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Something with ice cubes

Discussion in 'MCAT Study Question Q&A' started by Scarletblack, Jun 21, 2008.

  1. Scarletblack

    Scarletblack 2+ Year Member

    Jun 3, 2008
    There was a weird question that I found (I don't remember where):

    A large ice cube floats in a cup of water. Several coins are embedded in the ice cube. What happens when the ice cube melts?

    (a) The water level falls
    (b) The water level stays the same
    (c) The water level rises
    (d) Cannot be determined

    Ok so for a regular ice cube, the water level would stay the same because Archimede's principle states that

    "A body wholly or participally immersed in a fluid will be buoyed up by a force = weight of the fluid it displaces."

    So a smaller volume of water is displaced because the ice cube is less dense. However as it melts, it becomes more dense and has less volume so the water level would be the same.

    However, here, I thought the coins are even MORE dense and thus should make the water level rise.

    But the actual answer is that (a) it falls. Why is this?
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  3. seraph524

    seraph524 M0 2+ Year Member

    Sep 19, 2006
    This scenario was brought up a couple of days ago by another poster...

    The reason the water level falls is that an un-encapsulated coin displaces a volume of water equal to its own volume, while an encapsulated coin in ice displaces a volume of water that represents the mass of the coin in ice. And since it is in ice, it will displace an even higher volume since ice has lower density than water.

    In other words, if a coin is 2 grams, and is in ice, it will displace water by a volume of ice that weights 2 grams. However, if the coin is merely at the bottom of the cup, it will only displace a volume of water equal to its own metal volume.
  4. physics junkie

    physics junkie 5+ Year Member

    Nov 20, 2006
    There is actually no way to tell. If the ice cubes were very, very large or the coins were very small or of equal density to water you would get different answers. Seraph got the principles right but the actual question is bull****.
  5. nfg05

    nfg05 2+ Year Member

    May 19, 2008
  6. BerkReviewTeach

    BerkReviewTeach Company Rep & Bad Singer Exhibitor 10+ Year Member

    May 25, 2007
    SDN Exhibitor
    One can assume that metallic coins are more dense than water and therefore more dense than ice. But it's those damn wooden nickels that cause the problem on a question like this. What if they are balsa wood coins?

    Once again, it brings up the point, don't take any wooden nickels.
  7. physics junkie

    physics junkie 5+ Year Member

    Nov 20, 2006
    You know I was totally wrong in my previous post. The size of the ice cube has nothing to do with it. I was thinking that the fact that the ice cube is only partially submerged would compensate for the reduction of density when the ice melted AND for the additional density of the coin...but when I carried out the calculation it came out exactly even. So the only factor would be the density of the coin. Pennies have a density of ~7g/cm^3 and metallic coins can always be assumed of course. Learn something new every day.

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