Composition & Resolution of Forces

Composition and Resolution of Forces
1. Composition of Forces
Definition:
The composition of forces is the process of finding a single force (called the resultant) that can replace two or more forces acting on a body and produce the same effect as all those forces together.
2. Resultant Force
The resultant force (R) is the single force that represents the vector sum of all the given forces.
(a) When two forces act at an angle (θ):
R=√(F_1^2+F_2^2+2F_1 F_2 cos⁡θ)

and the direction (angle α with F₁) is given by:
tan⁡α=(F_2 sin⁡θ)/(F_1+F_2 cos⁡θ)

(b) When two forces act in the same line and direction:
R=F_1+F_2

(c) When two forces act in the same line but opposite direction:
R=∣F_1-F_2∣


3. Resolution of Forces
Definition:
The resolution of a force is the process of splitting a single force into two or more components, which together produce the same effect as the original force.
In simple terms —
Breaking one force into two or more parts (usually perpendicular).

4. Rectangular Components
If a force F makes an angle θ with the horizontal axis:
Horizontal component: F_x=Fcos⁡θ
Vertical component: F_y=Fsin⁡θ
Then,
F=√(F_x^2+F_y^2 )

and
tan⁡θ=F_y/F_x