3 **Title: Understanding Determinacy in Static Systems****Diagram Description:**The diagram depicts a horizontal beam supported by two ropes. The beam is 2 meters long and is segmented into three sections: from point A to point B (1 m), and from point B to point C (1 m). There is a downward force of 400 N acting at point C. This forms part of a statics problem typically used to determine the determinacy of a structure.**Option Selections:**1. O It is determinate because there is only one known force.2. O It is determinate because there are three unknowns and we can write three independent equations of equilibrium.3. O It is determinate because we have fewer than 6 unknowns.4. O It is indeterminate because there are no moments on the FBD.5. O It is indeterminate because there are more unknowns than available equilibrium equations.6. O It is indeterminate because we only have one known force and three unknown forces.**Explanation:**In statics, a system is determined to be in equilibrium if the sum of all forces and moments acting on the system are zero. For a structure to be determinate, the number of unknown forces should be equal to the number of equilibrium equations available. Typically, in a two-dimensional system, we have three equilibrium equations: 1. $\sum F_x = 0$ 2. $\sum F_y = 0$ 3. $\sum M = 0$ Analyzing the options:- Option 1: Incorrect. The number of known forces alone does not determine whether the system is determinate.- Option 2: Correct. If there are three unknowns, we can write three independent equilibrium equations making the system determinate.- Option 3: Incorrect. Having fewer than 6 unknowns does not ensure determinacy as we need to match the number of unknowns with the number of equilibrium equations.- Option 4: Incorrect. Moments need to be considered in Free Body Diagram (FBD) analysis; their absence would not alone determine system indeterminacy.- Option 5: Incorrect. This option conflates the concepts of statics determinacy, as we need to count unknowns and available equations directly.- Option 6: Incorrect. Having one known force and three unknown forces does not affect the determinacy.Therefore, the correct explanation ### Equilibrium of a Beam#### Problem StatementThe beam is supported by a pin at A and cables at B and C. The weight of the beam is negligible. Draw a complete, clearly labeled Free Body Diagram (FBD) of the beam on your paper.#### Question for DeterminacyWhich one of the following statements is true concerning the determinacy of your Free Body Diagram (FBD)?#### Diagram Description- **A** is the pin support on the left side.- **B** is a point 1 meter from A where one cable is attached.- **C** is another point 1 meter from B (and 2 meters from A) where another cable is attached.- A 400 N force is applied vertically downward at point C.- Points D and E are the locations where the cables attached to B and C respectively are anchored above the beam. The lengths of these cables are 2 meters each.#### Provided Answers1. **It is determinate because there is only one known force.**2. **It is determinate because there are three unknowns and we can write three independent equations of equilibrium.**#### ExplanationThe FBD should include:- The beam with dimensions marked.- The pin support at A with its reaction forces.- The cables at B and C showing the tension forces in the cables.- The downward force of 400 N at point C.This problem involves establishing equilibrium in a static system where the sum of forces and moments must equal zero.

Name: 3 **Title: Understanding Determinacy in Static Systems****Diagram Desc
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Description: 3 **Title: Understanding Determinacy in Static Systems****Diagram Description:**The diagram depicts a horizontal beam supported by two ropes. The beam is 2 meters long and is segmented into three sections: from point A to point B (1 m), and from poin

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Equilibrium: The beam is supported by a pin at A and cables at B and C. The weight of the beam is negligible. Draw a complete, clearly labeled FBD of the beam on your paper. Which one of the following statements is true concerning the determinacy of your FBD? D E

Equilibrium: The beam is supported by a pin at A and cables at B and C. The weight of the beam is negligible. Draw a complete, clearly labeled FBD of the beam on your paper. Which one of the following statements is true concerning the determinacy of your FBD? D E

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Question

**Title: Understanding Determinacy in Static Systems**

**Diagram Description:**

The diagram depicts a horizontal beam supported by two ropes. The beam is 2 meters long and is segmented into three sections: from point A to point B (1 m), and from point B to point C (1 m). There is a downward force of 400 N acting at point C. This forms part of a statics problem typically used to determine the determinacy of a structure.

**Option Selections:**

1. O It is determinate because there is only one known force.
2. O It is determinate because there are three unknowns and we can write three independent equations of equilibrium.
3. O It is determinate because we have fewer than 6 unknowns.
4. O It is indeterminate because there are no moments on the FBD.
5. O It is indeterminate because there are more unknowns than available equilibrium equations.
6. O It is indeterminate because we only have one known force and three unknown forces.

**Explanation:**

In statics, a system is determined to be in equilibrium if the sum of all forces and moments acting on the system are zero. For a structure to be determinate, the number of unknown forces should be equal to the number of equilibrium equations available. Typically, in a two-dimensional system, we have three equilibrium equations:

1. $\sum F_x = 0$
2. $\sum F_y = 0$
3. $\sum M = 0$

Analyzing the options:

- Option 1: Incorrect. The number of known forces alone does not determine whether the system is determinate.
- Option 2: Correct. If there are three unknowns, we can write three independent equilibrium equations making the system determinate.
- Option 3: Incorrect. Having fewer than 6 unknowns does not ensure determinacy as we need to match the number of unknowns with the number of equilibrium equations.
- Option 4: Incorrect. Moments need to be considered in Free Body Diagram (FBD) analysis; their absence would not alone determine system indeterminacy.
- Option 5: Incorrect. This option conflates the concepts of statics determinacy, as we need to count unknowns and available equations directly.
- Option 6: Incorrect. Having one known force and three unknown forces does not affect the determinacy.

Therefore, the correct explanation

### Equilibrium of a Beam

#### Problem Statement

The beam is supported by a pin at A and cables at B and C. The weight of the beam is negligible. Draw a complete, clearly labeled Free Body Diagram (FBD) of the beam on your paper.

#### Question for Determinacy

Which one of the following statements is true concerning the determinacy of your Free Body Diagram (FBD)?

#### Diagram Description

- **A** is the pin support on the left side.
- **B** is a point 1 meter from A where one cable is attached.
- **C** is another point 1 meter from B (and 2 meters from A) where another cable is attached.
- A 400 N force is applied vertically downward at point C.
- Points D and E are the locations where the cables attached to B and C respectively are anchored above the beam. The lengths of these cables are 2 meters each.

#### Provided Answers
1. **It is determinate because there is only one known force.**
2. **It is determinate because there are three unknowns and we can write three independent equations of equilibrium.**

#### Explanation

The FBD should include:
- The beam with dimensions marked.
- The pin support at A with its reaction forces.
- The cables at B and C showing the tension forces in the cables.
- The downward force of 400 N at point C.

This problem involves establishing equilibrium in a static system where the sum of forces and moments must equal zero.

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Step 1: First we will draw the free body diagram of the beam and show the forces.

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Step 2: Now we will write unknowns and equilibrium conditions and conclude the result.

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