Laws of Motion
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Question : 31
Total: 40
A train runs along an unbanked circular track of radius 30 m at a speed of 54 km h– 1 10 6
Solution:
Radius of circular bend, r = 30 m,
speed of train= v = 54 k m h − 1 = 54 ×
= 15 m s − 1
mass of train,m = 10 6 k g
angle of banking= θ = ?
The centripetal force is provided by the lateral thrust by the rails on the wheels. According to Newton’s third law of motion, the train exerts an equal and opposite thrust on the rails causing its wear and tear.
The angle of banking is given by
tan θ =
=
=
= 0.75
⇒ θ = tan − 1 ( 0.75 ) ≈ 37 °
speed of train
mass of train,
angle of banking
The centripetal force is provided by the lateral thrust by the rails on the wheels. According to Newton’s third law of motion, the train exerts an equal and opposite thrust on the rails causing its wear and tear.
The angle of banking is given by
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