physics

A foam plastic of density of 0.58g/cm^3 is to be used as a life jacket.What volume of the plastic must be used if it is to keep 20percent by volume of an 80kg physics student above water in a lake if the average density of the student is 1.04g/cm^3

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  1. first calculate the buoyancy of 80% of a physics student.

    Mass of student = 80 kg
    density of student = 1040 kg/m^3
    volume of student = 80/1040 = .0769 m^3

    buoyancy of 80% of student = 1000 g .8 .0769
    = 61.54 g Newtons

    so we need a force of 80 g - 61.54 g Newtons up from the foam
    that is 18.46 g Newtons up

    Volume of plastic = v
    weight of plastic = 580 g v
    buoyancy of plastic = 1000 g v
    up force from plastic = 420 g v Newtons
    so
    420 g v = 18.46 g
    v = 18.46/420 = .044 m^3

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