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

Learn the principles of equilibrium for particles in 2D cases, understanding equilibrium resultant force and vector forms. Explore scalar equations, general conclusions, and how to tackle statically underdetermined problems with supplementary equations.

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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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