Final answer:
To find the minimum coefficient of friction for a car to take a curve without slipping, the equation μ = v2 / (r * g) is used. Substituting the given values, the coefficient of friction is calculated to be 0.34, which is not listed in the given options. This indicates a potential inconsistency in the question or the provided options.
Step-by-step explanation:
To determine the minimum coefficient of friction needed for a car to negotiate an unbanked curve without slipping, we can use the formula for centripetal force, which is provided by the frictional force between the car tires and the road. The centripetal force (Fc) needed to keep the car on the curve can be calculated using the equation Fc = m * v2 / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
The frictional force (Ff) that provides this centripetal force is given by Ff = μ * N, where μ is the coefficient of friction and N is the normal force. Because the car is on a flat surface, the normal force is equal to the weight of the car, which is m * g, where g is the acceleration due to gravity. Thus, the frictional force also equals m * g * μ.
Setting the centripetal force equal to the frictional force, we get: m * v2 / r = m * g *μ, which simplifies to: v2 / r = g *μ. Solving for μ gives us: μ = v2 / (r * g). When we plug in the values (v = 13 m/s, r = 50 m, g = 9.8 m/s2), we get:
μ = (13 m/s)2 / (50 m * 9.8 m/s2)
μ = 0.34
However, since this value of the coefficient of friction is not among the options provided, we need to verify that the computations are correct. If the options listed are indeed correct, then we have an inconsistency, potentially an error in the provided options or in the question's velocity or radius. It is crucial in physics problems to make sure all components and given values are consistent.