Concurrent Forces:

If a number of coplanar concurrent forces are working on a body then there may exist a single resultant force passing through the point of intersection of all the concurrent forces. However there shall not presents any couple. The resultant force can have two components say R_x and R_y where x and y are any two mutually perpendicular co-ordinate axes. If the body is to be at rest then you should get both these components equal to zero. The circumstances for equilibrium in case of coplanar concurrent forces are, hence, as follows:

              R_x = 0

              R_y = 0

But

              R_x = ∑ F_x and R_y = ∑ F_y

Thus,

∴ ∑ F_x = 0      and        ∑ F_y = 0

1. The algebraic sum of the resolved parts of all of forces in any direction must be equal to zero.

2. The algebraic sum of the resolved parts of all of the forces in a direction at right angles of the first direction should be equal to zero.