Determine the force in link CD of the vise grip. 5 lb 0.75 in. 1 in. 20° -1.5 in.1 in. 3 in. 5 lb
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.
![### Topic: Analyzing Reactions and Member Forces in Structures
#### Problem Statement:
**(B) Determine the reactions and member forces in the structures/machines. Show all free-body diagrams.**
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#### Explanation:
When analyzing the forces in mechanical structures, it is crucial to determine the reactions and member forces accurately. The steps to solve these problems typically involve:
1. **Drawing Free-Body Diagrams (FBDs):**
- Free-Body Diagrams are used to visualize the forces acting on each part of the structure or machine.
- These diagrams help isolate a system or subsystem to highlight all applied forces, thus simplifying the analysis.
2. **Equilibrium Conditions:**
- Apply the conditions of static equilibrium to each FBD.
- The sum of forces in the horizontal and vertical directions should be zero.
- The sum of moments about any point should also be zero.
3. **Solving for Unknowns:**
- Use algebraic methods to solve for unknown forces and support reactions.
- In more complex systems, use methods like the method of joints or sections for trusses.
4. **Verification:**
- Check results to ensure all equilibrium conditions are satisfied.
- Review the diagrams to ensure all forces are accounted for correctly.
Free-body diagrams will typically include:
- Representation of the member/system.
- All external forces and moments.
- Support reactions.
- Applied loads.
For educational purposes, detailed steps and example problems can provide deeper understanding. Diagrams and calculations should be clearly labeled and solved step-by-step to aid learning.
---
This detailed textual reference aids in understanding the importance of free-body diagrams and systematic analysis in determining reactions and member forces in mechanical structures. Further examples and exercises are recommended to build proficiency.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ceacb0b-43f6-4b23-a073-44942bf7117a%2F65238338-d26a-4cfb-86a0-865ccb14e9d8%2Fqlqeeq_processed.png&w=3840&q=75)
![### Determining the Force in Link CD of the Vise Grip
#### Problem Statement:
Determine the force in link CD of the vise grip as shown in the diagram.
#### Diagram Explanation:
- The vise grip consists of pivot points and links that move to exert force.
- **Points A, B, D, E, and C** are the pivot points of the vise grip.
- Link CD, whose force we need to determine, is one of the links extending from point D.
- A force of 5 pounds is applied at the handles of the vise grip, denoted by arrows at two points along the handles.
#### Dimensions:
1. **Distance from A to B:** 0.75 inches
2. **Distance from A to E:** 1 inch
3. **Distance from A to the horizontal component of the force:** 1.5 inches
4. **Distance from E to the line of action at the handle:** 3 inches
5. **Angle between the line from A to E and the horizontal component of the force:** 20 degrees
#### Forces Acting on the Vise Grip:
- Two forces of 5 pounds each are acting on the handle of the vise grip. These forces create a moment about the pivot points leading to clamping action.
#### Steps to Determine Force in Link CD:
1. **Free Body Diagram (FBD):**
- Draw the FBD of each segment of the vise grip.
- Identify the points where forces and reactions occur (at pivots and points of force application).
2. **Moments and Equilibrium:**
- Use the equilibrium equations (ΣF = 0, ΣM = 0) to set up the moments about pivot points.
- Assume the force in link CD as \(F_{CD}\).
3. **Calculating Moments:**
- Select the pivot point (for example, point E) and calculate moments created by the 5 lb forces considering lever arms through the given dimensions.
4. **Solving for \(F_{CD}\):**
- Use trigonometric relationships to resolve the forces at various angles and distances.
- Apply the equilibrium conditions to solve for \(F_{CD}\).
### Graphs and Diagrams:
- The provided diagram is a crucial visual aid depicting the dimensions, forces, and structural components of the vise grip. The detailed measurements and angles assist in applying physics principles for calculation.
#### Conclusion:
By](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ceacb0b-43f6-4b23-a073-44942bf7117a%2F65238338-d26a-4cfb-86a0-865ccb14e9d8%2Fgsvqw7_processed.png&w=3840&q=75)
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