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

In summary, the conversation is about finding the tension of a string in a lever rod problem. The given information includes the length, weight, and angles of the rod and cable. The approach involves using torque and moment of inertia equations, with the distance from the pivot point being a key factor in solving for the tension. The final equation for finding the tension is T(L-b)sin(beta) - Fg(L/2)sin(alpha) = 0, with the answer being approximately 42.53 N.
  • #1
hoseA
61
0
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
 
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  • #2
I would begin by summing the moments about the hinge
 
  • #3
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.
 
  • #4
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:
 
  • #5
Maybe T(L-b) sin(beta) - Fg(L/2)sin(alpha) = O
 
  • #6
yeah that looks right
 
  • #7
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)
 

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

What is tension?

Tension is a force that is applied to an object in a way that stretches or pulls the object. It is typically measured in units of Newtons (N) and can be represented by a vector, meaning it has both magnitude and direction.

How do you find the tension of a string?

The tension of a string can be found by using the formula T = F * L, where T is the tension, F is the force applied to the string, and L is the length of the string. This formula assumes that the string is massless, has a constant cross-sectional area, and is under small deformations.

What factors affect the tension of a string?

The tension of a string is affected by several factors, including the force being applied, the length and thickness of the string, and the material properties of the string (such as elasticity and density). The tension can also be affected by external factors, such as temperature and humidity.

Why is finding the tension of a string important?

Knowing the tension of a string is important in many scientific and engineering applications. It can help determine the stability and strength of structures, predict the behavior of materials under stress, and ensure the safety of equipment and machinery.

What are some methods for measuring the tension of a string?

There are several methods for measuring the tension of a string, including using a force meter or scale, calculating the tension based on the deflection or displacement of the string, or using specialized equipment such as a tensionometer or dynamometer. The appropriate method will depend on the specific situation and the accuracy required.

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