Final answer:
The ideal banking angle for a railway track with a radius of curvature of 1500 m and a maximum train speed of 15 m/s is approximately 5.02°.
Step-by-step explanation:
Finding the Ideal Banking Angle for Railway Track
When a train travels around a curve, the ideal banking angle can be determined so that the horizontal component of the normal force provides the centripetal force necessary to keep the train moving in a circle. The formula for the banking angle θ is derived from the relationship between centripetal force, gravitational force, and the normal force on the banked curve. Mathematically, this is represented as:
tan(θ) = v²/(r·g)
Where:
v is the speed of the train (15 m/s)
r is the radius of curvature (1500 m)
g is the acceleration due to gravity (9.81 m/s²)
Substitute the known values into the formula to find the ideal banking angle:
tan(θ) = (15 m/s)² / (1500 m · 9.81 m/s²)
θ = tan⁻¹ (0.00153)
θ ≈ 0.0876 radians or ≈ 5.02°
Therefore, the ideal banking angle for the railway track is approximately 5.02°.