Question

A curve of radius 30.0 m has a maximum speed limit of 40.0 km/h.
(a) If it is essentially frictionless, determine what angle it must be banked at to make the turn successfully.
(b) If it is not banked (completely horizontal), what must the coefficient of friction be to make the turn successfully?

Answer 1

(a)\[\theta =\tan^{-1} \frac{ V^2 }{ mg }\]\[So, \theta=22.8 degree\]
(b)\[Ff=\mu mg=\frac{ mV^2 }{ r }\]\[\mu=\frac{ V^2 }{ rg } \]\[So, \mu=0.419\]