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Fundamentals of Statics and Dynamics - ENGR 3340

Fundamentals of Statics and Dynamics - ENGR 3340. Professor: Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering. Tentative Lectures Schedule.

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Fundamentals of Statics and Dynamics - ENGR 3340

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  1. Fundamentals of Statics and Dynamics - ENGR 3340 Professor: Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering

  2. Tentative Lectures Schedule

  3. One thing you learn in science is that there is no perfect answer, no perfect measure. A. O. Beckman Topic 5: Equilibrium of a Particle in 2-D Equilibrium

  4. 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

  5. Equilibrium of a Particle Applications For a spool of given weight, what are the forces in cables AB and AC ?

  6. Equilibrium of a Particle Applications (continued) For a given cable strength, what is the maximum weight that can be lifted ?

  7. Equilibrium of a Particle Applications (continued) For a given weight of the motor, what are the forces in the cables? What size of cable must you use ?

  8. Equilibrium of a Particle Applications (continued) Static Equilibrium

  9. Balancing Forks • Materials:

  10. Balancing Forks • Step 1:

  11. Balancing Forks • Step 2:

  12. Balancing Forks

  13. Coke Can Balancing • Materials:

  14. Coke Can Balancing • Step 1:

  15. Coke Can Balancing • Step 2:

  16. Coke Can Balancing • Step 3:

  17. Coke Can Balancing

  18. 3.1 Condition for the Equilibrium of a Particle. • Particle is said to be in EQUILIBRIUM if: • It remains at rest (v=0) if originally at rest. (Static Equilibrium) • It has a constant velocity if originally in motion. • To maintain EQUILIBRIUM, it is necessary to satisfy Newton’s first law of motion. Resultant force acting on a particle require to be zero. where ∑F is the vector sum of all the forces acting on the particle. Equation of Equilibrium

  19. 3.1 Condition for the Equilibrium of a Particle. • Consequently, the particle indeed moves with constant velocity or remains at rest. • For Equilibrium:

  20. 3.2 The Free-Body Diagram (FBD) • To apply the EQUATION OF EQUILIBRIUM, we must account for ALL THE KNOWN and UNKNOWN FORCESwhich act ON the particle • In order to account for all the forces that act on the particle, it is necessary to draw its FREE-BODY DIAGRAM (FBD). • The free-body diagram is simple a SKETCH which shows the particle “FREE”from its surrounding with ALL the forces that act on it. FBD

  21. Types of Connections • Two types of connections often encountered in particle equilibrium SPRINGS and CABLES and PULLEYS. • SPRINGS:The magnitude of force exerted on a linearly elastic spring is: which has a stiffness k and is deformed (elongate or compressed) a distance s, measured from its unloaded position. Where lothe original length and l the final length

  22. Types of Connections • CABLES and PULLEYS: All cables are assumed to have negligible weight and they cannot stretch. • A cable can support only a tension or “pulling” force, and this force always act in the direction of the cable. • The tension in a cable is constant throughout its length.

  23. Procedure for Drawing a Free-Body Diagram: • Draw Outlined Shape: Imagine the particle to be isolated or cut “free” from its surrounding with all the forces outlined shape. • Show All Forces: Indicate on this sketch all the forces that act on the particle. • Identify Each Force: The forces which are known should be labeled with their proper magnitudes and directions. Letter are used to represent the magnitudes and directions of forces that are unknown.

  24. Example 1 • The sphere has a mass of 6 kg and is supported as shown. Draw a free-body diagram of the sphere, the cord CE, and the knot at C.

  25. Solution 1 • Sphere: There are two forces acting on the sphere: • The weight of the sphere W=6kg(9.81m/s2)=58.9N • The force FCEof the cord CE acting on the sphere • The Free-Body Diagram

  26. Solution 1 • Cord CE: When the cord CE is isolated from its surroundings, its free-body diagram shows only two forces acting on it: • The force of the sphere and FCE. • The force of the knot FEC • The Free-Body Diagram FCE=FEC

  27. Solution 1 • Knot: The knot at C is subjected to three forces. They are caused by the cords CBA and CE and the spring CD: • The Free-Body Diagram

  28. 3.3 Coplanar Force Systems • If a particle is subjected to a SYSTEM OF COPLANAR FORCESthat lie in the x-y plane. Then each force can be resolved into iand j components • For EQUILIBRIUM, these forces must SUM to produce a ZERO RESULTANT. Hence:

  29. Example 2 • Determine the tensionin cables BA and BC necessary to support the 60-kg cylinder.

  30. Solution 2 • Due to EQUILIBRIUM, the weight of the cylinder causes the tension in cable BD to be: • The forces in cable BA and BC can be determined by investigating the equilibrium of the ring B. Its free body diagram is then:

  31. Solution 2 • The magnitudes of TA and TC are unknown, but their directions are known.

  32. Solution 2 • Equations of equilibrium along the x and y axes:

  33. ApplicationProblems

  34. Homework3  http://facultad. bayamon.inter.edu/omeza/ Omar E. Meza Castillo Ph.D.

  35. ¿Preguntas? Comentarios

  36. GRACIAS

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