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 P_{1}, P_{2}, P_{3}, P_{4}, and P_{5} acting at 'o'. Let OX and OY be the two perpendicular directions. Let the forces subtend angle a_{1}, a_{2}, a_{3}, a_{4}, and a_{5} 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 P_{1}, P_{2}, P_{3}, P_{4}, P_{5} along OX.
That is
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