Equilibrium and Statics involving a mass attached to three strings

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Homework Help Overview

The discussion revolves around a statics problem involving a mass attached to three strings, where participants are tasked with finding the forces in the strings based on the given setup. The problem context includes considerations of equilibrium and the forces acting on the mass.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to create equations for the x-axis and y-axis but encounters issues with the cancellation of forces. They question whether additional data is needed to proceed. Other participants note the problem's statically indeterminate nature and suggest that additional equations are necessary. Some discuss the implications of string extensibility and propose methods to approach the problem based on that assumption.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have offered insights into the implications of string properties, while others are questioning the assumptions made in the original setup. There is no explicit consensus on a solution, but various lines of reasoning are being examined.

Contextual Notes

Participants note that the problem may exceed typical grade 11 curriculum expectations, particularly regarding the extensibility of strings and the calculus involved in finding solutions. There is also mention of the problem being part of a previous exam, which raises questions about its appropriateness for the current discussion.

alingy1
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Homework Statement



Find the forces of the three strings of this image.

http://www.flickr.com/photos/79276401@N05/8395815988/in/photostream

Homework Equations



Using gravitational constant to find force of the mass.
Using algebra to find the forces of the three strings.

The Attempt at a Solution


I tried to create two equations, one for the x-axis and another for the y-axis. However, in the x-axis, the two strings of 25° cancel themselves. Do you think there is a missing data? This blocks me from using substitution to find the other forces. How would you proceed?
 
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You have three supports but only two equations of statics. Therefore, the problem is statically indeterminate. In order to solve this system, additional equations must be introduced.
 
If the strings are completely inextensible then there is no way to solve this. You can obtain consistent solutions by setting e.g. the tension in the centre string to 0, or by setting the other two to 0.
In the real world, all strings are at least a little extensible. If you consider a small extension to the centre string, you can calculate the extensions to the other two. Taking the tensions to be in proportion to these, a solution can be found.
 
Actually, I have never seen string extensibility in grade 11. Your reply interests me. Could you explain how we could proceed to find the three forces? How do we find how much they extend? Very bizarrely, the teacher said this question was in last year's exam...
 
It requires a little differential calculus, so I'm guessing that also puts it beyond your syllabus.
Let the two angled strings be attached w from the centre. If the centre string has length x, the other two have length √(x2+w2). If the centre string is stretched by amount δx the other two are each stretched √((x+δx)2+w2) - √(x2+w2) ≈ xδx/√(x2+w2) = δx sec(θ). So the tension in the side strings is sec(θ) times that in the centre string. That's enough extra info to solve it.
 

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