Equilibrium

An object is in equilibrium when all the forces acting on it are balanced. There is no resultant force, so the object stays at rest or moves with constant velocity: ΣF = 0.For forces acting in different directions, resolve each force into horizontal and vertical components. For equilibrium, the components in each direction must add up to zero: the total force to the left equals the total force to the right, and the total upward force equals the total downward force.For example, a weight W hanging from a washing line is held by tensions T₁ and T₂ at angles α and β to the horizontal. Resolving horizontally gives T₁cosα = T₂cosβ, and resolving vertically gives T₁sinα + T₂sinβ = W. These two equations can be solved for the two tensions.The flatter the line, the smaller the vertical components of the tensions, so the tensions must be larger to support the same weight. This is why a washing line can never be pulled perfectly straight when a load hangs from it.