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21 January, 04:25

Sphere rolling uphill a hollow sphere is rolling along a horizontal floor at 5.0 m/s when it comes to a 30 degree incline. how far up the incline does it roll before reversing direction?

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  1. 21 January, 04:51
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    The sphere has translational and rotational kinetic energy.

    Trans equation: Ek = ½mv²

    Rotation equation: Ek = ½Iω²

    substitute I = 2mr²/3

    and ω = v / r:

    rotat Ek = ½ (2mr²/3) (v/r) ² = (1/3) mv²

    Then total E = (½ + 1/3) mv²

    = (5/6) mv²

    = (5/6) m (5m/s) ²

    = m*20.8m²/s²

    The sphere attains a vertical height such that this E is converted into potential E:

    mgh = m*9.8m/s²*h = m*20.8m²/s²

    mass m cancels:

    = 20.8 / 9.8

    so h = 2.12 m

    This translates into a distance along the incline of s = 2.12 m / sin30º = 4.24 m
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