.3 m B 5 kN 75 A 2 kN .5 m 2 kN FIGURE P3-21 -2m- 3-22. Determine the moment about point A for the system shown in Figure P3-22. 10 lb 8 b A 80° 80 10 16 FIGURE P3-22

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### Engineering Mechanics: Statics

#### Problem 3-22: Determine the Moment About Point A

For the system shown in Figure P3-21 and Figure P3-22, calculate the moment about point A.

**Figure P3-21:**
- The diagram shows an object with forces acting on it. Key details include:
  - Two forces of 2 kN acting horizontally at different heights.
  - Another force of 5 kN acting at an angle of 75° to the horizontal.
  - Dimensions are given for different parts of the object: 0.3 m vertically and 2 m horizontally.
  - Points A and B are marked, and point A appears to be a support point or hinge.

**Figure P3-22:**
- The diagram depicts a horizontal structure subjected to forces.
  - A force of 10 lb acts at an 80° angle on both the left side and the right side of the structure.
  - Another force of 8 lb acts vertically downward.
  - Dimensions are given: 4 ft horizontally where the forces are applied, 6 ft horizontally for the entire length of the structure, and 8 ft vertically.
  - Points A and B are marked, with point A on the right end of the structure.

### Objective:
Determine the moment about point A for the system.

#### Steps to Solve:

1. **Identifying Forces and Their Components:**
   - Break down each force into its horizontal and vertical components.

2. **Calculating Moments:**
   - Use the moment formula: \( M = F \times d \times \sin(\theta) \)
   - Sum the moments caused by each force about point A.

3. **Result:**
   - The sum of all moments will give you the net moment about point A.

For detailed calculations, consider the geometry and forces at play explicitly. This will involve resolving the forces into their components and using the perpendicular distances from point A to each force's line of action.

Remember to consider the sign convention for moments (clockwise vs. counterclockwise) to ensure accurate summation.
Transcribed Image Text:### Engineering Mechanics: Statics #### Problem 3-22: Determine the Moment About Point A For the system shown in Figure P3-21 and Figure P3-22, calculate the moment about point A. **Figure P3-21:** - The diagram shows an object with forces acting on it. Key details include: - Two forces of 2 kN acting horizontally at different heights. - Another force of 5 kN acting at an angle of 75° to the horizontal. - Dimensions are given for different parts of the object: 0.3 m vertically and 2 m horizontally. - Points A and B are marked, and point A appears to be a support point or hinge. **Figure P3-22:** - The diagram depicts a horizontal structure subjected to forces. - A force of 10 lb acts at an 80° angle on both the left side and the right side of the structure. - Another force of 8 lb acts vertically downward. - Dimensions are given: 4 ft horizontally where the forces are applied, 6 ft horizontally for the entire length of the structure, and 8 ft vertically. - Points A and B are marked, with point A on the right end of the structure. ### Objective: Determine the moment about point A for the system. #### Steps to Solve: 1. **Identifying Forces and Their Components:** - Break down each force into its horizontal and vertical components. 2. **Calculating Moments:** - Use the moment formula: \( M = F \times d \times \sin(\theta) \) - Sum the moments caused by each force about point A. 3. **Result:** - The sum of all moments will give you the net moment about point A. For detailed calculations, consider the geometry and forces at play explicitly. This will involve resolving the forces into their components and using the perpendicular distances from point A to each force's line of action. Remember to consider the sign convention for moments (clockwise vs. counterclockwise) to ensure accurate summation.
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