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21 March, 06:14

An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. The acceleration of gravity is 9.8 m/s 2. If her speed is 450 m/s at this time, find the radius of the loop. Answer in units of km

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  1. 21 March, 10:02
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    The radius of the loop is 20.66 km

    Explanation:

    let the radius of the loop be r

    mass of airplane is m

    At the top, the pilot experiences two radial forces, which are

    1) Gravitational force is mg

    2) Centrifugal forces mv²/r out of the center

    When the pilot experiences no weight,

    then, mg = mv²/r

    r = v² / g

    = 450² / 9.8

    = 20.66 x 10³3

    = 20.66 km
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