F_{1}F_{2}F_{3}0'F 0'F_{X}0'F_{Y}0'F_{Z}0Application of Newton's LawsFORCE EQUILIBRIUMRev. 0Page 13CP-04Figure 6 Hanging ObjectThe first condition of equilibrium, a consequence of Newton's first law, may be written invector form, "A body will be in translational equilibrium if and only if the vector sum of forcesexerted on a body by the environment equals zero."For example, if three forces act on a body it is necessary for the following to be true for thebody to be in equilibrium.(4-3)This equation may also be written as follows.(4-4)This sum includes all forces exerted on the body by its environment. The vanishing of thisvector sum is a necessary condition, called the first condition of equilibrium, that must besatisfied in order to ensure translational equilibrium. In three dimensions (x,y,z), the componentequations of the first condition of equilibrium are:(4-5)This condition applies to objects in motion with constant velocity and to bodies at rest or instatic equilibrium (referred to as STATICS).Applying the knowledge that an object in equilibrium has a net force equal to zero, thefollowing example can be solved:Example:The object in Figure 6 has aweight of 125 lbf. The objectis suspended by cables asshown. Calculate the tension(T ) in the cable at 30- with1the horizontal.