## What are Force Systems?

When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.

When numerous amounts of forces are acting on a body simultaneously, they will form a system called force system. The line of action of forces may lie on single point or in a single plane, the force can also act in different plane of a 3 – dimensional object.

## Properties of Force

Force is a tension which changes or tries to change the direction of an object, state of an object. It also brings the body to rest, when body is travelling in a uniform motion. Force is an external agency, which can make the object to move or bring an object to rest. Force is normally calculated using Newton’s second law

The dimensional analysis of a force is $F=m×a=kg×m/{s}^{2}$. Force is always measured in N (NEWTON)

• Force is a vector quantity.
• Force has various names in various of its applications- it may rotate the body as rotational force, stop the body as equilibrium force, speed up the body or speed down the body as acceleration or deacceleration, the weight of body under gravity is also a type of potential force
• If two or more forces or couple join together to form an action of single force, it is termed as resultant force.
• If two forces are of equal in magnitude and actions in opposite direction, it is termed as equilibrant force.
• A force which always opposes the relative motion of other force is termed as friction force.
• If force is created in spring, it is spring force. If force created in a rope resultant is a tensile force.
• If a force reduces the area or volume of an object, the resultant force is termed as compressive force.

## Classification of Force System

The force system can be broadly classified into two types:

• Coplanar force system
• Non-coplanar force system

### Coplanar Force System

If numerous forces are acting on a body, if the entire forces act in a single plane then it is termed as coplanar force system.

### Non – coplanar force system

All the forces acting in a body will not act on a single plane, if each force act in a different system of plane then it is non – coplanar force system.

The above two system of forces can be sub classified into force component such as

• Concurrent force system
• Parallel force system
• Non- concurrent or general force system

### Concurrent Force System

When all the forces’ line of action passes through a single point it is concurrent. If line of all the forces passes through a single point and if all the forces lie in a same plane, it is termed as coplanar- concurrent force system.

If line of all the forces passes through a single point and if all the forces lie in a different plane, it is termed as non-coplanar- concurrent force system.

### Parallel Force System

If all the forces act in a system are parallel to each other then it is called as parallel force system.

Parallel forces can be sub-divided into two types

1. Like parallel forces
2. Unlike parallel forces
• If all the forces act in a same direction it is like parallel forces
• If all the forces act in different direction but parallel means unlike parallel forces.
• If it acts in a same plane, it is coplanar-parallel-like or unlike force system
• If it acts in a different plane, it is non-coplanar-parallel-like or unlike force system

### General Force System

If all the forces in the system is neither concurrent nor parallel it is termed as non-concurrent or non – parallel system of forces. The resultant of major engineering system falls under general force system.

## Principle of Superposition

In newtons mechanics, we can apply the concept of principle of superposition, for simplicity, calculation of resultant force by principle of superposition can be applied. All the forces can be simply added to get the resultant.

Imagine you are pushing a box with 50 N of force, by principle of superposition if the problem demands, you can change it as pulling the box with 50 N of force. It doesn’t affect the resultant force of the system. It helps in getting the resultant with simplicity.

## Composition of Forces

Multiple forces can be combined together to obtain a single force, which has the same effect as the original system of forces. This force is called the resultant. The process of finding the single force is known as composition of forces. Since force is a vector quantity, it can be joined together by just vector addition. Some of the methods are

• Parallelogram law of forces
• Triangular law of forces
• Method of resolution

### Parallelogram law of forces

If two forces start from a point simultaneously, their forces can be misplaced again as a adjacent side of a parallelogram by principle of superposition, the resultant will be the diagonal formed in the centre of the parallelogram, which passes through the two sides representing forces.

### Triangular law of forces

It is also same as parallelogram law of system, here to make it yet more simple, the two forces start from a single point and is replaced with one of the forces at opposite direction by principle of superposition. The two adjacent forces are joined with a resultant force line, which forms a triangle or half of parallelogram. The triangular law has been later simplified as Lami’s theorem.

### Method of resolution

If more than two forces act on a system, their actions can segregate as x components and y components, the process of breaking the force into number of components is called resolution of forces. The forces can also act in a system with angle of inclination, those forces can be resolved in both horizontal and vertical component directions. It can be resolved by taking the force has rectangular components in all four quadrants

Force also constitutes in a form of couple and moment, instead of force going in unidirectional direction, it rotates in its own axis forming a couple. The moment of force, creates a bending moment in a beam or object due to force stress acting in the object.

Calculation of various types of forces acting in a system such as friction, gravity, spring constant, body forces, moment and couples are summarized as force systems.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Science (Physics)
• Masters in Science (Physics)

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