A race car travels 110 m/s around a circular track of radius 197 m. The track is banked at 22 degrees from the horizontal with a friction constant of 0.14. What is the magnitude of the resultant force on the 2800 kg driver and his car of the car does not slip?
To find the magnitude of the resultant force acting on the car, we need to consider the centripetal force and the gravitational force acting on the car. Let's break down the steps to solve this problem:
1. Calculate the centripetal force:
- The centripetal force is provided by the friction force acting between the tires and the track.
- The formula for centripetal force is Fc = m * v^2 / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the circular track.
- Substituting the given values: m = 2800 kg, v = 110 m/s, and r = 197 m, we can calculate the centripetal force.
2. Calculate the gravitational force:
- The gravitational force is given by the formula Fg = m * g, where m is the mass of the car and g is the acceleration due to gravity.
- The value of g is approximately 9.8 m/s^2.
- Multiply the mass of the car (2800 kg) by the acceleration due to gravity (9.8 m/s^2) to calculate the gravitational force.
3. Calculate the magnitude of the resultant force:
- Since the car does not slip, the frictional force (centripetal force) acts towards the center of the circular track.
- The force of gravity acts vertically downward.
- To calculate the resultant force, we need to find the net force acting on the car.
- The net force is the vector sum of the centripetal force and the gravitational force.
- Use the formula for vector addition to find the magnitude of the resultant force.
By following these steps, you can calculate the magnitude of the resultant force acting on the car if it does not slip.