Resolving Triangle/Polygon of Forces, Resultant/Equilibrant

Resolving Triangle/Polygon of Forces

Basics

A force is a push or pull experienced by an object due to an interaction with another.
Vector quantities represent quantities possessing both magnitude and direction, and forces are vector quantities.
The practice of resolving forces is often referred to as vector resolution, which is the process of finding two vectors that add up to a given vector.
A triangle of forces or a polygon of forces is a graphical method to find the resultant of several forces acting at a single point.

Triangle of Forces

The triangle of forces relates to when three forces acting on a point can be represented by the three sides of a triangle taken in order.
Parallelogram law of forces is used to resolve two forces acting at a point into two components - the magnitude of the resultant force and the angle it makes with one of the forces.

Polygon of Forces

A polygon of forces relates to the case when multiple forces act on a point and can be represented with a closed polygon, where each side represents one force.
The forces are in equilibrium if the resultant of the vector sum of all forces is zero. This condition is satisfied when the polygon of forces forms a closed shape.

Resultant Force

The Resultant Force is the single force that has the same effect as all the forces acting together.
The resultant force can be calculated by vector addition of all forces acting on the body.

Equilibrant Force

The Equilibrant Force is an opposing force applied to maintain equilibrium, that is equal in magnitude but opposite in direction to the resultant force.

Applications in Engineering and Structural Design

Real-world structures such as bridges and buildings are subject to multiple forces such as wind force, gravitational force etc. The principles of triangle/polygon of forces and resultant/equilibrant forces offer methods to resolve these forces for safe design.
Understanding of these concepts is also vital in areas like fluid mechanics where forces exerted by fluid on an object must be resolved for the analysis of fluid motion and forces.

Problem Solving and Calculations

In order to calculate forces using these principles, trigonometry, specifically sine and cosine laws, are generally used.
It is crucial to carefully draw scaled vector diagrams to visualise the problem and resolve force vectors accurately.

These points will assist in understanding the concepts of “Resolving Triangle/Polygon of Forces, Resultant/Equilibrant”.