### Problem Description**Text:**The 9-kg uniform rod is pinned at point \( A \). It is also subjected to a couple moment of \( 50 \, \text{N} \cdot \text{m} \). The spring is unstretched when \(\theta = 0\), and has a stiffness of \( k = 60 \, \text{N}/\text{m} \). (Figure 1)**Task:**Determine the smallest angle \(\theta\) for equilibrium. Express your answer in degrees to three significant figures.### Figure DescriptionIn Figure 1, we have a system consisting of the following elements:- **Rod \( AB \)**: - A 9-kg uniform rod is pinned at point \( A \). - Point \( B \) is located at the top end of the rod. - The length from point \( A \) to point \( B \) is 2 meters.- **Pin at Point \( A \)**: - The rod is hinged at point \( A \), allowing rotation around this point.- **Couple Moment**: - There is a constant couple moment of \( 50 \, \text{N} \cdot \text{m} \) applied at point \( A \).- **Spring**: - A spring with a stiffness constant \( k = 60 \, \text{N}/\text{m} \). - The spring is attached horizontally from a fixed support to point \( B \). - When the angle \( \theta = 0 \), the spring is unstretched. - **Angle \( \theta \)**: - \( \theta \) is the angle made by the rod \( AB \) with the vertical. - The rod makes this angle \( \theta \) with the vertical as shown.**Diagram Details**:- The vertical distance from the hinge point \( A \) to the line where the spring is connected is given as \( 0.5 \, \text{m} \).- The rod makes an angle \( \theta \) with the vertical axis.- The spring is horizontally attached to the top end \( B \) of the rod.### InstructionsTo solve the problem, you need to determine the smallest angle \(\theta\) that allows for equilibrium. Ensure your answer is given in

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The 9-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 = 0, and has a stiffness of k = 60 N/m. (Figure 1) Figure k = 60 N/m -0.5 m 0 B HA 2 m 50 N·m 1 of 1 Determine the smallest angle for equilibrium. Express your answer in degrees to three significant figures. A= 15| ΑΣΦ ↓↑ vec 1 Submit Provide Feedback Request Answer ? 0

The 9-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 = 0, and has a stiffness of k = 60 N/m. (Figure 1) Figure k = 60 N/m -0.5 m 0 B HA 2 m 50 N·m 1 of 1 Determine the smallest angle for equilibrium. Express your answer in degrees to three significant figures. A= 15| ΑΣΦ ↓↑ vec 1 Submit Provide Feedback Request Answer ? 0

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter8: Engineering Materials

Section: Chapter Questions

Problem 85CQ

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Concept explainers

Laws of Equilibrium

A body is said to be in equilibrium if the system of forces acting on the body tends to keep the body at rest, in other words, there is no translation motion or net torque on the body. Under such conditions, the equilibrium conditions are to be applied to analyze the condition. The branch of mechanics that deals with this condition is known as 'statics'. Under equilibrium, there are no net forces on the body.

Question

### Problem Description

**Text:**
The 9-kg uniform rod is pinned at point \( A \). It is also subjected to a couple moment of \( 50 \, \text{N} \cdot \text{m} \). The spring is unstretched when \(\theta = 0\), and has a stiffness of \( k = 60 \, \text{N}/\text{m} \). (Figure 1)

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

Express your answer in degrees to three significant figures.

### Figure Description

In Figure 1, we have a system consisting of the following elements:

- **Rod \( AB \)**:
- A 9-kg uniform rod is pinned at point \( A \).
- Point \( B \) is located at the top end of the rod.
- The length from point \( A \) to point \( B \) is 2 meters.

- **Pin at Point \( A \)**:
- The rod is hinged at point \( A \), allowing rotation around this point.

- **Couple Moment**:
- There is a constant couple moment of \( 50 \, \text{N} \cdot \text{m} \) applied at point \( A \).

- **Spring**:
- A spring with a stiffness constant \( k = 60 \, \text{N}/\text{m} \).
- The spring is attached horizontally from a fixed support to point \( B \).
- When the angle \( \theta = 0 \), the spring is unstretched.

- **Angle \( \theta \)**:
- \( \theta \) is the angle made by the rod \( AB \) with the vertical.
- The rod makes this angle \( \theta \) with the vertical as shown.

**Diagram Details**:

- The vertical distance from the hinge point \( A \) to the line where the spring is connected is given as \( 0.5 \, \text{m} \).
- The rod makes an angle \( \theta \) with the vertical axis.
- The spring is horizontally attached to the top end \( B \) of the rod.

### Instructions

To solve the problem, you need to determine the smallest angle \(\theta\) that allows for equilibrium. Ensure your answer is given in

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