Final answer:
The minimum coefficient of friction between the car and the road is 0.884.
Step-by-step explanation:
To find the minimum coefficient of friction between the car and the road, we need to calculate the maximum speed at which the car can travel without slipping. We can use the centripetal force equation:
Fc = m * (v2 / r)
where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the curve. Rearranging the equation to solve for the velocity:
v = sqrt(Fc * r / m)
Substituting the given values, the maximum speed is:
v = sqrt(μ * g * r * tan(θ))
where μ is the coefficient of friction, g is the acceleration due to gravity, r is the radius of the curve, and θ is the angle of the banked curve.
Plugging in the given values:
v = sqrt(μ * 9.8 * 26 * tan(11°))
Simplifying the equation:
15 = sqrt(μ * 254.8)
Squaring both sides:
225 = μ * 254.8
Solving for μ:
μ = 225 / 254.8 = 0.884