Question

A train has to negotiate a curve of radius$400m$. By how much should the outer rail be raised with respect to the inner rail for a speed of$48km/h$. The distance between the rail is $1m$.

Answer 1

1. When a vehicle tends to make a turn along a curved road, there is a probability of skidding.
2. The banking of a road is done to provide that centripetal force for the safe turn.
3. The turn is made inclined with the horizontal such that the outer edge is lifted up.

Step 1: Given data

Radius of curve (R) = $400m$

Width = $1m$

Speed (v) = $48km/h=48\times \frac{5}{18}m/s=\frac{40}{3}m/s$

$g=9.8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Let the angle of banking be $\theta$.

Step 2: Formula used and calculation of height

We know that for the banking angle$\theta$.

$\tan \theta =\frac{v^2}{Rg}$, where $g$is the acceleration due to gravity.

$$\begin{gathered} \frac{h}{1}=\frac{v^2}{Rg} \\ \Rightarrow h=\frac{40\times 40}{3\times 3}\times \frac{1}{400\times 9.8} \\ \Rightarrow h=0.0453mor4.53cm \end{gathered}$$

Hence, the outer rail must be raised to $0.0453mor4.53cm$.