# Archimedes Principle - Mass floating on ice

## 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.

## The Attempt at a Solution

What am I getting wrong? I am so sure I am right, am I missing something really obvious?

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PeterDonis
Mentor
2020 Award
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?

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
Homework Helper
Gold Member
2020 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.

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