A Christmas decoration is suspended by two wires. Two equal tension forces in the wires each act at 110° to the weight force. Sketch a force diagram and the associated triangle of forces. Three forces, with magnitude 8, 11 and 15 N, are in equilibrium. What are the angles between them?

A Christmas decoration is suspended by two wires. Two equal tension forces in the wires each act at 110° to the weight force. Sketch a force diagram and the associated triangle of forces. Three forces, with magnitude 8, 11 and 15 N, are in equilibrium. What are the angles between them?

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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Question

### Equilibrium of Forces: Practical Examples

#### Example 1: Suspended Christmas Decoration
*A Christmas decoration is suspended by two wires. Two equal tension forces in the wires each act at 110 degrees to the weight force. Sketch a force diagram and the associated triangle of forces.*

In this example, a Christmas decoration is hanging from the ceiling by two wires. Each wire exerts an equal tension force, creating an angle of 110 degrees with the direction of the weight force of the decoration. The task involves sketching a force diagram that clearly illustrates these forces and forming the corresponding triangle of forces to analyze the situation.

#### Example 2: Forces in Equilibrium
*Three forces, with magnitudes 8 N, 11 N, and 15 N, are in equilibrium. What are the angles between them?*

This scenario involves three forces in a state of equilibrium, which means they perfectly balance each other out. The challenge is to determine the angles between these forces given their magnitudes of 8 N, 11 N, and 15 N. By applying principles of vector addition and geometric analysis, one can find the angles that result in equilibrium.

#### Force Diagrams and Triangles
For both examples, drawing detailed diagrams will aid in understanding the vector relationships and solving for unknown angles. Force diagrams represent vectors as arrows pointing in the direction of the force, while triangles of forces are geometric representations that help visualize how these vectors interact when in equilibrium.

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