Physics
Railway tracks are banked on curves so that

Necessary centripetal force may be obtained from the horizontal component of the weight of the train
No frictional force may be produced between the tracks and the wheels of the train
The train may not fall down inwards
Necessary centrifugal force may be obtained from the horizontal component of the weight of the train

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Physics
A cyclist leans inwards when he is negotiating a curve so that

He may increase his speed
No frictional force may be produced between the wheels and the axle
His weight may be reduced
Necessary centripetal force may be available from the horizontal component of the normal reaction due to the track to maintain the curved motion.

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