A circular racetrack of radius 300 m is banked at an angle of `15^(@)` If the coefficient of friction between the wheels of a race car and the road is 0.2 what is the (a) optimum speed of the race car to avoid wear and tear on its tyres , and (b) maximum permissible speed to aviod slipping ?

Explanation

On a banked road, the horizontal component of the normal force and the frictional force to keep the car moving on a circular turn without slipping. At the optimum speed, the normal reaction's component is enough to provide the needed centripetal force, and the frictional force is not needed. The optimum speed `nu_o` is given by Eq(5.22):
`nu_0 = (Rgtantheta)^(1/2)`
Here R = 300 m , `theta= 15^(@)` , g = 9.8 `ms^(-2)` , we have
`nu_o= 28.1 ms^(-1)` . The maximum permissible speed `nu_max` is given by Eq(5.21) :
`nu_max = 38.1 ms^(-1)` .