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.