Question

A circular racetrack of radius $300m$ is banked at angle of ${15}^o$ If the coefficient of friction between the wheels of a race car and the road is $0.2$ what is the (a) optimum speed of the race car to avoid wear and tear on its tyres and maximum permissible speed to avoid slipping?

Answer 1

Balancing the forces:

$N=mg\cos 15°$

and $f+mg\sin 15°=\frac{m{v}^2}{r}$

$\Rightarrow \mu N+mg\sin 15°=\frac{m{v}^2}{r}\Rightarrow 0.2\times mg\cos 15°+mg\sin 15°=\frac{m{v}^2}{r}\Rightarrow r(0.2g\cos 15°+g\sin 15°)=v^2\Rightarrow 300\times 0.2\times 10\times 0.96+300\times 10\times 0.25=v^2\Rightarrow 576+750=v^2\Rightarrow 1326=v^2\Rightarrow v=36.4m/s$