Car on Banked Curve Free Body Diagram
Introduction
When a car travels around a banked curve, it experiences a number of forces that keep it from sliding off the road. These forces include the force of gravity, the normal force exerted by the road, and the force of friction.
The free body diagram of a car on a banked curve is shown below.
Forces Acting on the Car
- Force of gravity (Fg): The force of gravity pulls the car downward toward the center of the Earth.
- Normal force (Fn): The normal force is exerted by the road on the car. It is perpendicular to the surface of the road and points upward.
- Force of friction (Ff): The force of friction is exerted by the road on the car. It is parallel to the surface of the road and points in the direction opposite to the car’s motion.
Equations of Motion
The equations of motion for a car on a banked curve are:
- ΣFx = ma: The sum of the forces in the x-direction is equal to the mass of the car times its acceleration in the x-direction.
- ΣFy = ma: The sum of the forces in the y-direction is equal to the mass of the car times its acceleration in the y-direction.
Solving for the Normal Force
To solve for the normal force, we can use the equation ΣFy = ma. In the y-direction, the only forces acting on the car are the force of gravity and the normal force. Therefore, we have:
Fn – Fg = ma
Solving for Fn, we get:
Fn = Fg + ma
Solving for the Force of Friction
To solve for the force of friction, we can use the equation ΣFx = ma. In the x-direction, the only forces acting on the car are the force of friction and the component of the normal force parallel to the surface of the road. Therefore, we have:
Ff – Fn sin θ = ma
Solving for Ff, we get:
Ff = Fn sin θ + ma
Conclusion
The free body diagram of a car on a banked curve shows the forces that are acting on the car. These forces include the force of gravity, the normal force exerted by the road, and the force of friction. The equations of motion for the car can be used to solve for the normal force and the force of friction.
