A train runs along an unbanked circular bend of radius 30 m at a speed of 54 kmh–1. What is the angle of banking required to prevent wearing out of the rail ? (g = 10 ms–2)A 53° B 45° C 60° D 37°
Question
A train runs along an unbanked circular bend of radius 30 m at a speed of 54 kmh–1. What is the angle of banking required to prevent wearing out of the rail ? (g = 10 ms–2)A 53° B 45° C 60° D 37°
Solution
To solve this problem, we first need to convert the speed of the train from km/h to m/s.
1 km = 1000 m 1 hour = 3600 seconds
So, 54 km/h = 54 * 1000 / 3600 = 15 m/s
The formula for the angle of banking (θ) is given by:
tan θ = v² / g*r
where: v = speed of the train = 15 m/s g = acceleration due to gravity = 10 m/s² r = radius of the bend = 30 m
Substituting these values into the formula, we get:
tan θ = (15)² / 10*30 tan θ = 225 / 300 tan θ = 0.75
To find the angle θ, we take the inverse tangent (arctan) of 0.75:
θ = arctan(0.75) θ = 36.87°
So, the angle of banking required to prevent wearing out of the rail is approximately 37°. Therefore, the correct answer is D) 37°.
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