How to Calculate the Tension in a Cable Supporting a Lever Rod?

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Homework Help Overview

The discussion revolves around calculating the tension in a cable that supports a lever rod in equilibrium. The lever rod has specific dimensions and weight, and the problem involves understanding the forces and moments acting on the system.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between tension, weight, and angles in the context of torque and equilibrium. There are questions about how to incorporate the distance variable 'b' into the calculations and how to set up the equations correctly.

Discussion Status

Some participants suggest summing moments about the hinge and discuss the role of the distance 'b' in the torque calculations. There is a general agreement on the approach to take, although the original poster expresses uncertainty about the equations to use.

Contextual Notes

The original poster indicates a time constraint due to an upcoming exam, which adds urgency to their request for help. They also mention that the problem may not appear on the exam, suggesting a focus on understanding rather than just solving this specific problem.

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http://img6.imageshack.us/img6/8772/leverrodtension3db.th.png
How do I find the tension of the string? (The image is from a homework problem)
I want to know how to approach it. (hence, I left the numbers out)
-----------------------------------------------------
<edit>
Here's the info they give in hopes of more response:

Consider a lever rod of length L = 7.34 m,
weight W = 69 N and uniform density. As
shown on the picture below, the lever rod is
pivoted on one end and is supported by a
cable attached at a point b = 2.15 m from the other end.
The lever rod is in equilibrium at angle beta =
55 degrees from the vertical wall. The cable makes
angle alpha = 70 degrees with the rod.

What is the tension of the supporting cable? Answer in units of N.
</edit>
--------------------------------------------------

All the variables in the picture are given. Now in terms of the variables, how do I solve it??
I think this is a torque and moment of inertia problem. But what equations will be used?
I came up with the following by comparing it was a somewhat similar problem. However, the "b" variable is throwing me off as to how that is utilized.
Help much appreciated. Thanks.

Is the following even close to helping finding T?

TL sin(beta) - Fg(L/2)sin(alpha) = O
 
Last edited by a moderator:
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I would begin by summing the moments about the hinge
 
b is simply there to give you the distance of the string from the pivot (d=L-b) it is at this point that a moment equal but oppposite to the moment caused by the weight of the bar.
 
I've added the actual problem. I'm in need of desperate help since my exam is tomorrow and I want to know how to do this problem -- although it probably won't be on it (I hope).

Help is much appreciated.:approve:
 
Maybe T(L-b) sin(beta) - Fg(L/2)sin(alpha) = O
 
yeah that looks right
 
Aneleh said:
yeah that looks right

Thanks for the confirmation. I worked it out and the answer came out correct. (42.5330474 or 42.53 N)
 

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