Briefly explain how is a vehicle able to go round a leveled curved track determine the maximum speed with which the vehicle can negotiate this curved track safely

Explanation

When a vehicle travels in curved path there must be a centripetal force acting on it that is provided by the frictional force between there forces acting on the vehicle when it moves are as shown in the figure . They are
`(i)` Gravitational force (mg) acting downwards
(ii) Normal force (mg) acting upwards
(iii) Frictional force `(F_(s))` acting horiozontally inwards along the road
Suppose the road is horizontal then the normal force and gravitational force are exectly equal and opposite . The centripetal force is provided by the force of static friction `F_(s)` between the tyre and surface of the road that acts towards the centre of the d circular track

`(mv^(2))/(r ) = F_(s)`
As we have already seen in the previous section the static friction can be increase from zero to a maximum value
`F_(s) gt mu_(s) mg`
For without skindding if `(mv^(2))/(r ) le mu_(s) mg.` or
`mu_(s) ge (v^(2))/( rg ) " or " sqrt(mu_(s) rg ) le v ` (safe turn)
Necessary centripetal force to bend the car on the road provided by the static friction