Final answer:
the coefficient of static friction is μs ≈ 0.0767.
Step-by-step explanation:
To determine the coefficient of static friction between the tires and the road, we need to consider the centripetal force exerted on the car as it rounds the curve. The centripetal force is given by the equation Fc = mv^2/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve.
First, we need to convert the speed from km/h to m/s. So, 95 km/h is equal to 26.4 m/s.
Next, we plug the values into the equation and solve for the frictional force:
Fc = (900 kg)(26.4 m/s)^2 / 85 m = 679.76 N
The frictional force is equal to the product of the coefficient of static friction (μs) and the normal force (N). Since the car is on a level curve, the normal force is equal to the weight of the car, which is given by the equation N = mg, where g is the acceleration due to gravity.
We can solve for the coefficient of static friction by rearranging the equation:
μs = Ff / N = Ff / (mg), where Ff is the frictional force.
Substituting the values, the coefficient of static friction is μs = 679.76 N / (900 kg x 9.8 m/s^2) ≈ 0.0767.