# Archimedes Principle - Mass floating on ice

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1. Nov 23, 2014

### Mike Dacre

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.

3. The attempt at a solution

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. Nov 23, 2014

### Staff: Mentor

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

3. Nov 23, 2014

### 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.

4. Nov 23, 2014

### 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.

5. Nov 23, 2014

### 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