Find out the horizontal and vertical components of the force:

A force of 120 N is exerted on a hook in the ceiling as illustrated in Figure. Find out the horizontal and vertical components of the force.

Solution

As θ is to be measured in anticlockwise direction from positive x axis, then clearly θ = 300^o.

F_x  = F cos θ = 120 cos 300^o  = + 60 N (that means along positive x-direction)

F_y  = F sin θ = 120 sin 300^o  = - 103.92 N (that means along negative y-direction)

Thus, the vector components of force F¯ are following,

F¯x  = (+ 60 N) i¯           and      F¯_y  = (-103.92 N) j¯

Thus, F¯ can be expressed as

F¯ = + 60 i ¯- 103.92 j¯

 [Note: One may also arrive at these results, through drawing the diagram, and visually, by inspection, fix the direction of the component forces - and working out cosine and sine for 60^o.]