A banked circular highway curve is designed for traffic...

Name: Problem 56, Chapter 6: Principles of Physics
Uploaded: 2022-03-19T12:27:55-08:00
Duration: 6 min 8 s
Channel: Sandeep Kumar Dhania
Description: A banked circular highway curve is designed for traffic moving at 65 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day.What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

A banked circular highway curve is designed for traffic moving at 65 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day.What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

A banked circular highway curve is designed for traffic moving at 65 km/h. The radius of the curve is 200 m. Traffic is moving
along the highway at 40 km/h on a rainy day.What is the minimum
coefficient of friction between tires
and road that will allow cars to take
the turn without sliding off the
road? (Assume the cars do not have
negative lift.)

Key Concepts

Frictional Force and Coefficient of Friction

Frictional force is the resistance that occurs when two surfaces, such as a tire and a road, are in contact. The coefficient of friction is a dimensionless value that quantifies the amount of grip available between the surfaces. On a banked curve, this coefficient is critical when the component of the normal force is insufficient to provide the necessary centripetal force, especially under adverse conditions like rain.

Force Decomposition on an Inclined Surface

In analyzing motion on a banked curve, it is essential to decompose forces into components parallel and perpendicular to the inclined surface. This decomposition allows for the assessment of the contributions of gravitational, normal, and frictional forces in maintaining the circular motion and determining the conditions where a vehicle will not slide off the roadway.

Banked Curve

A banked curve is a roadway design where the surface is inclined at an angle relative to the horizontal. This inclined design helps vehicles negotiate curves at higher speeds by providing a component of the normal force to contribute to the required centripetal force, reducing the reliance solely on friction.

Centripetal Force

Centripetal force is the necessary force that acts toward the center of a circular path, enabling an object to follow a curved trajectory. In the context of a banked curve, part of this force is supplied by the horizontal component of the normal force, while friction may provide the remainder if the speed or conditions differ from the designed values.

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