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A velodrome is built for use in the Olympics. The radius of curvature of the surface is 19.6 m. At what angle should the surface be banked for cyclists moving at 11.5 m/s? (Choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are used in velodromes.)

  • Physics - ,

    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,
    ΣFx = N• sin θ = m•v²/R,
    Dividing the 2nd equation by the 1st equation, we obtain
    tan θ = v² /R•g =11.5²/19.6•9.8 = 0.67
    θ = 34.5 º

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