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18 June, 12:26

A flat slab of styrofoam, with a density of 32 kg/m3, floats on a lake. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. What minimum volume must the slab have so that a 38 kg boy can sit on the slab without it sinking? Express your answer with the appropriate units.

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  1. 18 June, 15:12
    0
    0.0392 m³

    Explanation:

    Given:

    Density of the styrofoam, ρ' = 32 kg/m³

    Now, let the volume of the slab = V

    the submerged volume be = V;

    now, the volume of water displaced will be V

    thus,

    the buoyant force acting will be = ρVg

    where,

    ρ is the density of water

    g is the acceleration due to gravity

    now, the

    total downward force acting = weight of the boy + weight of the slab

    total downward force acting = 38 * g + ρ' * V * g

    for the no sinking condition,

    bouyant force should be equal to the total downward force

    thus,

    ρ * V * g = 38 * g + ρ' * V * g

    or

    ρ * V = 38 + ρ' * V

    on subtituting the values

    V (1000 - 32) = 38;

    or

    V = 0.0392 m³
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