Archimedes Principle - Mass floating on ice

[Mike Dacre]

Homework Statement

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?

Homework Equations

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

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

The Attempt at a Solution

[PLAIN]https://lh6.googleusercontent.com/qRkIpr7Mg9TFQYXwa2Xoj5jv3vcBNP7hPUxT5Xk1inIv-Qdk_KhZWF-Pha5AJ_Aq9_e7ZQPUGeUrMdRCb7vTUgQKtYY4sGutyIYtGiLW6bspSIuL6-sdiCDjIHaN7viYGQ

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

https://lh6.googleusercontent.com/kH5QjwyHmXZcrpHD2JM1sggbdDI43yXiUxr7e17NopEUM4dRfYHKsU19hO6lTbb9Pui_TCMytxYtHLXHTK_8Wj_EegNUFy3263FZEDVXh-h7eQMoWycZ0S09_kYp5Mhnig

https://lh5.googleusercontent.com/sDINzVNO1G2GzJlJnTrYY80Q1E9a9crTVdNyR1hm0jX8ru3R4WB7sWrZDla_CVpij173_N1r6yI-gaFr7DnQqwABqi1r-AeN9FotFK11RrRbhivhHm9GUqeTqZC79P_I_g

https://lh4.googleusercontent.com/_x3gT0FzL5kRBHNLUVXT24OZAh_9KJZAmBfRqQuYbxUMl92CvDL9Pkx7or1qoCZHyl8bz-4PdUA5Zc0PC61I1siMKjuDGoqgQtApYxSfyfiJO28kzZv8wDaMytKlKuz_IA

https://lh4.googleusercontent.com/joYLqXziuC1oujBIhA6YwQF6y8R8YIWBo10XaC8kaFNKSnFq44Bwh4hpQYUIZCAeFrMz-IZY5r_KYrLYSejPhz-_urptxyIWSiEIo4qRhbjOFm8SBc3Ui4WazZO_AtAAtQ

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

https://lh6.googleusercontent.com/xiV61mYNtopcHzoTYWVaiLDUnuWlUOwlnuxAa9JGvK5zJt9brfkrL4FKCPzR4b8a4R5Ta54dk3vbDFRM6jggqErfnkKbDxBIlRfa0R4T9IOnpdv5AHYJPGrWT5cwwo6oNg

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?

 

[PeterDonis]

What am I getting wrong?

Where did you get the values for the density of water and ice? Did masteringphysics.com use the same values?

 

[Mike Dacre]

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.

 

[haruspex]

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.

 

[Mike Dacre]

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