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 150 mm at a speed of 126 km/h?

897

Explanation:

Speed of the car, v = 126 km/h, converting to m/s, we have v = 35 m/s and

Radius of the curve, R = 150 mm = 0.15 m

The centripetal acceleration a(c) is given by the formula = v² / R so that

a(c) = 35² / 0.15

a(c) = 1225 / 0.15

a(c) = 8167 m/s²

The force that causes the acceleration is frictional force = µ m g, where

µ = coefficient of friction

m = the mass of the car and

g = acceleration due to gravity, 9.81

From Newton's law:

µ m g = m a(c) , so that

µ = a(c) / g

µ = 8167 / 9.81

µ = 897

Therefore, the coefficient of static friction must be as big as 897

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