# Depression of Water Surface by a Needle

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

1. The maximum depression in the water surface; and
2. 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?

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Given the volume of the needle and it's mass density, you can calculate the surface tension force based on a simple free body diagram. You might need to use the concept of a contact angle perhaps and some trigonometry to figure out what the depression is. – drN Mar 1 '13 at 20:21
@drN wouldn't both the contact angle and the amount of needle in contact with water affect things? mathematically I can think of two configurations where the contact angle is identical but the surface area in contact is different, and thus the angle between the surface tension force and the weight of the needle is different. – Vincent Tjeng Mar 2 '13 at 1:57