ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases) Equilibrium Equations: Equilibrium Resultant force For ANY given direction Vector form For a Cartesian System given 2D Case Total projection in ANY given direction is zero 1D Case Scalar form

ES2501: Statics/Unit 6-2: Equilibrium of Particles (2D cases) General Conclusions: For each particle there is ONE vector equilibrium equation, which is equivalent to THREE scalar equations for 3D problems, TWO scalar equations for 2D problems, and ONE scalar equations for 1D problems. If there are more unknowns than the number of scalar equilibrium equations it is a STATICALLY UNDERMINATED problem, for which some supplementary equations are needed for solution If two forces are in equilibrium, they are collinear; If three forces are in equilibrium, they are coplanar If three forces are in equilibrium For three forces ONLY Equivalent but more convenient

ES2501: Statics/Unit 6-3: Equilibrium of Particles (2D cases) Example 1: Find tensions of cables Note: Sign convention Step 1: Free-Body Diagram Step 2: List Eqs FBD of point C Action and reaction Staticaly determinant vs statically underminant problems FBD of block Step 3: Solution three eqs for three unknowns Alternative Solution:

ES2501: Statics/Unit 6-4: Equilibrium of Particles (2D cases) Example 2: Find the friction between block A and the slope And tension in the cable Step 1: Free-Body Diagram FBD of A Step 2: List Eqs FBD of A three eqs for three unknowns Direction of friction is uncertain depending on tendancy of motion Upwards or downwards Step 3: Solution