Based on facts,
A. The centripetal force on a moving object (the car) varies jointly with its mass and its squared velocity speed and varies inversely to the radius of the curved path.
B. The centripetal force of the car is also jointly related to the coefficient of static friction of the tire and road, mass, and acceleration to gravity.

Now you want to investigate the possible maximum velocity speeds and possible radius of the curved path so the car can turn safely without skidding out of a curved road.

To do this you must do and answer the following questions.

1. Set up the equation of the centripetal force of the moving object in both A and B. What type of variations are described in both equations?

2. Derive an equation for the squared velocity speed of the car relating both equations of centripetal force.

3. In your initial ocular visit to the site, you measured the radius of the curved path that is 40 meters. Complete the table below.
How is the squared velocity speed related to the coefficient of static friction? What are the velocity speeds in meters per second given their coefficient of static friction?

4. A car’s maximum velocity speed of
410m/s can turn safely on a curved path that has 40 meters radius and 0.4 coefficient of static friction between tire and road. What must be the curved path radius if the maximum velocity speed of the car must be 10 m/s, with 0.5 as the coefficient of static friction so that the car can still turn safely without skidding out of a curved road?