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7 October, 16:34

A 75 kg runner taking part in a 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 32 meters. if he completes the 200 m dash in 20.33 s and runs at constant speed throughout the race, what is the magnitude of his centripetal force as he runs the curved portion of the track?

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  1. 7 October, 16:50
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    F = - 226.7874N

    Explanation:

    Initially we must determine the speed at which the runner runs that is given by the following equation:

    v = velocity = (200m) / (20.33s) = 9.8377 m/s

    To determine the centripetal force of the corridor in the curve we must use the following equation:

    Fc = centripetal force = - m * ω² * r

    m = mass of the runner

    ω = angular speed

    r = ratio of the curve

    The angular velocity is the swept angle per unit of time, so we determine that perimeter has a complete turn of the curve, 2π radians, and calculate the time it would take to travel it to the runner to know the angular velocity it takes:

    Perimeter = 2π * r = 2π * 32m = 201.0619m

    The time it would take to travel would be:

    t = (201.0619m / 9.8377 m/s) = 20.4379s

    ω = (2π) / (20.4379s) = 0.3074 (rad/s)

    After obtaining these values we can calculate the centripetal force to which the runner is exposed in the curve:

    F = - 75kg * (0.3074 rad/s) ² * 32m = - 226.7874N

    The minus sign corresponds to the sense of force being outward of the radius of curvature.
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