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2012 BFY Abstract Detail Page

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Abstract Title: W23 - New configurations for a hanging chain covered by soap film: Measurement of surface tension from the triangular configuration
Abstract: A chain assumes the familiar shape known as a catenary when it hangs loosely from two points in a gravitational field. The derivation of the catenary equation was one of the early triumphs of the newly invented calculus of variations at the end of the 17th century.

We will show that three new and distinct configurations are possible if a soap film covers the area bounded by the catenary as it hangs from a horizontal support rod. We will demonstrate how the chain can assume a concave, triangular, or convex configuration. Furthermore, we will show how the chain can be transformed smoothly from one configuration to another and shall discuss the conditions necessary for each configuration. Not surprisingly, the deciding factor is the strength of the surface tension relative to the gravitational force per unit length normal to the chain.

The conditions under which the chain assumes a perfect triangular configuration is particularly simple and provides an elegant method for measuring the surface tension of the soap film. Naturally the triangular configuration is visually striking but students are more intrigued when they learn that by measuring just one angle of the triangle they can obtain the surface tension of the soap solution.

The convex and concave configurations require more sophisticated analysis and can form the basis of a lab experiment for more advanced students.
Abstract Type: Workshop

Workshop Documents

Workshop Document: Download the Workshop Document
Workshop Document (2): Download the Workshop Document (2)
Workshop Document (3): Download the Workshop Document (3)
Workshop Document (4): Download the Workshop Document (4)

Author/Organizer Information

Primary Contact: Fred Behroozi
Univ. of Northern Iowa