Question

when does a car in motion on a banked road skids and when it manages to be in the circular motion without skidding:

i.e., what happens when

centripetal force friction force

and when

friction force centripetal force

Answer 1

$$\begin{gathered} Inthebankingofroad,Centrepitalforceactingonthecarwhenmovingincircularmotion,isbalancedbythe\sin \theta componentoftehnormalreaction. \\ Downwardweightofthecarisbalancedbythe\cos \theta componentofthenormalreaction. \\ \frac{m{v}^2}{r}=N\sin \theta \\ mg=N\cos \theta \\ whereristheradiusofthecircularpath \\ visthemaximumvelocitywithwhichcarcantravelwithoutskidding. \\ Nisnormalreactionand\theta isthebankingagle. \\ onsolvingthesetwoequationsweget \\ V=\sqrt{rg\tan \theta } \end{gathered}$$