Banking of Roads I

Summary

This video script explains the role of friction and road banking in safe vehicle turns. It covers how friction provides the centripetal force needed to maintain a car's path through a curve, with the maximum speed being determined by the static friction coefficient and the curve's radius. The script also explores the concept of banked roads, where an inclined road reduces the reliance on friction, allowing for a calculated safe speed. The key formulas presented provide insights into calculating the maximum safe speed for a vehicle on both horizontal and banked roads.

Takeaways

• 😀 The role of friction in circular turns and banked roads is crucial for determining vehicle speed and safety.
• 😀 When a car takes a turn, each curvilinear section can be approximated as an arc of a circle with a certain radius.
• 😀 Centripetal force is required for the car to move along the turn and is provided by static friction on the road surface.
• 😀 The maximum static frictional force that can act towards the center of the arc is given by mu * mg.
• 😀 The required centripetal force for a turn is calculated using the formula mV²/R.
• 😀 The velocity of the car must satisfy the relation mV²/R ≤ mu * mg for a safe turn.
• 😀 If the car's velocity exceeds the limiting value, it will skid away from the center of the turn.
• 😀 Banking of roads helps avoid reliance on friction by raising the outer edge of the road to provide additional centripetal force.
• 😀 In a banked turn, the horizontal component of the normal force (n sin θ) provides the necessary centripetal force, while n cos θ balances the car's weight.
• 😀 The rated speed of a curve, which ensures a vehicle remains on its path without friction, is given by V = √(RG tan θ).
• 😀 The rated speed of a banked road curve depends on the angle of inclination (θ) and the radius of curvature (R), but not on the mass of the vehicle.

Q & A

What is the primary objective of studying the role of friction at circular turnings and banked roads?

The primary objective is to understand the role of friction in enabling a vehicle to make safe turns without skidding, and to determine the maximum allowed speed for a vehicle while taking a turn.

How is the circular turn approximated when a vehicle takes a turn?

Each curvilinear section of the turn is approximated as an arc of a circle with a specific radius.

What force is necessary for a vehicle to move along a curved path in a turn?

A centripetal force must act towards the center of the arc to enable the vehicle to move along the curved path.

What provides the centripetal force for a vehicle making a turn?

The centripetal force is provided by the static friction between the vehicle's tires and the road surface.

What is the maximum static frictional force that can act towards the center of the arc?

The maximum static frictional force that can act towards the center of the arc is given by the equation mu * mg, where mu is the coefficient of static friction and mg is the weight of the vehicle.

What relationship must the velocity of the car satisfy for a safe turn?

The velocity of the car must satisfy the equation V^2 / R ≤ mu * g, where V is the velocity, R is the radius of the turn, and g is the acceleration due to gravity.

What happens if the car exceeds the limiting velocity while making a turn?

If the car moves at a velocity greater than the limiting value, it will skid away from the center of the turn.

Why is friction not always reliable in banked turns?

Friction is not always reliable because external factors like rain or frost can significantly reduce the coefficient of static friction, which could lead to skidding.

How does banking a road help avoid skidding during turns?

Banking a road raises the outer edge of the road, creating an angle with the horizontal, which helps provide the necessary centripetal force without relying solely on friction.

What is the formula for the rated speed or balancing speed of a vehicle on a banked road?

The rated speed or balancing speed of a vehicle on a banked road is given by the formula V = √(R * g * tan(θ)), where R is the radius of curvature, g is the acceleration due to gravity, and θ is the angle of banking.