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28 February, 00:10

Hoop rolling up an inclined plane A hollow cylinder (or hoop) is rolling along a horizontal surface with speed v = 3.3 m/s when it reaches a 15◦ incline. (a) How far up the incline will it go? (b) How long (in seconds) will it be on the incline before it arrives back at the bottom?

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  1. 28 February, 00:23
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    For rolling up or down an incline plane, the acceleration or deceleration of the rolling body is given by the following expression

    a = g sinθ / (1 + k²/r²)

    where k is radius of gyration of rolling body and θ is angle of inclination

    a = g sin15 / (1 + 1) [ for hoop k = r ]

    a = 9.8 x. 2588 / 2

    = 1.268 m / s²

    a)

    Let s be the distance up to which it goes

    v² = u² - 2as

    0 = 3.3² - 2 x 1.268 s

    s = 4.3 m

    b) Let time in going up be t₁

    v = u - at₁

    0 = 3.3 - 1.268 t₁

    t₁ = 2.6 s

    Time in going down t₂

    s = 1/2 a t₂²

    4.3 =.5 x 1.268 t₂²

    t₂ = 2.60

    Total time

    = t₁ + t₂

    = 2.6 + 2.6

    = 5.2 s
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