Banking of Roads and the Vertical Circle
A banked track provides a horizontal component of the normal reaction, giving the ideal speed v = √(rg tan t); a vertical circle requires a minimum top speed vtop = √(gr).
What is Banking of Roads and the Vertical Circle?
A banked track provides a horizontal component of the normal reaction, giving the ideal speed v = √(rg tan t); a vertical circle requires a minimum top speed vtop = √(gr).
Key formula / rule: Ideal banking speed: v = √(rg tan t), independent of mass.
Key points
- Derive the ideal banking angle for a curve.
- Analyse tension variation in a vertical circular loop.
Common exam trap
Assuming the banking angle depends on the vehicle mass.
Definitions
- Term
Banking of Roads and the Vertical Circle
- Meaning
A banked track provides a horizontal component of the normal reaction, giving the ideal speed v = √(rg tan t); a vertical circle requires a minimum top speed vtop = √(gr).
- Term
Banking of Roads and the Vertical Circle — explanation
- Meaning
Banking lets a curve be taken safely without relying on friction. In a vertical circle, gravity assists at the top and opposes at the bottom, so the tension varies through the loop and the critical condition is tension just reaching zero at the top.
Learning objectives
Derive the ideal banking angle for a curve.
Analyse tension variation in a vertical circular loop.
Formulae
- Key point
Ideal banking speed: v = √(rg tan t), independent of mass.
- Key point
With friction the safe range widens on both sides.
- Key point
Vertical circle: vtop(min) = √(gr); vbottom(min) = √(5gr).
Prerequisites
PHY-U1-NLM-T2-S2-C1
Common mistakes
Assuming the banking angle depends on the vehicle mass.
Taking the speed as constant throughout a vertical circle.
Keywords
Banking
Roads
Vertical
Circle
Practice preview
What is the primary purpose of banking a road on a curve?…
easy
A circular track of radius 300 m is banked at an angle of 15 degrees. The coefficient of static friction between the tires and the road is 0.2. What is the maximum safe speed with which a car can travel on this track? (G…
medium
A stone tied to a string of length 1.0 m is whirled in a vertical circle. What is the minimum speed required at the lowest point of its path for the stone to complete the circle? (Take g = 10 m/s^2)…
medium