Highway design is strongly influenced by physical analyses, as apparent in const

Question

Highway design is strongly influenced by physical analyses, as apparent in construction of safe circular turns at common highway speeds. The following analyses represent common highway design concerns.

What is the influence of friction on banked highway turns? To address this question, first consider a car that encounters a circular highway curve of radius 256m banked toward the turn center. At what speed v0 can this car safely negotiate the turn without friction for a uniform 6.72º banking angle? Under what real-world situation(s) might this circumstance occur? To illustrate the effect of friction upon the vehicle, reanalyze the previous situation in the presence of frictional coefficient 0.751, and determine the maximum speed vmax the car may safely negotiate the turn. Should this coefficient be for static or kinetic friction? By what proportion did the safe turn speed increase in the presence of friction?

Explanation / Answer

Given Radius of the curve, r = 256 m Banking angle, ? = 6.72^0 The speed of the car is v = vr g tan6.72     = v256 m *9.8 m/s^2 *0.117 vo ˜ 17 m/s --------------------------------------------------------------- coefficient of friction, µ = 0.751 Since Fc = f mv^2/r = µ mg v = vµ r g    = v0.751 *256 m *9.8 m/s^2 v = 43.4 m/s The friction should be maximum value of static friction because it is on the verge of skidding outward. In presence of friction, the speed is 2.55 times of vo

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