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23 September, 03:46

A twin-sized air mattress used for camping has dimensions of 75 cm by 225 cm by 17.5 cm when blown up. The weight of the mattress is 2 kg How heavy a person, in newtons, could the air mattress support if it is floating in freshwater, with density1000 kg/m^3?

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  1. 23 September, 04:21
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    2870 N

    Explanation:

    There are three forces on the mattress. Weight of the mattress, weight of the person, and buoyancy.

    ∑F = ma

    B - mg - Mg = 0

    Buoyancy is equal to the weight of the displaced fluid.

    ρVg - mg - Mg = 0

    ρV - m = M

    Plugging in values:

    M = (1000 kg/m³) (0.75 m * 2.25 m * 0.175 m) - 2 kg

    M = 293 kg

    The person's weight is therefore:

    Mg = 293 kg * 9.8 m/s²

    Mg = 2870 N
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