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25 January, 01:53

A curve of radius 78m is banked for design speed of 85km/h. If coeficient of static friction is 0.3[wet pavement]at what range of speeds can a car safelymake the curve?

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  1. 25 January, 02:10
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    The speed of the car safely make the curve, V = 65.23 Km/h

    Explanation:

    Given,

    The radius of the curve, r = 78 m

    The designed speed of the curve, v = 85 km/h

    = 23.61 m/s

    The coefficient of static friction, μₓ = 0.3

    The static friction of the curve is given by the relation,

    Fₓ = μₓ η

    The acceleration responsible for the static friction

    aₓ = μₓ x g

    Substituting the values in the equation

    aₓ = 0.3 x 9.8

    = 2.94 m/s²

    The designed acceleration of the curve

    a₀ = v²/r

    = 23.61²/78

    = 7.15 m/s²

    The acceleration supported by the static friction, aₓ can be subtracted from the designed acceleration of the curve.

    Therefore the net acceleration,

    a = a₀ - aₓ

    = 7.15 - 2.94

    = 4.21 m/s²

    The centripetal velocity associated with this acceleration is

    a = V²/r

    ∴ V² = a x r

    V = √ (a x r)

    =√ (4.21 x 78)

    = 18.12 m/s

    = 65.23 Km/h

    Hence, the speed required by the car to safely make the curve is, V = 65.23 Km/h
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