Question

The distance between two rails of rail track is 1.6 m along a curve of radius 800 m. The outer rail is raised about the inner rail by 10 cm. With what maximum speed can a train be safely driven along the curve.​

Answer 1

Hey there!

Distance b/w two railway tracks = 1.6 m

Radius of curve (r)  = 800 m

Outer rail is raised by  = 10 cm = 0.1 m

♣ Finding Banking Angle:

Here,

tan Ф = 0.1 / 1.6

where, Ф is the baking angle.

tan Ф = 1 / 16

♣ Apply standard Formula:

We know,

tan Ф = v²/ r * g

Let g = 10 m/s².

1/16 = v² / 800 * 10

800 * 10 / 16 = v²

500 = v²

or, v = √500

or, v = 10√5 m/s

Hence, the maximum speed can a train be driven along the curve is 10√5 m/s.

Hope It Helps You!