A motivating example:
A friend and I noticed a frozen water bottle melting at work and began to wonder - at what point in the melting process would the remaining ice be floating in the water generated from melting, as opposed to resting on the bottom of the bottle?
The actual question:
Assume a block of ice completely fills an open-top, cube-shaped container with side length L. As the container sits in ambient air, the ice begins to melt. To simplify, we can assume the melting rate results in a constant reduction in all dimensions (i.e. the side length of the cube of at any time is L-x, where x is the current depth of melting). We can also ignore surface tension and anything else that may cause the melted water to "stick" to the ice. At what point in the melting process does the ice float?
My intuition and preliminary math say that it would float immediately, but I'm interested to hear the thoughts of others.
Note that this similar question has been asked, but refers to a case where the ice cube and the container have different initial geometry.