ENGI 1313 Mechanics I Lecture 10 Particle Equilibrium

ENGI 1313 Mechanics I Lecture 10: Particle Equilibrium, Free-Body Diagrams and Coplanar Forces Shawn Kenny, Ph. D. , P. Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr. mun. ca

Chapter 3 Objectives to introduce the concept of the free-body diagram for a particle. n to show to solve particle equilibrium problems using the equations of equilibrium n 2 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Lecture 10 Objectives n 3 to examine and apply Chapter 3 objectives in 2

Particle Equilibrium n Newton’s 1 st Law – Inertia Ø +Y V = 0, v F 1 Particle equilibrium +X • Rest (Static) • Constant velocity F 3 F 2 Scalar components = 0 2 Equations Solve for at most 2 Unknowns 4 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Free-Body Diagram (FBD) n What is it? Ø n Purpose? Ø n Sketch or diagram illustrating all force vectors acting on a particle (body) A visual aid in developing equilibrium equation of motion What is the procedure? Ø Ø Ø Draw isolated or “free” outlined shape Show all forces Characterize each force • • • 5 Magnitude Sense Direction © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Example 10 -01 +Y n FBD Procedure Draw isolated or “free” outlined shape Ø Show all forces Ø Characterize each force Ø +X • Magnitude • Sense • Direction 6 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Comprehension Quiz 10 -01 n Select the Correct FBD of Particle A n Answer:

Applications Hibbeler (2007) 8 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI

Example 10 -01 n 9 For the engine in static equilibrium, using a free body diagram, solve for the force magnitudes FAD and FAB. The engine mass is 255 kg. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Example 10 -01 n Draw FBD +Y FAB A = 30 FAD +X W

Example 10 -01 n State Equilibrium Equation +Y FAB A = 30 FAD W

Example 10 -02 n 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. 12 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Example 10 -02 (cont. ) n FBD at Point A 600 lb A 25

Example 10 -03 (cont. ) n 600 lb Equilibrium at Point A Ø Rearrange

Example 10 -03 n Find the forces in the cables and weight of sack

Example 10 -03 (cont. ) Unknown force magnitudes at Point C n FBD at

Example 10 -03 (cont. ) n 17 Equilibrium at Point E Ø Rearrange Ø

Example 10 -03 (cont. ) n 18 FBD at Point E and Point C

Example 10 -03 (cont. ) n 19 Equilibrium at Point C © 2007 S.

Homework Problem n 20 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. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10

Quiz #2 Examining concepts from Tutorial Problem Set #2 n Only approved calculators allowed n Any formulae, conversion factors will be provided n Ancillary information may also be provided n 21 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 10