1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Archimedes Principle - Mass floating on ice
  1. Floating Ice (Replies: 5)