the curve. What is the minimum radius of curvature of the curve and at what angle should the road be banked?
2.A highway curve has a radius of 129 m. At what angle should the road be banked so that a car traveling at 27.2 m/s has no tendency to skid sideways on the road? [Hint: No tendency to skid means the frictional force is zero.]
3.A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is u, and the coefficient of static friction is m.
(a) Determine the range of speeds the car can have without slipping up or down the road.
(b) What is the range of speeds possible if R = 100 m, θ = 10°, and μ = 0.10 (slippery conditions)?
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4.A car negotiates a banked circular road of radius 50m at a speed of 72km/hr.Calculate the angle of banking so that the car can safely take a trun at the above speed.
5. A curve with a 120-m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s. what is the minimum coefficient of static friction needed between tires and road to prevent skidding?
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