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a circular curve of highway is designed for traffic moving at 60 km/h. (a) if the radius of the curve is 150 m, calculate the correct angle of banking of the road. (b) if the curve were not banked, calculate the minimum coefficient of friction between tires and road that would keep traffic from skidding at this speed.

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Qwarrowidn

The angle of banking of the road is 11° and The minimum coefficient of friction between tires and road is 0.19

The attached free-body diagram to the query illustrates the forces operating on the car if the road is banked at an angle without utilizing friction (i.e., frictionless road).

mg = N cos θ (Eqn 1)

mg = weight of the car.

N = normal reaction of the plane on the car

And in the direction parallel to the inclined plane,

(mv²/r) = N sin θ (Eqn 2)

(mv²/r) = force keeping the car in a circular motion

Divide (Eqn 2) by (Eqn 1)

(v²/gr) = Tan θ

v = velocity of car = 60 km/h = 16.667 m/s

g = acceleration due to gravity

r = 150 m

(16.667²/(9.8×150)) = Tan θ

θ = Tan⁻¹ (0.18896)

θ = 10.7° ≈ 11°

b) In the absence of banking, the force maintaining the car in a circular motion must be balanced by the frictional force of the road.

That is,

Fr = (mv²/r)

Fr = μN = μ mg

μ mg = mv²/r

μ = (v²/gr) = (16.667²/(9.8×150)) = 0.19

Know more about the coefficient of friction at:

https://brainly.com/question/19291861

#SPJJ4

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