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?

Question

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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Cherry 3 months 2021-08-30T21:33:59+00:00 1 Answers 0 views 0

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    2021-08-30T21:35:57+00:00

    Answer:

    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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