(a) Find the maximum speed at which a vehicle can turn round a curve of `20m` radius on a level road, `mu_(s)=0.5`.
(b) A circular track of radius `100 m` is to be designed for vehicles at an average speed of `72km//h`. Find the angle of banking of the track.

Explanation

(a) Maximum speed for no slipping or skidding
`v_(max)=sqrt(mu_(s)Rg)`
`=sqrt(0.5xx20xx10)`
`=10m//s`
(b) `tan theta=(v^(2))/(Rg),v=72km//h=72xx(5)/(18)=20m//s`
`=(20xx20)/(100xx10)=(2)/(5)=0.4`
`theta=tan^(-1)(0.4)`
where `theta` is the angle of banking.