Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 10 - Fluids - Problems - Page 289: 71

Answer

1.5 mm.

Work Step by Step

Draw the free-body diagram for the needle, which is similar to Figure 10–36a (page 281). Assume that the surface tension force acts vertically. The needle is of length L. The needle’s weight equals the net surface tension force. $$mg=2F_T$$ $$\rho_{needle}\pi(0.5d_{needle})^2Lg=2\gamma L$$ $$ d_{needle}=\sqrt{\frac{8\gamma }{\rho_{needle}\pi g}} $$ $$ d_{needle}=\sqrt{\frac{8(0.072\;N/m) }{(7800\;kg/m^3)\pi (9.8\;m/s^2)}}\approx 1.5\;mm $$
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