Composition and Resolution of Forces

Resultant Force

A resultant force is the force which can replace two or more forces and produce the same effect on the body as the forces.

Principle of  resolved parts

The sum of resolved parts of two forces acting at a point in any given direction is equal to the resolved parts of their resultant in that direction. 

Composition of Forces 

It is a process to replaces number of forces acting on a body by a single force, without changing net effect acting on a body.

Example - Resultant force  

Laws of Forces

the various laws are used for the composition of forces are as follows

1. Parallelogram law of forces. 
2. Triangle law of Forces.
3. Polygon law of forces

Parallelogram law of forces-

    

      "If two forces acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent sides of a parallelogram then their resultant may be the diagonal of the parallelogram which passes through their point of intersection." 

FIGURE 1 

Two Concurrent force P and Q are acting along the two sides of Parallelogram, R is the resultant of the parallelogram.

Equation 1 and equation 2 shows a relation to find the value of resultant and direction of resultant respectively.

Triangle law of forces-

    "If the forces acting simultaneously on a body are represented in magnitude and direction by the two sides of triangle taken in order then their resultant  may be represented in magnitude and direction by third side taken in opposite order."

Polygon law of forces

      "If a number of coplanar concurrent forces, acting simultaneously on a body are represented in magnitude and direction by the sides of polygon taken in order then their resultant  may be represented in magnitude and direction by closing side of a polygon, taken in opposite order."