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Definition of Equilibrium:
Equilibrium is the condition in which all the individual forces acting upon an object are balanced.
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If an object is at equilibrium, then the individual forces acting upon the object are balanced. There is no unbalanced force - the net force is 0 Newton. All the vertical forces balance and all the horizontal forces balance. When added as vectors, they must add to 0 N. There are two cables directed at angles to the horizontal and vertical axes. These cables exert tension forces on the sign and have horizontal and vertical components. The only other force acting on the sign is the force of gravity. The two vertical components of tension must act together to balance the force of gravity. The horizontal components of the tension force are the only horizontal forces and must balance each other.
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Some students have the improper habit of thinking that an object at equilibrium is an object upon which all forces are equal. After all, the word equilibrium sounds like the word equal. But don't be fooled! Equilibrium has to do with a balance of forces. While it is possible that all the forces might be equal, they don't have to be equal to be balanced. For instance, an object with an up force of 20 N and a down force of 20 N and a right force of 8 N and a left force of 8 N is at equilibrium. Are all the forces balanced? Yes! Are all the forces equal? No! The 20 N is not equal to the 8 N.
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