Final answer:
The maximum speed at which the car can travel around the curve without sliding is approximately 21.20 m/s.
Step-by-step explanation:
To determine the maximum speed at which the car can travel around the curve without sliding, we need to calculate the minimum coefficient of static friction.
The centripetal force exerted on the car is given by the equation Fc = m * (v^2/r), where m is the mass of the car, v is the velocity, and r is the radius of the curve.
Since the car is not sliding, the maximum static friction force (Fs) can be written as Fs = µs * N, where µs is the coefficient of static friction and N is the normal force. On a flat curve, the normal force is equal to the weight of the car, which can be written as N = m * g.
Setting Fs equal to Fc, we can solve for the maximum speed (v) using the equation µs * N = m * (v^2/r).
Substituting the given values into the equation, we have µs * m * g = m * (v^2/r). Rearranging the equation, we get v = √((µs * g * r)).
Plugging in the values, we have v = √((0.540 * 9.80 * 291.0)).
Simplifying the equation, we find that the maximum speed at which the car can travel around the curve without sliding is approximately 21.20 m/s.