# At what radius of curvature of the road will the car not skid at a speed of 74 km / h?

At what radius of curvature of the road will the car not skid at a speed of 74 km / h? The coefficient of friction between the tires and the road is 0.4 m.

Given:

v = 72 kilometers per hour = 20 meters per second – vehicle speed;

k = 0.4 is the coefficient of friction between the road and the car;

g = 10 meters per second squared – the acceleration of gravity (constant near the surface of the earth).

It is required to determine r (meter) – at which rounding of the road the car will not skid.

A car that has entered a curve in the road will be subject to centripetal acceleration within the curve and a frictional force. To prevent the car from skidding, the following condition must be met:

F friction = m * a, where m is the mass of the vehicle;

k * m * g = m * v ^ 2 / r;

k * g = v ^ 2 / r;

r = v ^ 2 / (k * g) = 20 ^ 2 / (0.4 * 10) = 400/4 = 100 meters.

Answer: the radius of curvature should be 100 meters.

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