Bear asked in Science & MathematicsPhysics · 2 months ago

A sphere is released?

A sphere is released from rest at the top of an inclined plane. What is the speed of the sphere at a distance 3.0 m below its starting point. Assume that the sphere rolls without slipping.

1 Answer

  • NCS
    Lv 7
    2 months ago
    Favorite Answer

    Is the sphere hollow or solid with uniform density? It matters.

    If solid, the moment of inertia about its center isI = (2/5)mR²,

    and rolling without slipping means that ω = v/R. Then

    KE = ½mv² + ½Iω² = ½mv² + ½*(2/5)mR²*(v/R)² = (7/10)mv²

    PE becomes KE:

    mgh = (7/10)mv²

    v = √(10gh/7) = √(10 * 9.8m/s² * 3.0m / 7) = 6.5 m/s ◄

    If hollow, then I = (2/3)mR² and KE = (5/6)mv²

    leads to v = 5.9 m/s

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    Source(s): Please revisit this q/a:
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