Question

A 70kg car drives through a curve with radius 50m. What is the minimum angle the road should be tilted to keep the car on the road at a speed of 80km/h and the coefficient of friction is near 0 on a rainy day.

Answer 1

when car moves along a circular path then centripetal force for taking turn will be provided by the component of normal force

Let the road is tilted by some angle

so force equations are given as

$F_n cos\theta = mg$

$F_n sin\theta = \frac{mv^2}{R}$

now divide two equations

$tan\theta = \frac{v^2}{Rg}$

now as it is given to us that

$v = 80 km/h$

$v = 80* \frac{5}{18} = 22.2 m/s$

$R = 50 m$

now we have

$tan\theta = \frac{22.2^2}{50*9.8}$

$tan\theta = 1$

$\theta = tan^{-1}1$

$\theta = 45^0$

so it is inclined at an angle of 45 degree