Draw forces of polygon:

Let five forces each of 80 N working at point O of a body. Draw forces of polygon & show the resultant of all the forces.

 Solution

Let us build a polygon such that the forces, A¯ ,B¯ ,C¯ ,D¯ and E¯ represent the sides of a polygon taken in order, each force being drawn from the end of earlier force then their resultant is represented by the line joining the starting point of the first force A¯ to the end of the last force E¯ .

Resolution

In several engineering problems, this is desirable to resolve a force into rectangular components. This procedure of splitting the force into components is called as the resolution of a force. The resolution of forces also helps in finding the resultant of a number of forces working on a body as it decrease vectorial addition to algebraic addition.

A force F¯ making an angle θ with respect to x axis as illustrated in Figure may be resolved into two components F_x and F_y working along x and y axes, respectively. If i¯ and j¯ are the unit vectors acting respectively along x and y axes, then the force F may be expressed as

F¯ = F_x  i ¯+ F _y   j¯

Where F_x and F_y are the magnitudes of the components along with x and y axes. With reference to Figure, F_x and F_y are find out as

F_x = F cos θ

F_y = F sin θ       and tan θ = F_x/ F_y

Note : θ is measured in anticlockwise direction w.r.t.  positive x axis. The magnitude of the force may also be expressed as: