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25 February, 10:53

Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle ɵ. A car can safely travel along the unbanked curve at a maximum speed v under conditions when the coefficient of static friction between the tires and the road is μs = 0.787. The banked curve is frictionless, and the car can negotiate it at the same maximum speed v. Find the angle ɵ of the banked curve.

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  1. 25 February, 11:14
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    For unbanked curve, centripetal force is provided by friction and for banked curve, centripetal force is provided by component of reaction from the ground.

    centripetal force = m v² / r, m is mass, v is velocity and r is radius of curve.

    friction force (maximum) = μ mg, μ is coefficient of friction,

    for motion on unbanked curve

    m v² / r = μ mg

    v² = μ gr

    =.787 x 9.8 x r

    = 7.712 r

    In case of motion on banked curve having angle of banking θ

    If R be the ground reaction

    R cosθ = mg

    Rsinθ = centripetal force

    = m v² / r

    Dividing the two

    Tanθ = v² / rg

    = 7.712 r / 9.8 r

    tanθ =.787

    θ = 38 degree.
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