The curves on a race track are banked to make it easier for cars to go around the curves at high speed. Draw a free-body diagram of a car on a banked curve. From the motion diagram, find the direction of the acceleration.
(a) What exerts the force in the direction of the acceleration?
(b) Can you have such a force without friction? (Explain.)
To draw a free-body diagram of a car on a banked curve, we need to consider the forces acting on the car. In this case, the following forces are important:
1. Gravity (Weight): The force due to gravity acts vertically downward, toward the center of the Earth. It can be represented by a vector pointing downward from the center of the car.
2. Normal force: The normal force is the force exerted perpendicular to the surface of contact between the car and the track. On a banked curve, the normal force can be separated into two components: one perpendicular to the surface (N⊥) and the other parallel to the surface (N∥). N⊥ acts toward the center of the curve and can be represented by a vector pointing inward, while N∥ acts in the opposite direction.
3. Friction force: The friction force opposes the direction of motion or tendency of motion. On a banked curve, the friction force points toward the center of the curve, helping the car to turn. It can be represented by a vector pointing inward.
Now, let's determine the direction of acceleration. From the motion diagram, we observe that the car is turning left, which means it is accelerating towards the center of the curve. Therefore, the direction of acceleration is inward towards the center of the curve.
(a) The force that exerts the force in the direction of the acceleration is the friction force. It is responsible for providing the centripetal force necessary to keep the car on the curved path.
(b) No, you cannot have such a force without friction. In the absence of friction, the car would not be able to generate the required centripetal force and would slide off the banked curve. Friction provides the necessary force to counteract the tendency of the car to slide outward and allows it to maintain a curved path.