Solving Tension in Cables: 20 kg Speaker 2.5 m, 2 Cables 20°

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Homework Help Overview

The problem involves a 20 kg loudspeaker suspended by two cables at an angle of 20 degrees from the vertical, with a height of 2.5 m from the ceiling. The focus is on determining the tension in the cables while considering the forces acting on the loudspeaker.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about the equations relevant to tension, indicating a lack of prior discussion on the topic in class. Some participants suggest using vectors and trigonometry to analyze the forces involved. Others describe the equilibrium of forces acting on the loudspeaker and the relationship between the tension components.

Discussion Status

The discussion includes various insights on how to approach the problem, with some participants providing guidance on using equilibrium conditions and vector analysis. There is an acknowledgment of the need to consider both the x and y components of tension, but no consensus has been reached on a specific method or solution.

Contextual Notes

The original poster notes a lack of familiarity with the concept of tension, which may impact their ability to engage with the problem effectively. Additionally, the problem's setup and the angle of the cables are critical factors under discussion.

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Homework Statement



A 20 kg loudspeaker is suspended 2.5 m below the ceiling by two cables that are each 20 degrees from vertical. What is the tension the cables?

Homework Equations





The Attempt at a Solution



I have no idea on what equation to use, considering we haven't even talked about tension at all in class. These problem seems simple but I don't know how to start it. I don't need the answer, just maybe some information on what I'm supposed to do with the information provided. Thank you in advance!
 
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Tension is a force. And these forces in this problem are in equilibrium.

Use vectors and trigonometry.
 
Drawing out the picture, you can see that for the loudspeaker to hang stationary, the downward pull of gravity must be counteracted by an equal upward force, which is the force of tension provided by the two cables. Note also that the two cables have tension in the x and y directions, with total tension given by [tex]F_T = \sqrt{F_T_x^2 + F_T_y^2}[/tex].

Because of this, [tex]2F_T_y = F_g[/tex], because both cables are exerting an equal upward force on the loudspeaker.

Once you've found the y-component of the tension, you can find the total tension in the cable by analyzing the right triangle made by the cable and its x- and y- components. In this case, [tex]F_T_y = \frac{F_T}{cos \theta}[/tex]. With your value for the angle, you can now solve for the tension in the cable, which is identical for both cables due to the symmetry of the problem.
 
Thank you! I appreciate your help!
 

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