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10 January, 23:32

what is the height of an inclined plane in order that a circular disk will roll from rest to the bottom with a final velocity of 20 m/s?

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  1. 10 January, 23:38
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    30 m

    Explanation:

    Potential energy = kinetic energy + rotational energy

    PE = KE + RE

    mgh = ½ mv² + ½ Iω²

    For a disk, I = ½ mr². For rolling without slipping, ω = v/r.

    mgh = ½ mv² + ½ (½ mr²) (v/r) ²

    mgh = ½ mv² + ¼ m v²

    mgh = ¾ m v²

    gh = ¾ v²

    h = 3v² / (4g)

    h = 3 (20 m/s) ² / (4 * 10 m/s²)

    h = 30 m
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