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Homework Help: Two cups are filled with the same level of Water - one has ice cubes.

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Two cups are filled to the same level with water. One of the two cups has ice cubes floating in it. When the ice cubes melt, which cup has the higher level of water?
    1. Same for both
    2. Cup with ice cubes
    3. Cup without ice cubs

    2. Relevant equations

    3. The attempt at a solution
    I thought it was the 2. Cup with ice cubs.

    Actual answer is 1. Same for both.

    My Dilema: The question does not specify which came first - the water or the ice cubes.
    If the cups were filled to the same level and THEN the ice cubes were added, then the cup with ice cubes would have a higher level. Essentially adding "more water" in the form of ice cubes.
    Vice versa, if the ice cubes were orignially in the cup, and THEN both cups filled to the same level, then yes - they'd be the same level of water after melting.

    Can anyone validate my claim that this question does not provide enough information? Or am I simply daft
  2. jcsd
  3. Mar 27, 2012 #2


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    Gold Member

    You have found an ambiguity in the letter of the question.

    One interpretation of the question results in a trivial problem with a trivial answer. (A six year could say that the one that's had something dropped into it after the water levels were balanced will have a higher water level.)

    The other interpretation results in a problem that requires you to think about the physics of density and buoyancy and what happens to the water level when the ice melts. i.e. the stuff you're studying.

    Your education as designed to help you not merely find answers to problems, but to also correctly interpret what the problem is you're trying solve.

    i.e. your exploitation of an ambiguity such as this will not fly in the real world. You will be expected to demonstrate "common sense".
    Last edited: Mar 27, 2012
  4. Mar 27, 2012 #3


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    Staff: Mentor

    Hi dnkim64! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    Maybe it should be worded simply: Two cups are filled to the same level.

    We know what is meant, this is not a new question. :smile:
    Last edited by a moderator: May 5, 2017
  5. Mar 27, 2012 #4


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    Gold Member

    One of the things that the problem would (or SHOULD if properly worded) have you think about is this:

    Which has the greater volume, an ice cube or the water that exists when it melts.
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