Forces acting on a object can be approximated as vectors with a magnitude and direction. When there are unknowns in the system, the equations of equilibrium can be used to find those unknowns.

Recall in the previous section, the equation for equilibrium is

     ΣF = 0

This equation can be expanded for each direction (only x- and y-direction is examined in this section, the next section includes the z-direction)

     ΣF = ΣF_xi + ΣF_yj = 0

For the expanded equation, each direction must be in equilibrium, or

     ΣF_x = 0
     ΣF_y = 0

This means that when an object is in equilibrium, the components of forces acting along the arbitrary coordinate system will cancel each other out. These relationships can be used to determine the unknown forces using simple algebra.

A pulley redirects the force of ropes and cables. If no mass is given for the pulley (mass-less pulley), then the tension forces in a rope will be the same on either side of the pulley.