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ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases)

Equilibrium Equations:. ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases). 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

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ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases)

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  1. Equilibrium Equations: ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases) 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

  2. General Conclusions: ES2501: Statics/Unit 6-2: Equilibrium of Particles (2D cases) • 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

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

  4. Example 2: Find the friction between block A and the slope And tension in the cable Step 1: Free-Body Diagram ES2501: Statics/Unit 6-4: Equilibrium of Particles (2D cases) 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

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