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¯