Question

Determine the minimum angle at which a roadbedshould be banked

Answer 1

To solve this problem, apply the concepts related to the relationship given between the centripetal Force and the Weight.

The horizontal force component is equivalent to the weight of the car, while the vertical component is linked to the centripetal force exerted on the car, therefore,

$T cos\theta = mg \rightarrow T = \frac{mg}{cos\theta}$

$Tsin\theta = \frac{mv^2}{r} \rightarrow T = \frac{mv^2/r}{sin\theta}$

Equating both equation we have that,

$\frac{mv^2}{r} = mgtan\theta$

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

Rearranging to find the angle we have that,

$\theta = tan^{-1} (\frac{v^2}{rg})$

Our values are given as,

$r = 2.00*10^2m$

$v = 20m/s$

$\theta = tan^{-1}(\frac{20^2}{(2*10^{2})(9.8)})$

$\theta = 11.53 \°$

Therefore the minimum angle will be 11.53°