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ERIC Number: EJ825955
Record Type: Journal
Publication Date: 2009-Jan
Pages: 12
Abstractor: As Provided
Reference Count: 13
ISSN: ISSN-0143-0807
The Stability of the Catenary Shapes for a Hanging Cable of Unspecified Length
Mareno, A.; English, L. Q.
European Journal of Physics, v30 n1 p97-108 Jan 2009
It has long been known that when a cable of specified length is hung between two poles, it takes the shape of a catenary--a hyperbolic cosine function. In this paper, we study a variation of this problem. First, we consider a cable hanging between two poles in which one end of the cable is fixed to one pole; the other end of the cable runs over a pulley, attached to the other pole, and then down to a table. Here, the length of the cable can vary as the pulley rotates. For a specified horizontal distance between the two poles, we vary the height of the fixed cable end. We then determine both experimentally and analytically the stability of the resulting catenary-cable shapes. Interestingly, at certain heights there are two catenaries of different lengths--we use Newtonian mechanics to show that only one of these is stable. Below a certain critical height, no catenary exists and the cable is pulled down to the table. Finally, we explore a related problem in which one end of the cable runs over a pulley, but the other end can now freely move vertically along a pole. These experiments nicely lend themselves as teaching tools in a classroom setting. (Contains 2 tables and 7 figures.)
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A