### Equilibrium of a Uniform Rod with Spring System#### Problem Statement:A 10.5-kg uniform rod is attached to a pivot at end \( A \). It is subjected to a couple moment of \( 50 \, \text{N} \cdot \text{m} \). The spring connected to the rod is unstretched when the angle \( \theta = 0 \), and it has a stiffness constant \( k = 60 \, \text{N/m} \).**Determine the smallest angle \( \theta \) for equilibrium.**Express your answer in degrees to three significant figures.#### Parameters:- Mass of the rod: \( 10.5 \, \text{kg} \)- Couple moment: \( 50 \, \text{N} \cdot \text{m} \)- Spring stiffness: \( 60 \, \text{N/m} \)- Spring is unstretched at \( \theta = 0 \)#### Figure Description:The accompanying figure shows the rod pinned at point \( A \) with a spring attached at point \( B \). In the diagram:- The length from \( A \) to the point where the spring is attached is \( 2 \, \text{m} \).- The spring has a stiffness constant \( k = 60 \, \text{N/m} \) and is not stretched when \( \theta = 0 \).- The rod forms an angle \( \theta \) with the vertical.- A couple moment of \( 50 \, \text{N} \cdot \text{m} \) is applied to the rod.#### Graph/Diagram Explained:The figure shows:1. A vertical rod \( AB \) with a pivot at point \( A \).2. A spring attached at \( B \), which lies horizontally in the unstretched position when \( \theta = 0 \).3. The length \( AB \) is \( 2 \) meters.4. A measurement indicating that the spring is \( 0.5 \) meters above the pivot when \( \theta = 0 \).5. A couple moment of \( 50 \, \text{N} \cdot \text{m} \) applied at the base of the rod.### Interactive Question:##### Part A:**Determine the smallest angle \( \theta \) for

Stiffness, k = 60 N/ m Mass of rod = 10.5 Kg

The 10.5-kg uniform rod is pinned at end A. It is also subjected to a couple moment of 50 Nm. The spring is unstretched when = 0, and has a stiffness of k = 60 N/m. (Figure 1) Figure k = 60 N/m -0.5 m B 2 m 50 Nm < 1 of 1 Part A Determine the smallest angle for equilibrium. Express your answer in degrees to three significant figures. 0= Submit VE ΑΣΦvec 1 Provide Feedback Request Answer ?

The 10.5-kg uniform rod is pinned at end A. It is also subjected to a couple moment of 50 Nm. The spring is unstretched when = 0, and has a stiffness of k = 60 N/m. (Figure 1) Figure k = 60 N/m -0.5 m B 2 m 50 Nm < 1 of 1 Part A Determine the smallest angle for equilibrium. Express your answer in degrees to three significant figures. 0= Submit VE ΑΣΦvec 1 Provide Feedback Request Answer ?

Structural Analysis

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ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Mechanics of Solids

It is the study of the behavior of solid materials, their characteristics under various circumstances such as variation in external forces, temperature, and other internal factors. It is one of most important study in the field of engineering science, especially chemistry and mechanical engineering. In rigid body, the idealization of the solid body in which deformation is neglected. Deformation is known as the force acting on the solid state system which exerts change in its shape of the body but it continues to be at rest or in a uniform motion but it cannot accelerate. But those solid systems do have elasticity, compressibility and can be bent. This field is very vast since there are wide range of materials around us.

Question

### Equilibrium of a Uniform Rod with Spring System

#### Problem Statement:

A 10.5-kg uniform rod is attached to a pivot at end \( A \). It is subjected to a couple moment of \( 50 \, \text{N} \cdot \text{m} \). The spring connected to the rod is unstretched when the angle \( \theta = 0 \), and it has a stiffness constant \( k = 60 \, \text{N/m} \).

**Determine the smallest angle \( \theta \) for equilibrium.**

Express your answer in degrees to three significant figures.

#### Parameters:

- Mass of the rod: \( 10.5 \, \text{kg} \)
- Couple moment: \( 50 \, \text{N} \cdot \text{m} \)
- Spring stiffness: \( 60 \, \text{N/m} \)
- Spring is unstretched at \( \theta = 0 \)

#### Figure Description:
The accompanying figure shows the rod pinned at point \( A \) with a spring attached at point \( B \). In the diagram:
- The length from \( A \) to the point where the spring is attached is \( 2 \, \text{m} \).
- The spring has a stiffness constant \( k = 60 \, \text{N/m} \) and is not stretched when \( \theta = 0 \).
- The rod forms an angle \( \theta \) with the vertical.
- A couple moment of \( 50 \, \text{N} \cdot \text{m} \) is applied to the rod.

#### Graph/Diagram Explained:
The figure shows:

1. A vertical rod \( AB \) with a pivot at point \( A \).
2. A spring attached at \( B \), which lies horizontally in the unstretched position when \( \theta = 0 \).
3. The length \( AB \) is \( 2 \) meters.
4. A measurement indicating that the spring is \( 0.5 \) meters above the pivot when \( \theta = 0 \).
5. A couple moment of \( 50 \, \text{N} \cdot \text{m} \) applied at the base of the rod.

### Interactive Question:

##### Part A:
**Determine the smallest angle \( \theta \) for

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