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Archimedes Principle - Mass floating on ice

  1. Nov 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Question: What minimum volume must a slab of ice in a freshwater lake have for a 50.0kg woman to be able to stand on it without getting her feet wet?

    2. Relevant equations
    Archimedes principle.
    [PLAIN]https://lh6.googleusercontent.com/qRkIpr7Mg9TFQYXwa2Xoj5jv3vcBNP7hPUxT5Xk1inIv-Qdk_KhZWF-Pha5AJ_Aq9_e7ZQPUGeUrMdRCb7vTUgQKtYY4sGutyIYtGiLW6bspSIuL6-sdiCDjIHaN7viYGQ [Broken] [Broken]

    [PLAIN]https://lh5.googleusercontent.com/csDszB-wBCqIGI4g9bRCmLfDFgEbQcXTKjieRXO3BVOUmGCYJoq7CdCpd844FOemjb_MrhnaHitt0Dk0mBssD6-QSdQ2S51f3WpZ6tyamq5xrxfjmc64gZNMTqNR0NGq7g [Broken] [Broken]

    3. The attempt at a solution
    [PLAIN]https://lh6.googleusercontent.com/qRkIpr7Mg9TFQYXwa2Xoj5jv3vcBNP7hPUxT5Xk1inIv-Qdk_KhZWF-Pha5AJ_Aq9_e7ZQPUGeUrMdRCb7vTUgQKtYY4sGutyIYtGiLW6bspSIuL6-sdiCDjIHaN7viYGQ [Broken] [Broken]

    [PLAIN]https://lh5.googleusercontent.com/csDszB-wBCqIGI4g9bRCmLfDFgEbQcXTKjieRXO3BVOUmGCYJoq7CdCpd844FOemjb_MrhnaHitt0Dk0mBssD6-QSdQ2S51f3WpZ6tyamq5xrxfjmc64gZNMTqNR0NGq7g [Broken] [Broken]

    https://lh6.googleusercontent.com/kH5QjwyHmXZcrpHD2JM1sggbdDI43yXiUxr7e17NopEUM4dRfYHKsU19hO6lTbb9Pui_TCMytxYtHLXHTK_8Wj_EegNUFy3263FZEDVXh-h7eQMoWycZ0S09_kYp5Mhnig [Broken]

    https://lh5.googleusercontent.com/sDINzVNO1G2GzJlJnTrYY80Q1E9a9crTVdNyR1hm0jX8ru3R4WB7sWrZDla_CVpij173_N1r6yI-gaFr7DnQqwABqi1r-AeN9FotFK11RrRbhivhHm9GUqeTqZC79P_I_g [Broken]

    https://lh4.googleusercontent.com/_x3gT0FzL5kRBHNLUVXT24OZAh_9KJZAmBfRqQuYbxUMl92CvDL9Pkx7or1qoCZHyl8bz-4PdUA5Zc0PC61I1siMKjuDGoqgQtApYxSfyfiJO28kzZv8wDaMytKlKuz_IA [Broken]

    https://lh4.googleusercontent.com/joYLqXziuC1oujBIhA6YwQF6y8R8YIWBo10XaC8kaFNKSnFq44Bwh4hpQYUIZCAeFrMz-IZY5r_KYrLYSejPhz-_urptxyIWSiEIo4qRhbjOFm8SBc3Ui4WazZO_AtAAtQ [Broken]

    https://lh3.googleusercontent.com/19SQ3f8VkxjzitZKKnrCuilqBRVW4NsYhopELqqT2BRcxhcBwstvHpXf8ME0Fbg58_7pshIuW51QFxzPRwUH5xCLBWEeel1X-Xn-bG86FZIm3zq0RwhOXHgHzEZWgtAtJg [Broken]

    https://lh6.googleusercontent.com/xiV61mYNtopcHzoTYWVaiLDUnuWlUOwlnuxAa9JGvK5zJt9brfkrL4FKCPzR4b8a4R5Ta54dk3vbDFRM6jggqErfnkKbDxBIlRfa0R4T9IOnpdv5AHYJPGrWT5cwwo6oNg [Broken]

    My answer: 0.601 m^3. masteringphysics.com answer: 0.625 m3

    What am I getting wrong? I am so sure I am right, am I missing something really obvious?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Nov 23, 2014 #2

    PeterDonis

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    2016 Award

    Staff: Mentor

    Where did you get the values for the density of water and ice? Did masteringphysics.com use the same values?
     
  4. Nov 23, 2014 #3
    Those are from wikipedia and pubchem, masteringphysics.com didn't provide any values to use with the question. I tried with a number of different values including 1000 kg/m3 for water and 917 kg/m3 for ice, which comes to 0.602 instead of 0.601... still a good deal less the 0.625.
     
  5. Nov 23, 2014 #4

    haruspex

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    2016 Award

    On the net I see two values commonly, 917 and 931. At a guess, the latter corresponds to a pure crystalline form, Ih, while the former is for naturally occurring ice. But I could be wrong.
    To get the given answer you need 920, very close to 917. The key point is that the difference in the densities is a small difference between two large numbers, so a small error in one of the numbers leads to a relatively large error in the result.
     
  6. Nov 23, 2014 #5
    Ah you are right. Well, at least the problem wasn't with the method, I can accept a silly mistake like that.

    It is just interesting that they chose the density of ice at - 10 ºC, rather than at 0 ºC or at -180 ºC, which is the other commonly cited density.

    Thanks for the help
     
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