For the log brace shown, select the set of 3 Free Body Diagrams that would be used to solve for the tension in the rope EF given the weight of the log. Assume the ground and log are frictionless 4 ft A B C A 1.25 ft K F 1.5 ft U 25 4ft 3 ft A RA H FK 2.5 ft E TEF TE 130. 3 ft TEF B 3 f W 35 FK Foy 2.5 ft D D RD Fox ERD 1 ft 2.30 K K ft 14 F LC RA A A RA 2.5 ft 730 TEF 1.SA EF / ft G 3 ft 4 3 FK KFGy Fox ERD D RD > D 5 RA A 4 ft 48 1.30 FK 3 ft 73 RA 2.5 ft CON TE 43 75A 1.25 ft G Fox RD D RD D Foy Fox -TEF /ft 지 2.58 BAZAART >
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.
![**Educational Transcription: Log Brace Free Body Diagrams**
**Introduction:**
The image above presents a mechanical problem involving a log brace setup where various Free Body Diagrams (FBDs) are used to analyze the forces involved. The objective is to identify the correct set of FBDs required to determine the tension in the rope EF, given the weight of the log.
**Setup:**
- A log is held by a brace composed of two crossed beams, AB and CD.
- Dimensions:
- Beam lengths: AB and CD are 4 feet.
- Segments KG, KH: 1.75 feet.
- Segment GE: 1.5 feet.
- Segment DE: 1 foot.
- Distance between points A and D: 3 feet.
**Constraints:**
- The ground and log are considered frictionless.
**Free Body Diagrams (FBDs):**
The collection of diagrams below each illustrates different force interactions and components involved in the problem:
- **Diagram A:**
- Displays triangle forces on part of the frame.
- Forces marked include \(T_{EF}\), \(R_A\), \(R_D\), and \(W\) (weight).
- **Diagram B:**
- Highlights forces at a midpoint of grip by the log.
- Depicts forces \(F_{FK}\) and \(F_{FH}\), with the weight \(W\) shown downward.
- **Diagram C:**
- Illustrates the horizontal component scheme.
- Shows \(T_{EF}\), \(R_D\), parallel and perpendicular force analysis.
- **Diagram D:**
- Focuses on inclined plane analysis.
- Details include forces like \(T_{EF}\), \(R_A\), \(R_D\), and external weight \(W\).
- **Diagram E:**
- Emphasizes vector components at nodes.
- Forces shown: \(F_{GX}\), \(F_{GY}\), \(F_{FK}\), and \(T_{EF}\).
- **Diagram F:**
- Represents the overall force balance.
- The main forces include \(R_A\), \(R_D\), and weight \(W\).
- **Diagram G:**
- Explores top view symmetry.
- Forces \(R_A\), \(R_D\), and weight \(W\) depicted.
- **Diagram H:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e18a88-13ba-47d2-8c84-ec9d29397d2a%2F60142659-1d14-45e8-8f28-fc0d82593c47%2Fvwgcjc6_processed.jpeg&w=3840&q=75)
![### Diagram J Description
This diagram illustrates a system of two intersecting rods arranged in an X-shape. The rods are labeled as follows:
- **C to K** and **A to F** on the left side
- **B to H** and **D to E** on the right side
Key dimensions and forces:
- Each rod segment is 2.5 feet long.
- Vertical distance from point A to point C and B to point D is 4 feet.
- Horizontal distance from point A to point D is 3 feet.
Forces:
- \(F_K\) and \(F_H\): Red arrows at 45-degree angles pointing upward from points K and H with magnitudes forming a 3-4-5 triangle.
- \(T_{EF}\): Horizontal red arrows pointing right from E and F.
Other notable points:
- The system has pivot points labeled G and O.
The base has a brown rectangular area at the bottom.
### Diagram K Description
This diagram shows a simplified version of Diagram J with a single rod arranged diagonally.
Key dimensions and forces:
- The rod \(C\) to \(D\) is 3.75 feet long.
- Vertical distance from point C to the ground is 4 feet, and the horizontal distance from point C to point D is 3 feet.
Forces:
- \(F_K\): A red arrow forming a right triangle with magnitudes 3 and 4 indicating a force at point K.
- \(T_{EF}\): A horizontal red arrow pointing left from point E.
- \(R_D\): A red arrow extending from point D at a 45-degree angle, indicating reaction force.
The base ground distance from point D is 1 foot.
Both diagrams are used to understand the forces acting on the rods and their alignment, demonstrating principles of static equilibrium and structural analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e18a88-13ba-47d2-8c84-ec9d29397d2a%2F60142659-1d14-45e8-8f28-fc0d82593c47%2Fk6hualg_processed.jpeg&w=3840&q=75)
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