Banking of Road Formula with Problems

Banking of Road Formula :

The velocity of a vehicle on a curved banked road: v= √(rg(tanΦ+μs))/1-μs tanΦ

For a given pair of roads, and Tyre μ= tanλ, then the velocity of a vehicle on a curved banked road is: v = √rg tan (Φ+λ)

The safe velocity on an unbanked road is: vmax = √ μ * r*g

The expression for the angle of banking of road is: θ = tan-1 [v02 / Rg]

Expression for the safe velocity on the banked road is: vmax = √rg tan Φ

Centripetal Force F= mv2 / r = mw2r

Sample Problems :

Problem1 :

Calculate the maximum speed of a car with which it can be safely driven along a curve of radius 100m and the coefficient of friction between tires and road is 0.2. (take g = 9.8 m/s2)

Solution :

Given ,

Radius (r) = 100m

Coefficient of friction (μ) = 0.2

Gravity (g) = 9.8 m/s2

Formula: v= √(μrg)

v = √(μrg)

= √(0.2 * 100 * 9.8)

= √196

v = 14 m/s

Thus maximum speed of car is 14 m/s.

Problem2 :

Calculate the angle which the bicycle and its rider make with the vertical when going at 18 km/hr around a curved road of radius 10m on level ground. (take g = 9.8 m/s2)

Solution :

Given ,

Radius (r) = 10 m

Max speed of rider (v) = 18 km/hr

Gravity (g) = 9.8 m/s2

Formula: tanθ = v2 / rg

v = 18 km/hr

= 18 * 1000 / 3600

= 5 m/s

Tangent angle of banking is tanθ = v2 / rg

= 5 * 5 / 10 * 9.8

= 5 / 2 * 9.8

tanθ = 0.251

θ = tan-1 (0.2551)

θ = 14° 19

Thus the angle which the bicycle and rider make is 14° 19 .

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