A 1500 kg car is moving on a flat, horizontal flat road. If the radius of the curve is 35 m and the coefficient of static friction between tires and dry road, Ms = 0.5. Calculate the maximum
speed the car can have and still make the turn successfully

The net force on the car is the friction that keeps it on the road, which points toward the center of the circle of the curve. Then by Newton's second law, we have

• net vertical force:

∑ F = N - W = 0

• net horizontal force:

∑ F = Fs = m a

where

N = magnitude of normal force

W = car's weight

Fs = mag. of static friction

m = car's mass

a = v ²/R = mag. of the centripetal acceleration

v = car's speed

R = radius of curve

Now,

• compute the car's weight:

W = m g = (1500 kg) (9.8 m/s²) = 14,700 N

• solve for the mag. of the normal force:

N = 14,700 N

• solve for the mag. of the friction force, using the given friction coefficient:

Fs = 0.5 N = 7350 N

• solve for the (maximum) acceleration:

7350 N = (1500 kg) a   →   a = 4.9 m/s²

• solve for the (maximum) speed:

4.9 m/s² = v ²/ (35 m)   →   v ≈ 13 m/s

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