Calculating Coefficient of Static Friction for Properly Banked Curve

What is the coefficient of static friction required for a car not to skid when traveling at 89 km/h on a properly banked curve with a radius of 82 m?

A. 0.30
B. 0.35
C. 0.40
D. 0.45

Answer:

The coefficient of static friction required for a car not to skid when traveling at 89 km/h on a properly banked curve with a radius of 82 m is 0.40.

To calculate the coefficient of static friction for a car traveling at 89 km/h on a properly banked curve, we need to follow a few steps:

1. First, convert the speed from km/h to m/s:
   • 89 km/h = (89 * 1000) / 3600 m/s = 24.7 m/s
2. Next, use the formula μ = tan(θ) where θ is the angle of the banking.
3. The angle of banking can be determined using the formula tan(θ) = (v^2) / (g * r), where v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), and r is the radius of the curve.
4. Plug in the values: tan(θ) = (24.7^2) / (9.8 * 82)
5. Solve for θ using the inverse tangent function (tan^-1)
6. Finally, calculate the coefficient of static friction: μ = tan(θ)

By following these calculations, we find that the coefficient of static friction required for the car not to skid when traveling at 89 km/h on a properly banked curve with a radius of 82 m is 0.40.