**Problem Statement:**A solid cylindrical shaft anchored to the wall at point O is subjected to 70 N and 85 N couples and a concentrated moment at point E. Determine the resultant couple moment. **Solution Approaches:**1. **Scalar Approach:** - Evaluate the individual moments of the x, y, and z components of the 70 N and 85 N forces. - Take positive moments in the positive coordinate directions according to the right-hand rule.2. **Vector Approach:** - Utilize 3D position vectors using the general cross product definition for the force moment.**Diagram Explanation:**- The figure shows a cylindrical shaft anchored at point O.- A 70 N force is applied at two points: one at point A directed along the positive z-axis and another at point B angled in the yz-plane.- The angles are specified using coordinate direction angles for the force vectors.- An 85 N force is applied at two points: one at point C angled in the yz-plane and another at point D.- A concentrated moment of 200 Nm is applied at point E along the x-axis.- Dimensions and directions provided for each force help in calculating the moments around the various axes using either approach described.

Resultant couple moment is -42i + 120 j + 80k

A solid cylindrical shaft anchored to the wall at point O is subjected to 70 N and 85 N couples and a concentrated moment at point E. Determine the resultant couple moment. Hint: You can do this in either of two ways by applying (1) a "scalar" approach by evaluating the individual moments of the x, y, and z components of the 70N and 85N forces, taking positive moments to be in the positive coordinate directions according to the right-hand rule., or (2) the "vector approach" utilizing 3D position vectors using the general cross product definition for the force moment.

A solid cylindrical shaft anchored to the wall at point O is subjected to 70 N and 85 N couples and a concentrated moment at point E. Determine the resultant couple moment. Hint: You can do this in either of two ways by applying (1) a "scalar" approach by evaluating the individual moments of the x, y, and z components of the 70N and 85N forces, taking positive moments to be in the positive coordinate directions according to the right-hand rule., or (2) the "vector approach" utilizing 3D position vectors using the general cross product definition for the force moment.

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

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

**Problem Statement:**

A solid cylindrical shaft anchored to the wall at point O is subjected to 70 N and 85 N couples and a concentrated moment at point E. Determine the resultant couple moment.

**Solution Approaches:**

1. **Scalar Approach:**
- Evaluate the individual moments of the x, y, and z components of the 70 N and 85 N forces.
- Take positive moments in the positive coordinate directions according to the right-hand rule.

2. **Vector Approach:**
- Utilize 3D position vectors using the general cross product definition for the force moment.

**Diagram Explanation:**

- The figure shows a cylindrical shaft anchored at point O.
- A 70 N force is applied at two points: one at point A directed along the positive z-axis and another at point B angled in the yz-plane.
- The angles are specified using coordinate direction angles for the force vectors.
- An 85 N force is applied at two points: one at point C angled in the yz-plane and another at point D.
- A concentrated moment of 200 Nm is applied at point E along the x-axis.
- Dimensions and directions provided for each force help in calculating the moments around the various axes using either approach described.

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