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15 August, 05:59

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the road way is icy (and the frictional force is zero)

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  1. 15 August, 06:27
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    The banking angle of the road is 16.38 degrees.

    Explanation:

    Given:

    Radius of the roadway on curve, R = 50 m

    velocity of the moving car, V = 12 m/s

    The banking angle can be calculated by using the formula below:

    If there's no frictional force, then net force is equal to centripetal force.

    MgTanΦ = (MV^2) / R

    TanΦ = V^2 / gR

    Where;

    Φ is the banking angle

    g is acceleration due to gravity

    TanΦ = (12 x 12) / (9.8 x 50)

    TanΦ = 0.2939

    Φ = arctan (0.2939)

    Φ = 16.38 degrees

    Therefore, the banking angle of the road is 16.38 degrees.
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