Banking of Track and Angle of Banking

Banking of Track

• On a curved road, the outer portion is raised more than the inner portion to reduce friction and wear on tyres.
• This phenomenon is called banking of track, applied to roads and railway tracks.

Angle of Banking

• The angle of banking is the angle through which the outer edge of the curved road is raised above the inner edge.
• The angle of banking (θ) is related to the speed (v) and radius (r) of the curved path.

Equilibrium of a Vehicle

• The normal reaction (R) exerted by the ground makes an angle θ with the vertical, with two components: R cos θ (balancing weight) and R sin θ (providing centripetal force).
• The equations for equilibrium are R cos θ = mg and R sin θ = mv2/r.

Expression of Angle of Banking

• The expression for the angle of banking is tan θ = v2/rg, which shows the road is banked.
• The equation can be rewritten as v = √(rg tan θ), giving the speed at which a vehicle can negotiate a circular road banked at angle θ.

Maximum Speed and Friction

• For maximum speed, tan θ = 1 and v = √(rg).
• The angle θ depends on speed and radius, but not on the mass of the vehicle.
• If the speed is too high, even maximum friction cannot prevent a skid or slip.

Advantages of Banking of Track

• Provides necessary centripetal force.
• Reduces frictional wear and tear of tyres.
• Avoids skidding.
• Avoids overturning of vehicles.

Understanding the concept of banking of track, angle of banking, and equilibrium of a vehicle on curved roads and railway tracks.