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12 November, 05:24

A wooden cylinder (0 02 x 0 02 x 0 1m) floats vertically in water with one-third of ts length immersed. a) - Determine the density of wood b) - Determine if this is a stable condition c) - Determine if the plece of wood would float stably in alcohol with density 700 kg/m3

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  1. 12 November, 07:37
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    a) - the density of wood is 333.33 Kg/m³

    b) - unstable condition

    c) - unstable condition

    Explanation:

    Given data

    wooden cylinder = 0.02m x 0.02m x 0.1m

    floating = 1/3 * Length

    to find out

    density of wood, is it stable condition and wood would float stably in alcohol with density 700 kg/m3

    Solution

    First we find out density of wood

    we know density of water is 1000 kg/m³

    and we know wood float 1/3 of length so fraction of density will be

    density of wood / density of water = 1/3

    density of wood = 1/3 * density of water

    density of wood = 1/3 * 1000 = 333.33 Kg/m³

    Now in 2nd part we know for stable condition in partially submerged of body the metacentric height is greater than the centroid of body

    we check these condition now,

    metacentric height (GM) = I/v

    I = (0.02 * 0.02³ / 12)

    v = (0.02 * 0.02 * 0.1)

    (GM) = I/v = (0.02 * 0.02³ / 12) / (0.02 * 0.02 * 0.1) = 0.000333

    and we know centroid of body (BM) = 0.05 - 0.033 = 0.017

    we know height is 0.1m so G act at 0.05 and B act at (0.1 * 0.3) = 0.033

    we can see that now metacentric height is less than centroid of body so our body is unstable condition

    Now in 3rd part we use alcohol so we calculate ratio of density of wood and density of alcohol i. e. = 333.33 / 700 = 0.48

    so now our new G will be 0.05 and B will be (0.1 * 0.48) = 0.048

    metacentric height (GM) = I/v = (0.02 * 0.02³ / 12) / (0.02 * 0.02 * 0.1) = 0.000333

    centroid of body (BM) = 0.05 - 0.048 = 0.002

    we can see that now metacentric height is less than centroid of body so our body is unstable condition
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