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}.]