How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 110 m at a speed of 101 km/h

The magnitude of static friction is

f = mv ²/r

(i.e. the net force acting on the car parallel to the road points toward the center of the curve)

while the net vertical force must be

∑ F = n - mg = 0

because the car is otherwise in equilibrium. Then

==>   n = mg

==>   f = µn = µmg = mv ²/r

==>   µ = v ²/(rg)

We have

v = 101 km/h ≈ 28.1 m/s

r = 110 m

g = 9.80 m/s²

so that

µ = (28.1 m/s)² / ((110 m) g) ≈ 0.730

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