A turn of radius 20 m is banked for vehicles travelling at a speed of 36 km/h . If the coefficient of static friction between the road and the tyre is 0.4 , determine the possible speeds of a vehicle such that it neither slips down nor skids up.

Step-by-step solution

Given: Radius of the turn, R = 20 m Optimum speed, v₀ = 36 km/h = 36 5 18 m/s = 10 m/s Coefficient of static friction, _s = 0.4 Acceleration due to gravity, g = 10 m/s ^2 The angle of banking is given by: = v₀^2 Rg = 10^2 20 10 = 0.5 The minimum speed to avoid slipping down is: v_ min = Rg ( - _s 1 + _s ) v_ min = 20 10 ( 0.5 - 0.4 1 + 0.4 0.5 ) = 200 ( 0.1 1.2 ) = 50 3 m/s Converting to km/h : v_ min = 50 3 18 5 14.7 km/h The maximum speed to avoid skidding up is: v_ max = Rg ( + _s 1 - _s ) v_ max = 20 10 ( 0.5 +