What is the maximum speed at which a car can pass a bend in a road with a radius of curvature of 400 m

What is the maximum speed at which a car can pass a bend in a road with a radius of curvature of 400 m if the coefficient of friction between the tires of the car and the road is 0.1?

R = 400 m.

g = 10 m / s2.

μ = 0.1.

V -?

Since the car moves uniformly along the road, which has a rounding, it moves with a centripetal acceleration a, the value of which is expressed by the formula: a = V ^ 2 / R, where V is the speed of the car, R is the radius of curvature of the road.

To prevent the car from being blown off the road into a ditch, it is necessary that the friction force Ffr be equal to the product of the car’s mass m by the centripetal acceleration a, that is, Newton’s 2 law is fulfilled: m * a = Ffr.

The friction force Ffr is expressed by the formula: Ffr = μ * m * g.

m * a = μ * m * g.

V ^ 2 / R = μ * g.

V = √ (μ * g * R).

V = √ (0.1 * 10 m / s2 * 400 m) = 20 m / s.

Answer: the car must go through a turn at a speed not exceeding V = 20 m / s.