March 28, 2017

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A hollow rubber ball with a diameter of 5.57 cm and a mass of 38.9 g is cut in half to make a boat (in a bathtub) for American pennies made after 1982. The mass and volume of an American penny made after 1982 are 2.5 g and 0.36 cm3. How many pennies can be placed in the boat without sinking it?

  • physics - ,

    I explained how to do this yesterday.

    The solution utilizes Archimedes' Principle.

    [(pi*Dball^3)/12]*Pwater = (1/2)*38.9g + Mp

    where Pwater = 1.00 g/cm^3 is density of water and Mp is the mass of copper pennies, in grams.

    45.24 g = 19.45 g + Mp
    Mp = 25.79 g

    Mp is a bit more than the mass of ten pennies. An eleventh would sink it.

  • physics - ,

    thank you drwls !

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