1. **Problem Statement:**Replace the loading system with a single force (specify magnitude and direction) and couple moment acting at point \( O \).2. **Diagram Explanation:**- The diagram provided depicts a rigid body subjected to multiple forces and a couple moment.- A force of 200 N is applied vertically downward.- A couple moment of 600 N·m is acting counterclockwise.- A force of 500 N is applied at an angle of 60° from the horizontal, directed upward to the right.- A force of 300 N is applied horizontally to the right.- The dimensions given are: - From point \( O \) to the line of action of the 200 N force: 450 mm. - From point \( O \) to the right along the horizontal beam: 450 mm. - Distance from the horizontal beam to the 500 N force along its direction: 300 mm from the horizontal axis. - Vertical distance from the base to the 500 N force: 400 mm.3. **Problem Requirements:**Calculate and report the magnitude and direction of the single resultant force and the couple moment at point \( O \).- **Force:** \[ \text{Force} = \underline{\hspace{4cm}} \]- **Angle (\( \theta \)):** \[ \theta = \underline{\hspace{4cm}} \]- **Couple Moment:** \[ \text{Couple Moment} = \underline{\hspace{4cm}} \]

given: A loading system is given

Answered: 1. Replace the loading system with a…

1. Replace the loading system with a single force (specify magnitude and direction) and couple moment acting at point O. 500 N 60° 200 N 600 N-m 300 mm 300 N 400 mm 450 mm -450 mm

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

1. **Problem Statement:**

Replace the loading system with a single force (specify magnitude and direction) and couple moment acting at point \( O \).

2. **Diagram Explanation:**

- The diagram provided depicts a rigid body subjected to multiple forces and a couple moment.
- A force of 200 N is applied vertically downward.
- A couple moment of 600 N·m is acting counterclockwise.
- A force of 500 N is applied at an angle of 60° from the horizontal, directed upward to the right.
- A force of 300 N is applied horizontally to the right.
- The dimensions given are:
- From point \( O \) to the line of action of the 200 N force: 450 mm.
- From point \( O \) to the right along the horizontal beam: 450 mm.
- Distance from the horizontal beam to the 500 N force along its direction: 300 mm from the horizontal axis.
- Vertical distance from the base to the 500 N force: 400 mm.

3. **Problem Requirements:**

Calculate and report the magnitude and direction of the single resultant force and the couple moment at point \( O \).

- **Force:**

\[ \text{Force} = \underline{\hspace{4cm}} \]

- **Angle (\( \theta \)):**

\[ \theta = \underline{\hspace{4cm}} \]

- **Couple Moment:**

\[ \text{Couple Moment} = \underline{\hspace{4cm}} \]

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