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13 January, 09:33

A roadway for stunt drivers is designed for racecars moving at a speed of 97 m/s. A curved section of the roadway is a circular arc of 420 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?

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Answers (2)
  1. 13 January, 10:42
    0
    Given that,

    The speed of the car is

    Vc = 97m/s

    The radius of circular path of the car is

    Rc = 420m

    We want to find the angle of roadway banked β?

    To determine the angle of roadway banked, we will use the formula

    tanβ = Vc² / Rc•g

    Where Vc = 97m/s, Rc = 420m and

    g = 9.8m/s²

    Then

    tanβ = 97² / (420 * 9.8)

    tanβ = 2.28596

    β = ArcTan (2.28596)

    β = 66.37°

    The railway banked at an angle of 66.37°
  2. 13 January, 11:27
    0
    Banking angle is 66.35°

    Explanation:

    Given radius r=420m

    Speed=97m/s

    banking angle is A

    Note before

    (V) = √ (r*gtanA)

    √97=√420*9.81*tanA) taking square of both sides

    97^2=420*9.81*tan A.

    tanA=66.35°

    A=66.35°
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