Question

A circular race course track has a radius of 500 m and is banked to ${10}^0$. If the coefficient of friction between tyres of vehicle and the road surface is 0.25. Compute :
(a) the maximum speed to avoid slipping.
(b) the optimum speed to avoid wear and tear

Answer 1

We know the formula for maximum speed and optimum speed in this case.
$V_{max}=\sqrt{Rg\tan (\theta +\varphi )}\theta ={10}^0\left(given\right)\varphi ={\tan }^{-1}\mu ={\tan }^{-1}\left(0.25\right)={14}^o{V}_{max}=\sqrt{500\times 10\times \tan (10+14)}{V}_{max}=47.18m/s{V}_{optimum}=\sqrt{Rg\tan \theta }=\sqrt{500\times 10\times \tan {10}^0}=29.69m/s$