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ENGI 1313 Mechanics I

ENGI 1313 Mechanics I . Lecture 10: Particle Equilibrium, Free-Body Diagrams and Coplanar Forces. Chapter 3 Objectives. to introduce the concept of the free-body diagram for a particle. to show how to solve particle equilibrium problems using the equations of equilibrium.

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ENGI 1313 Mechanics I

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  1. ENGI 1313 Mechanics I Lecture 10: Particle Equilibrium, Free-Body Diagrams and Coplanar Forces

  2. Chapter 3 Objectives • to introduce the concept of the free-body diagram for a particle. • to show how to solve particle equilibrium problems using the equations of equilibrium

  3. Lecture 10 Objectives • to examine and apply Chapter 3 objectives in 2D space

  4. +Y V = 0, v F1 +X F3 F2 Particle Equilibrium • Newton’s 1st Law – Inertia • Particle equilibrium • Rest (Static) • Constant velocity  Scalar components = 0 2 Equations  Solve for at most 2 Unknowns

  5. Free-Body Diagram (FBD) • What is it? • Sketch or diagram illustrating all force vectors acting on a particle (body) • Purpose? • A visual aid in developing equilibrium equation of motion • What is the procedure? • Draw isolated or “free” outlined shape • Show all forces • Characterize each force • Magnitude • Sense • Direction

  6. +Y +X Example 10-01 • FBD Procedure • Draw isolated or “free” outlined shape • Show all forces • Characterize each force • Magnitude • Sense • Direction

  7. Comprehension Quiz 10-01 • Select the Correct FBD of Particle A • Answer: D Hibbeler (2007)

  8. Applications Hibbeler (2007)

  9. Example 10-01 • For the engine in staticequilibrium, using a free body diagram, solve for the force magnitudesFAD and FAB. The engine mass is 255 kg.

  10. Example 10-01 • Draw FBD +Y FAB A  = 30 FAD +X W = FAC = mg W = (255 kg)(9.806m/s2) = 2.5kN

  11. +Y FAB A  = 30 FAD +X W = FAC = 2.5kN Example 10-01 • State Equilibrium Equation

  12. Example 10-02 • The car is towed at a constant speed by the 600 lb force and the angle  is 25°. Find the forces in the ropes AB and AC.

  13. 600 lb A 25 30 FAC FAB Example 10-02 (cont.) • FBD at Point A 2 Equations 2 Unknowns

  14. 600 lb A 25 30 FAC FAB Example 10-03 (cont.) • Equilibrium at Point A • Rearrange • Substitute

  15. Example 10-03 • Find the forces in the cables and weight of sack B. • What point is first selected for the FBD?

  16. Example 10-03 (cont.) • Unknown force magnitudes at Point C •  FBD at Point E 2 Equations 2 Unknowns

  17. Example 10-03 (cont.) • Equilibrium at Point E • Rearrange • Substitute

  18. Example 10-03 (cont.) • FBD at Point E andPoint C

  19. Example 10-03 (cont.) • Equilibrium at Point C

  20. Homework Problem • Each cord can sustain a maximum tension of 200 lb. Determine the largest weight of the sack that can be supported. Also, determine θ of cord DC for equilibrium.

  21. Quiz #2 • Examining concepts from Tutorial Problem Set #2 • Only approved calculators allowed • Any formulae, conversion factors will be provided • Ancillary information may also be provided

  22. Classification of Textbook Problems Hibbeler (2007)

  23. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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