Chapter 3, Problem 198P

The density of stainless steel is about 8000 kg/m³ (eight times denser than water), but a razor blade can float on water, even with some added weights. The water is at 20°C. The blade shown in the photograph i$ 4.3 cm long 2nd 2.2 cm wide. For simplicity, the center cut-out area of the razor blade has been taped so that only the outer edges of the blade contribute to surface tension effects. Because the razor blade has sharp comers, the contact angle is not relevant. Rather, the limiting case is when the water contacts the blade vertically as sketched (effective contact angle along the edge of the blade is 180^sl (a) Considering surface tension done, estimate (in grams) how much total mass (razor blade - weights placed on top of it) can be supported, (b) Refine your analysis by considering that the razor blade pushes the water down, and thus hydrostatic pressure effects are also present. Hint You will also need to know that due to the curvature of the meniscus, the maximum possible depth is
   $h=\sqrt{\frac{2{\sigma }_t}{\vartheta g}}$ .