Composition And Resolution Of Forces | Engineering Mechanics

In engineering mechanics Composition And Resolution Of Forces have immense importance. So if  you want to understand this concept in easiest possible way and want to get good marks in Engineering Mechanics then you are at the right place.

1. Composition And Resolution Of Forces :–

1.1) Composition of forces:-

• It is also known as compounding.
• Composition is the process of find out single resultant force of a whole force system

But wait what is resultant?

Resultant:–
• it is basically the single force which can produce the same effect produced by number of forces when acting together.
• This one force which is producing the combined effect of all forces is known as .
• It is represented by “R”.
See the following image, you will get the whole concept about resultant and composition.

• Composition of two Perpendicular forces:-

• Composition of more than two forces:'

Here as shown in fig, there are 7 coplanar concurrent forces. So as we discussed earlier by using the method of composition of forces we can conpound these forces and find out one single force which is known as resultant as shown in fig.
So the single force shown in fig is the resultant of the 7 forces. Effect of both will remain same. 85.28° is the angle made by resultant with horizontal axis, we'll discuss this next how to calculate this angle and magnitude.

Watch our youtube video to get more information:-

1.1.1) Method Of Composition (To find “R”) 

A) Composition of perpendicular or orthogonal forces:-

When two or more coplanar concurrent or non-concurrent forces acting on a body then the resultant can determine by following procedure.

If F1 and F2 are the two forces which are perpendicular to each other as shown in fig,

Then resultant can be found out by following equation.

Read also:-

• System of forces 
• Engineering Mechanics

B) Composition by parallelogram law of forces:-

As per law of parallelogram “If two forces which are simultaneously acting at a point represented by in magnitude and direction by the two adjacent sides of a parallelogram, the diagonal of the parallelogram will represent the resultant in magnitude and direction, but passing through the point of intersection of two forces”.

Where,

             F₁ and F₂ = forces whose resultant is to be find out
             θ = Angle between the force F₁ and F₂
             α = angle made by the resultant with any force here force F₁ .
Cor,

Case 1) if θ=0 i.e. both forces acting along the same line then,
R=F₁+F₂ …………since cos(0)=1

Case 2) if θ=90º i.e. both forces are perpendicular to each other then,
R=√(F₁²+F₂²) …………since cos(90)=0

Case 3) if θ=180º i.e. both forces are acting along the same straight line but having opposite direction then,
R=F₁-F₂ …………since cos(180)=-1


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1.2) Resolution of forces:-

•It is exactly opposite to the composition.
•It is the process in which one single force (i.e. Resultant) is split into number of components without changing the effect of the same.
•Process of splitting is known as resolution.
•We can resolved or split a force into number of components but generally we resolve it into two perpendicular or non-perpendicular components.

See the following image you will understand easily what is resolution .

Here, resultant "R" is resolved into two Perpendicular components but we can resolve the force into number of forces as discussed earlier.

1.2.1)Method Of Resolution:-

Forces can be resolved by following two methods:-

A) Orthogonal or perpendicular resolution B) Non-Perpendicular resolution

Let us discuss each one in detail:

A)Orthogonal or perpendicular resolution:-

• In this method the resultant force is split into two Perpendicular components.
• These two Perpendicular components will be acting along X-axis and Y-axis or any two Perpendicular axis.

As shown in fig R may be any force which is inclined at an angle θ with X-axis. So by using this method we can easily resolved this force into two Perpendicular or orthogonal components as shown in fig.

• Rx= horizontal component of force R
• Ry= vertical component of force R

Now from where these Rcosθ  & Rsinθ came from. Let us discuss this

Now you understand how does a force can be resolved into perpendicular direction.

• Various conditions in resolution of forces:-

• Sign convention:-

1. Components which are acting along towards right hand side are considered as positive 

2. Components which are acting left hand side are considered as negative 

3. Components acting along vertical upward direction are considered as positive 

4. Components acting along vertical downward direction are considered as negative

5. As per the quadrant system following table will help you in determining the sign for 'sine' and 'cosine' 

B) Non-Perpendicular resolution:-

• In this method the resultant force is split into two directions which are not perpendicular co components.
Steps to resolve the resultant by Non-Perpendicular resolution method:-

Step 1) Construct a parellelogram by keeping original given resultant (R) along the diagonal and two components adjacent sides of the parallelogram which are passing through same point

Step 2) Now find out 3 angles of any one triangle

Step 3) Apply sine rule in that triangle.

• Important rule:-
While constructing the parallelogram the resultant force should be keep un between the two forces or components and all the three forces should be directed away from the joint.