  Question

A turn of radius 20 m is banked for the vehicle going at speed of 36 km/hr. If the coefficient of static friction between the road and the tyre is 0.4. What of the following speeds are possible such that the vehicle neither slips down nor skids up ?

A
20 km/hr  B
30 km/hr  C
40 km/hr  D
50 km/hr  Solution

The correct options are A 20 km/hr B 30 km/hr C 40 km/hrSpeed of vehicle (v) = 36 km/hr = 10 m/sec Let θ be the angle at which the road is banked. Let us find out all the forces that are acting on this moving vehicle (i) Mg in downward direction  (ii) N (normal reaction) acting perpendicular to the surface of road (iii) pseudo force acting in radially outward direction (iv) frictional force acting parallel to the road, either in inward or outward direction  Case 1: To avoid slipping of the vehicle  In this case friction will act in outward direction Let us now resolve all the forces in the direction along the surface and perpendicular to the surface. Now we get ,  N=Ma sinθ+Mgcosθ.......(i) Mgsinθ=μN+Ma cosθ...(ii) To calculate θ we know  tanθ=ag tanθ=v2rg tanθ=(10)220g = 0.5........(iii) Put (iii) in (ii) and (i) we get  Vmin=10√6 m/s = 14.7 km/h Case 2: To avoid vehicle from skidding up In this case friction will act inward direction. Again resolve the forces along the surface and perpendicular to the surface. μN+mg sinθ=ma3 cosθ.......(v) N=ma3 sinθ+mg cosθ.....(vi) a3=v2maxr...(vii) on solving (v), (vi) and (vii) this we get  vmax= 44.1 km/h ∴ Options A, B and C are correctPhysics

Suggest Corrections  0  Similar questions
View More  People also searched for
View More 