Evaluate maximum inclination that can climb:

Q: A four wheel drive can as shown in the figure has mass of 2000Kg with the passengers. The roadway is inclined at the angle with the horizontal. If the coefficient of friction in between tyres and road is 0.3, what is maximum inclination that can climb?

Sol.: Let the maximum value for the inclination is θ for body to remain stationary.

Let 0.25m distance is distance between inclined surface and C.G. Now, Sum of forces parallel to plane = 0

Wsin   = µ(R₁ + R₂)                                                                                                                     ...(i)

The sum of forces perpendicular to plane = 0

R₁  + R₂ = Wcosθ                                                                                                                            ...(ii)

By putting the value of equation (ii) in (i), We get

Wsinθ   = µ(Wcosθ ) Or       µ = tanθ

θ= tan^-1(0.3)

θ= 16.69º                                                                 .......ANS