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A train has to negotiate a curve of radius400m. By how much should the outer rail be raised with respect to the inner rail for a speed of48km/h. The distance between the rail is 1m.


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Solution

  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=48×518m/s=403m/s

g=9.8ms2

Let the angle of banking be θ.

Step 2: Formula used and calculation of height

We know that for the banking angleθ.

tanθ=v2Rg, where gis the acceleration due to gravity.

h1=v2Rgh=40×403×3×1400×9.8h=0.0453mor4.53cm

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


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