Angle of banking, Physics

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Angle of banking:

The angle made by the line joining the outer raised edge of the road to the inner edge with the horizontal line is called the angle of banking.

Let AC represents the horizontal path and AB be the path of width ‘l' with raised edge.
Let θ be the angle of banking.
Let a body of mass ‘m' turn around a curved path of radius ‘r' moving with velocity ‘v'.
The normal reaction ‘R' of the path acts perpendicular to AB.
It is at an angle θ to the vertical OY at ‘O'. This reaction ‘R' can be resolved into vertical and horizontal complements R cosθ and Rsinθ along OX and OY respectively.

 

1881_Angle of banking.png

Then the vertical component balances the weight of the body
i.e.Rcosθ mg  .................... (1)

Where ‘g' is acceleration due to gravity
The horizontal component provides the centripetal force

Rsinθ=mv2/R

From 1 and 2 

1191_Angle of banking1.png


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