Given a needle of mass $m$ modeled by a cylinder of length $l$ and radius $r$ placed on an infinitely large water surface, what is
- The maximum depression in the water surface; and
- The equation of the shape of the water surface when depressed?
I'm quite sure this is a simple question that already has been modeled theoretically somewhere, but I haven't been able to find a theoretical treatment of the problem with experimentally verifiable quantities.
In addition, can the treatment of the problem be extended to thin films, for example a thin soap film?