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 216m banked toward the turn center. a) At what speed v0 can this
car safely negotiate the turn without friction for a uniform 5.73º banking angle? Under what real-world
situation(s) might this circumstance occur? b) To illustrate the effect of friction upon the vehicle, reanalyze the
previous situation in the presence of frictional coefficient 0.821, 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 = 216 m Banking angle, ? = 5.73 The speed of the car, v0 = sqrt(g*r*tan?) = 36.13m/s Given coefficient of friction, µ = 0.821 Friction force = centrifugal force mv^2/r = µmg v = sqrt(rµg) = sqrt(216*0.821*9.8) = 41.68 m/s Final velocity is greater than the initialone. So the coefficient is for kinetic friction.

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