Short Answer 
The solution outlines the steps to calculate the coefficient of static friction on a track with a radius of 516 m. Initially, it notes the given values, computes the radial acceleration as approximately 2.085 m/s², then determines the total acceleration to be around 19.4791 m/s², leading to a coefficient of static friction of approximately 1.987.
Step 1: Identify Given Values
Start by noting the important values provided in the problem. These include the radius of the track and the various accelerations that will be useful in our calculations. The key values are:
- Radius of the track, r = 516 m
- Tangential acceleration, a_r = 3.89 m/s²
- Speed, v = 32.8 m/s
Step 2: Calculate Radial Acceleration
Next, compute the radial acceleration using the formula a_R = v²/r. Substitute the known values to find:
- Substituting into the formula gives a_R = (32.8)² / 516.
- This results in a_R ≈ 2.085 m/s².
Step 3: Find the Coefficient of Static Friction
Now that you have both the tangential and radial accelerations, calculate the total acceleration using total acceleration = √(a_r² + a_R²). This leads to the coefficient of static friction via:
- Total acceleration calculated is approximately 19.4791 m/s².
- The formula for the coefficient of static friction becomes μ = g / total acceleration.
- Substituting g = 9.8 gives μ ≈ 1.987.