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

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.Â

### Composition and resolution of forcesÂ

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.Â

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

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

### 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.Â

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

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.Â

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.Â

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

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.Â

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.Â

### Resolution of forcesÂ

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.Â

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

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

Now, there will be two components of this force F i.e. Fx and Fy and their value will be as mentioned here.Â
Fx = F cos Î¸Â
Fy = F Sin Î¸Â
Tan Î¸ = Fx/FyÂ
Magnitude of the force, F = Square root of {Fx2 + Fy2}Â

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

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

### Reference:Â Â

Engineering Mechanics, By Prof K. RameshÂ

Governing of impulse turbine or Pelton turbine