Turns along roads are banked at an angle so that vehicles can safely negotiate the turns. A turn with a radius of 300 m has a banking angle

Question

Turns along roads are banked at an angle so that vehicles can safely negotiate the turns. A turn with a radius of 300 m has a banking angle of 10°. What is the ideal velocity at which a vehicle can negotiate this turn?

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Thái Dương 4 years 2021-08-08T11:36:26+00:00 1 Answers 25 views 0

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  1. Philomena
    0
    2021-08-08T11:37:44+00:00
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    Answer:

    Explanation:

    For ideal velocity,

    The centripetal force must be equal to the net horizontal force that balances the centripetal force

    Given that,

    Radius of path is r=300m

    Banking angle = 10°

    Centripetal acceleration is given as

    Fc= mv²/r

    And the net horizontal force is given as

    Fnet, x=mgtanθ

    Therefore,

    Fc=Fnet, x

    mv²/r = mgtanθ

    Cross multiply

    mv² = rmgtanθ

    Divide from sides by m

    v² = rgtanθ

    Take square of both sides

    v=√(rgtanθ)

    Since r=300m, g=9.81m/s² & θ=10°

    v=√(300×9.81×tan10)

    v=√518.93

    v=22.78m/s

    the ideal velocity at which a vehicle can negotiate this turn is 22.78m/s

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