If a system is in equilibrium under several coplanar concurrent forces

If a system is in equilibrium under several co-planar concurrent forces:

               i.        The forces on their free vectors must form a closed polygon

             ii.        To verify the condition of equilibrium

a)   SUM _x = 0    b)     SUM_y = 0 

Apparatus

Apparatus having pulleys and a board in the vertical plane, steel rule, protractor, weight with string hanger

Procedure

Apply the number of forces F₁, F_2, F_3, F_4, F₅ on the strings passing over the pulleys, line of action of all the forces are acting at a point, which is shown by string attached to a small ring. Note the angles of the forces and their directions.

Tabulate theses angles and forces. Draw vectors of these forces by their directions on any scale using head to tail rule.

Their free vectors must form a polygon by joining the point of vectors and the end of the last to the start of the first force.

Also if ∑ F_x = 0 and ∑ F_y = 0 then the conditions of equilibrium are met.

 Table of Observations

Sr no	Forces (N)	Angles (θ)	FX	FY	Remarks
1	F1	Ψ1	F1cos Ψ1	F1sin Ψ1
2	F2	Ψ2	F2 cos Ψ2	F2 sin Ψ2
3	F3	Ψ3	F3 cos Ψ3	F3 sin Ψ3
4	F4	Ψ4	F4 cos Ψ4	F4 sin Ψ4
5	F5	Ψ5	F5 cos Ψ5	F5 sin Ψ5
6	F6	Ψ6	F6 cos Ψ6	F6 sin Ψ6
7	F7	Ψ7	F7 cos Ψ7	F7 sin Ψ7
		Total = x = 0   y = 0