# Equilibrium of Concurrent Forces

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Updated on: September 25th, 2023

We must first understand equilibrium before going into the specifics of equilibrium of Concurrent Forces. A force has a magnitude and a direction because it is a vector quantity. If the magnitude and direction of the forces acting on an object are precisely balanced, there is no net force applied, and it is regarded as being in equilibrium.

Herve Langevin created the term Equilibrium of Concurrent Forces (ECF). It first occurs in Langevin’s 1911 article, “Applications des équations de la dynamique statistique,” where it is described as a concept that generalises the concept of force. According to the theory, forces are a system’s tendency to alter its route of least effort so that its motion is continuous rather than a series of leaps. Let’s dive further into the concepts regarding the equilibrium of concurrent forces.

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## What is Equilibrium of Concurrent Forces?

A body is said to be in equilibrium when all its forces are balanced (canceled out), and no net force is operating on it. The concept of equilibrium is essential to understand. When a body experiences a net resultant force of zero, it likewise experiences a net acceleration of zero (from the second law of motion).

Concurrent forces are those that intersect at a single point. When dealing with concurrent forces, we can add them as vectors to get the net resultant. It’s important to remember that acceleration is zero when a body is at equilibrium. This is one of the Equilibrium criteria for concurrent forces.

## Types of Equilibrium of Concurrent Forces

There are two main categories of concurrent force equilibrium. These include dynamic equilibrium and static equilibrium. The state of the body is such that all resulting forces equal zero when it is in static equilibrium. There is no acceleration and no velocity. The net force in dynamic equilibrium is zero, although velocity is not.

### Static Equilibrium

This type of equilibrium occurs when the sum of all forces acting on the body is zero, meaning that the body’s velocity and net acceleration are zero. It denotes the body’s state of rest. In other words, if a body is at rest and its net acceleration is zero, it is in static equilibrium.

For Example, Let’s say a block is lying on a floor and is being acted upon by two forces, each of which is 5 N in magnitude. The forces would balance one another out, leaving the block with no net force. It will be in static equilibrium because the block is at rest.

### Dynamic Equilibrium

This type of equilibrium occurs when the sum of all forces acting on the body is zero, meaning that the body’s net acceleration is zero, but its velocity is not. It indicates that the body is moving continuously. The body is considered in dynamic equilibrium if the net force exerted on it is zero, and it is still traveling at a constant speed.

For example, Dynamic equilibrium is sometimes demonstrated with a block linked to a spring and moving under the influence of Simple Harmonic Motion (S.H.M.). The block is in dynamic equilibrium at the mean position since there is no net force acting on it, yet the block’s velocity is at its maximum.

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## Coplanar Forces

Forces acting in the same plane are referred to as coplanar forces. Coplanar forces may also be in equilibrium in certain circumstances.

•  For forces to be deemed coplanar, the sum of all forces must equal zero.
•  The total sum of moments of forces at a particular instance on the clockwise route equals the sum of moments of forces at the same location on the anticlockwise route.

It is critical to note that many different coplanar forces exist. The forces in one plane must intersect at a single location for concurrent coplanar forces of equilibrium to exist. Both algebraic and graphical methods can be used to calculate it. Two other varieties of coplanar force are parallel and non-concurrent. The force vectors of a coplanar system that are non-concurrent do not have to be parallel or even intersect at any point. Forces that act in parallel on an entity are known as parallel coplanar forces.

## Conditions of Static Equilibrium of Concurrent Forces

An object is considered to be in an equilibrium condition when all of the forces acting on it are in balance. If the upward forces are equal to the downward forces and the rightward forces are equal to the left, then the forces are said to be balanced. However, this does not imply that all the forces are equal. The conditions of static equilibrium of concurrent forces are as follows:

• The sum of all forces in the y-direction, or vertical, is zero. ΣFy=0 or ΣFV=0
• The sum of all forces is zero in the horizontal or x-direction. ΣFx=0 or ΣFH=0

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## Important Points About Equilibrium of Concurrent Forces

• Equilibrium is a state of two equal forces acting in opposite directions.
• The vectors do not intersect at a point where non-concurrent coplanar forces can act since they are not parallel to one another.
• three concurrent forces of the same magnitude are in equilibrium.
• When a body is subjected to a single force, equilibrium cannot be reached.
• A close polygon results from the head-to-tail coupling of three or more equilibrium forces.

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