Civil engineers bank a road to help a car negotiate a curve. While designing a road they usually ignore friction. However, a young engineer decided to include friction in his calculation while designing a road. The radius of curvature of the road is R and the coefficient of friction between the tire and the road is `mu`.
(a) What should be the banking angle `(theta_(0))` so that car travelling up to a maximum speed `V_(0)` can negotiate the curve.
(b) At what speed `(V_(1))` shall a car travel on a road banked at `theta_(0)` so that there is no tendency to skid. (No tendency to skid means there is no static friction force action on the car).
(c) The driver of a car travelling at speed `(V_(1))` starts retarding (by applying brakes). What angle (acute, obtuse or right angle) does the resultant friction force on the car make with the direction of motion?

Answer

(a) `theta_(0) = tan^(-1)((V_(0)^(2)/(Rg) - mu)/(1 + (muV_(0)^(2))/(Rg)))`
(b) `V_(1) = sqrt(rg"tan"theta_(0))`
(c) Obtuse