Resultant of coplanar concurrent force system:
The resultant force, of given system of forces can be found out by the resolution method, which is discussed below:
Assume the forces be P1, P2, P3, P4, and P5 acting at 'o'. Let OX and OY be the two perpendicular directions. Let the forces subtend angle a1, a2, a3, a4, and a5 with Ox respectively. Let R be the resultant and inclined at the angle with OX.
Resolved part of 'R' along OX = Sum of the resolved parts of P1, P2, P3, P4, P5 along OX.
Resolve all the forces horizontally and find algebraic sum of all horizontal components
(which is ∑H)
Resolve all the forces in vertical direction and find the algebraic sum of all the vertical components (that is, ∑V)
The resultant R of given forces can be given by equation:
And the resultant force will be inclined at the angle 'θ' with the horizontal, so that
tanθ = ∑V/∑H