kinematics

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A car is travelling on a banked circular racetrack, Given that the track is banked at an angle of 16degree to the horizontal and the radius of the track is 50 metres and there are no friction forces present

a) draw a free body diagram of the car
b)calculate the linear velocity of the car
c) Describe what will happen to a car that is travelling on the same track but with a higher linear velocity

  • kinematics -

    Let the x-axis point toward the center of curvature and the y-axis point upward. Use Newton’s second law.
    ΣFy = N• cos θ − mg − f •sin θ = 0
    ΣFx = N• sin θ + f •cos θ = m•v²/R,
    Solving the 1st equation for N, we obtain
    N =( f •sin θ + m•g)/cos θ,
    Substitute N to the 2nd equation and obtain friction force
    f =m[(v²•cosθ/R) - g•sinθ].
    f=0 =>
    (v²•cosθ/R) - g•sinθ = 0,
    v²•cosθ/R = g•sinθ,
    v² /R•g = sinθ/cosθ = tanθ.
    v =sqrt(R•g•tanθ) = sqrt (50•9.8•tan16º)=11.85 m/s

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