What is the influence of friction on banked highway turns? To address this quest

Question

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

Radius of the curve, r = 256 m Banking angle, = 6.720 The speed of the car, v0 = sqrt(g*r*tan) = 17 m/s The speed of the car, v0 = sqrt(g*r*tan) = 17 m/s Given coefficient of friction, = 0.751 Friction force = centrifugal force mv^2/r = mg v = sqrt(rg) = sqrt(256*0.751*9.8) = 43.4 m/s Final velocity is greater than the initialone. So the coefficient is for kinetic friction. So final speed is 2.55 times of the initial one Given coefficient of friction, = 0.751 Friction force = centrifugal force mv^2/r = mg v = sqrt(rg) = sqrt(256*0.751*9.8) = 43.4 m/s Final velocity is greater than the initialone. So the coefficient is for kinetic friction. So final speed is 2.55 times of the initial one

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