EXPLAIN COMPOSITION AND RESOLUTION OF FORCES

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force system, principle of transmissibility of forces and its limitations and classification of force system in mechanics. 

As we have the basic information about the force system and its principle after reading the previous post. Now, we will be interested to understand here the composition and resolution of forces in mechanics with the help of this post. 

Composition and resolution of forces 

Composition and resolution of forces are very important tools in engineering mechanics to solve the problems where multiple forces are acting. Depending on the types of problem, we will apply the basics of composition and resolution of forces. 

Further, composition and resolution of forces will be used in various engineering mechanics problems. Therefore, we need to understand the both tools. 

First we will see here the composition of forces and after that we will find out the basics of resolution of forces. 

Composition of forces

Composition is basically defined as the process of reducing a force system to an equivalent and simplest force system, which will have the same external effect on the body as the original force system. 

Composition of forces are based on the principle of transmissibility of forces and law of parallelogram for vector addition. 

Let us consider the following case where two forces i.e. F₁ and F₂ are acting on the body as displayed here in following figure. Line of actions of these two forces are meeting with each other at point P. 

In order to determine the resultant of these two forces, we will use the principle of transmissibility of forces and law of parallelogram for vector addition. 

Let us first recall the principle of transmissibility of forces and move the forces F₁ and F₂ as displayed here in following figure. 

Now we will use the law of parallelogram for vector addition and the resultant of these two forces will be R as displayed here in following figure. 

We must note it here that the resultant R of these two forces i.e. F₁ and F₂ will have the same external effect on the body as that of the original forces F₁ and F₂. 

Resolution of forces 

Resolution of forces is basically defined as the process of determining two components of a force which will have the same external effect on the body as the force itself. 

Resolution of forces could be seen as the opposite of composition of forces. 

Let us consider the following case where a force F is acting on the body and its angle is θ. 

Now, there will be two components of this force F i.e. F_x and F_y and their value will be as mentioned here. 

F_x = F cos θ 

F_y = F Sin θ 

Tan θ = F_x/F_y 

Magnitude of the force, F = Square root of {Fx² + F_y²} 

Therefore, we have seen here the composition of forces and resolution of forces with the help of this post. 

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Further we will find out, in our next post, body forces and surface forces, in engineering mechanics. 

Reference:  

Engineering Mechanics, By Prof K. Ramesh 

Image courtesy: Google 

Also read 

Fundamental of Pelton wheel or Pelton hydraulic turbine 

Basics of radial flow reaction turbines 
Difference between inward radial flow reaction turbine and outward radial flow reaction turbine 
Francis turbine 
Axial flow reaction turbine 
Specific speed of turbine 
Draft-tube 
Governing of turbines 
Governing of impulse turbine or Pelton turbine