1. ENGR 3340: Fundamentals of Statics and Dynamics 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. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics 2 Tentative Lectures Schedule TopicLecture Equilibrium of a Particle in 3-D 7

3. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Equilibrium Topic 7: Equilibrium of a Particle in 3-D 3 One thing you learn in science is that there is no perfect answer, no perfect measure. A. O. Beckman

4. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics 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 4

5. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Three-Dimensional Force System. Equilibrium Three unknowns Three equations  Three unknowns Mathematical manipulation vs. Physical interpretation Particle moves with constant velocity or remains at rest. Resolve the forces into their i, j, k components 5

6. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Types of Forces Weight:Spring: Three-Dimensional Force System - Physical Interpretation Free Body Diagram Establish the x, y, z axes in any suitable orientation. Label all known and unknown force magnitudes and directions. The sense of a force having an unknown magnitude can be assumed. 6

7. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Three-Dimensional Force System - Mathematical Manipulation Position Vectors Projection angles (depends on each problem) Direction Cosines 7

8. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics 8

9. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Plan: A F B F C F D 1) Draw a free body diagram of Point A. Let the unknown force magnitudes be F B, F C, F D. 2) Represent each force in the Cartesian vector form. 3) Apply equilibrium equations to solve for the three unknowns. Given: Given: A 600 N load is supported by three cords with the geometry as shown. Find: ABAC AD Find: The tension in cords AB, AC and AD. Example 1 9

10. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics F B = F B (sin 30  i + cos 30  j ) N = {0. 5 F B i + 0. 866 F B j } N F C = – F C i N F D = F D ( r AD /r AD ) = F D { (1 i – 2 j + 2 k ) / (1 2 + 2 2 + 2 2 ) ½ } N = { 0. 333 F D i – 0. 667 F D j + 0. 667 F D k } N FBD at A FCFC FDFD A 600 N z y 30˚ FBFB x 1 m 2 m Solution 1 10

11. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Solving the three simultaneous equations yields F C = 646 N F D = 900 N F B = 693 N Solution 1 Now equate the respective i, j, k components to zero.  F x = 0.5 F B – F C + 0. 333 F D = 0  F y = 0.866 F B – 0. 667 F D = 0  F z = 0.667 F D – 600 = 0 FBD at A FCFC FDFD A 600 N z y 30˚ FBFB x 1 m 2 m 11

12. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics Homework5  http://facultad. bayamon.inter.edu/omeza/http://facultad. bayamon.inter.edu/omeza/ Omar E. Meza Castillo Ph.D. 12

13. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics 13 ¿Preguntas? Comentarios

14. MSP21 Universidad Interamericana - Bayamón ENGR 3340: Fundamentals of Statics and Dynamics 14 GRACIAS