Cables of negligible weight support the loading shown. (Figure 1) If W1 = 5.00 lb, W2 = 71.0 lb , yp = 4.50 ft , yc = 7.50 ft , yp = 2.50 ft , and æc = 2.00 ft , find æg-
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
 [Figure 1]
In the diagram, a system of cables and pulleys is depicted. The respective positions and weights are labeled as follows:
- Point \(A\) is the starting point at the top of the structure.
- Point \(B\) is directly to the right of \(A\) at a horizontal distance \(x_B\) and a vertical distance \(y_B\).
- Point \(C\) is directly below \(A\) at a distance \(x_C\) and \(y_C\).
- Point \(D\) is directly below \(A\) at a distance \(y_D\).
- \(W_1\) is hanging from the intersection at \(C\) and \(D\).
- \(W_2\) is suspended via a pulley system from point \(H\) which is to the right of \(B\).
### Steps to Solve the Problem:
1. Analyze the forces and displacement constraints in the system.
2. Apply principles of static equilibrium for points where forces are acting.
3. Use trigonometric relations to express horizontal and vertical components relative to the given values.
The detailed diagram below helps to visualize the system:
**Figure: Cable Support System**
Here, the diagram illustrates:
- Point \(A\) as a fixed point where the cables originate.
- Point \(B\) is shown horizontally at a distance \(x_B\) from \(A\) and vertically higher by \(y_B\).
- Point \(C\) is indicated at a distance \(x_C\) horizontally from \(D\) and vertically lower by \(y_C\).
- Weights \(W](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb575d4aa-617f-4320-be65-135468ab142e%2F7dbf51d7-54f7-451e-9b70-4cf17c4558a3%2Fpmlucdc_processed.png&w=3840&q=75)
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