Picture of figure goes with this question **Problem 6:**Write the necessary equations of equilibrium of the object shown in Figure P8.6. Take the origin of the torque equation about an axis perpendicular to the page through the point O.**Explanation:**In this problem, you are asked to write the equations of equilibrium for an object. Equilibrium conditions typically involve ensuring that the sum of all forces and the sum of all torques (moments) acting on an object are zero. This ensures the object is at rest or in uniform motion. You need to reference Figure P8.6 for specifics about the forces and geometry of the object.**Steps:**1. **Identify Forces:** Determine all forces acting on the object, such as gravitational forces, normal forces, applied forces, etc.2. **Sum of Forces:** Write equations ensuring the sum of forces in both the x and y directions are zero. \[ \sum F_x = 0 \] \[ \sum F_y = 0 \]3. **Sum of Torques:** Write the torque equation about the specified axis through point O. Ensure the sum of torques is zero. \[ \sum \tau = 0 \]These equations should use relevant force vectors and distances (lever arms) based on the information provided in the figure. Use point O as the pivot for calculating torques. The image depicts a force diagram for a rigid bar. Here's a detailed explanation:- The diagram shows a bar connected at a pivot point labeled \( O \).- The bar has a length labeled \( \ell \) and is positioned at an angle \( \theta \) from the horizontal axis.- A force \( \vec{F}_g \) is acting vertically downward at the center of the bar, representing the gravitational force (weight).- The pivot point \( O \) experiences a reaction force decomposed into two components: - \( R_x \), acting horizontally to the right. - \( R_y \), acting vertically upwards.- At the other end of the bar, there are external forces \( \vec{F}_x \) and \( \vec{F}_y \) acting horizontally to the right and vertically upwards, respectively.- The diagram highlights the equilibrium and force interactions on the bar, demonstrating concepts in mechanics, such as force balance and torque.

Given: A force system is given in which point 'O' is the origin,To make this object in equilibrium,we have 3 equilibrium equation,∑ Fx=0∑ Fy=0 ∑ Mo=0 ∑ Fx=0Fx-Rx=0∑ Fy=0Fy+Ry-Fg=0∑ Mo=0Clockwise moment is positivecounterclockwise moment is negative,FxAO'+FgOO''-FyOO'=0Fx(l sinθ)+Fg(l2 cosθ)-Fy(l cosθ)=0

Answered: S Write the necessary equations of…

Engineering

Mechanical Engineering

S Write the necessary equations of equilibrium of the object shown in Figure P8.6. Take the origin of the torque equation about an axis perpendicular to the page through the point 0.

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

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

Question

Picture of figure goes with this question

**Problem 6:**

Write the necessary equations of equilibrium of the object shown in Figure P8.6. Take the origin of the torque equation about an axis perpendicular to the page through the point O.

**Explanation:**

In this problem, you are asked to write the equations of equilibrium for an object. Equilibrium conditions typically involve ensuring that the sum of all forces and the sum of all torques (moments) acting on an object are zero. This ensures the object is at rest or in uniform motion. You need to reference Figure P8.6 for specifics about the forces and geometry of the object.

**Steps:**

1. **Identify Forces:** Determine all forces acting on the object, such as gravitational forces, normal forces, applied forces, etc.

2. **Sum of Forces:** Write equations ensuring the sum of forces in both the x and y directions are zero.

\[
\sum F_x = 0
\]
\[
\sum F_y = 0
\]

3. **Sum of Torques:** Write the torque equation about the specified axis through point O. Ensure the sum of torques is zero.

\[
\sum \tau = 0
\]

These equations should use relevant force vectors and distances (lever arms) based on the information provided in the figure. Use point O as the pivot for calculating torques.

The image depicts a force diagram for a rigid bar. Here's a detailed explanation:

- The diagram shows a bar connected at a pivot point labeled \( O \).
- The bar has a length labeled \( \ell \) and is positioned at an angle \( \theta \) from the horizontal axis.
- A force \( \vec{F}_g \) is acting vertically downward at the center of the bar, representing the gravitational force (weight).
- The pivot point \( O \) experiences a reaction force decomposed into two components:
- \( R_x \), acting horizontally to the right.
- \( R_y \), acting vertically upwards.
- At the other end of the bar, there are external forces \( \vec{F}_x \) and \( \vec{F}_y \) acting horizontally to the right and vertically upwards, respectively.
- The diagram highlights the equilibrium and force interactions on the bar, demonstrating concepts in mechanics, such as force balance and torque.

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