Determine the horizontal component of the force:
A force of 80 N is working on a bolt as illustrated in Figure. Determine the horizontal and vertical components of the force.
Figure
Solution
Through the principle of transmissibility of a force, any force may be considered to be working at any other point on the line of action of the force.
∴ θ = 60^{o }+ 180^{o} = 240^{o}
w.r.t. positive x axis measured in anticlockwise direction
∴ F_{x} = F cos θ = 80 cos 240^{o} = - 40 N
(or, F_{x} = 80 cos 60^{o} = 40 N along with the negative x-direction, as is clear by visual inspection).
F_{y} = F sin θ = 80 sin 240^{o} = - 69.28 N
∴ F¯ = (- 40 N) i¯ + (- 69.28 N) j¯
= - 40 i¯ - 69.28 j¯