Question

A car is traveling around an unbanked curve at a maximum speed. Which force(s) is(are) responsible for keeping it on the road?

Short answer

Answer: The force responsible for keeping a car on the road while it travels around an unbanked curve at maximum speed is the frictional force between the tires and the road surface. This force provides the necessary centripetal acceleration to maintain the car's circular motion.

Step-by-step solution

Identify the forces acting on the car

When a car is moving along an unbanked curve, two main forces are acting on it: gravitational force and frictional force. The gravitational force acts vertically downward, while the frictional force acts horizontally, in the direction opposite to the car's motion relative to the road.

Understand the role of centripetal force

To stay on a curved path, an object needs centripetal force, which is directed toward the center of the circular path. This force provides the necessary acceleration for the object to change its direction continuously and maintain the circular motion.

Determine which force provides the centripetal force

In the case of a car moving on an unbanked curve, the only available horizontal force is frictional force. The frictional force between the tires and the road surface acts in the direction toward the center of the curve, providing the required centripetal force to keep the car moving in a curved path.

Conclusion

The force responsible for keeping a car on the road while it travels around an unbanked curve at maximum speed is the frictional force between the tires and the road surface. This force provides the necessary centripetal acceleration to maintain the car's circular motion.

Key concepts

Frictional Force

When discussing the forces at play as a car travels around a curve, frictional force emerges as a key player. Frictional force is the resistance that one surface or object encounters when moving along another. It's the gripping effect between the car's tires and the road surface that prevents slipping or skidding.

In a scenario where a car navigates an unbanked curve, the frictional force acts laterally between the tires and the road surface. This force operates parallel to the ground and perpendicular to the direction of gravity. It’s the key to why a car doesn’t just slide out of the curve when driving at high speeds. For students, imagining friction as tiny hands gripping the road helps solidify this abstract concept.

The power of friction is dependent on two factors: the types of surfaces in contact (tire rubber and asphalt, for instance) and the normal force pressing the two surfaces together, which in this case is influenced by the gravitational force acting on the car.

Gravitational Force

The gravitational force is a mutual force of attraction between any two masses. On Earth, it gives objects weight and pulls them toward the planet's center. This same force acts on a car traversing an unbanked curve, pulling it downward and ensuring the tires stay in contact with the road, thus enhancing friction.

The gravitational force acting on the car is expressed as the product of the mass of the car and the acceleration due to gravity, with the relation being \( F_{gravity} = m \cdot g \), where \( m \) is the mass, and \( g \) is the acceleration due to gravity, roughly \( 9.8 \text{ m/s}^2 \). Students may find it useful to think of gravitational force as an anchor, keeping the vehicle grounded so that other forces, like friction, can do their job effectively.

Circular Motion

Circular motion refers to the movement of an object along a curved path or circular trajectory. This type of motion is characterized by the continuous change in the direction of the moving object. For motion to be circular, there must be some form of centripetal force acting upon the object, pulling it toward the center of its circular path.

Think of twirling a ball on a string; the tension in the string is similar to the role of frictional force for the car on the road -- it keeps the object moving in a circle. The concept behind circular motion helps explain why cars need to slow down when taking sharp turns; without enough frictional force to act as centripetal force, the car would not follow the circular path and could potentially lose control.

In an unbanked turn, the frictional force is unopposed in the horizontal plane and, therefore, supplies the necessary centripetal force to maintain the circular motion. Without this force, the car cannot change its direction continuously and would instead move in a straight line off the curve, illustrating the significance of circular motion in everyday driving.