Answer to Question #161851 in Classical Mechanics for Gill Allain

Question

A racing car of 1000kg moves round a banked track at a constant speed of 108 km/h. Assuming the total reaction at the wheels is normal to the track, and the horizontal radius of the track is 100m, calculate the angle of inclination of the track to the horizontal and the reaction at the wheels.

Answer 1

$m\vec g+\vec a+\vec N=\vec 0,$

$a=\frac{mv^2}{r},$

$Ox: a-Nsin\alpha=0, \\ Oy: -mg+Ncos\alpha=0,$

$tan \alpha=\frac{v^2}{rg},$

$N=\frac mr \sqrt{v^4+r^2g^2},$

$\alpha=arctan0.9=42°,$

$N=13.45~\text{kN}.$