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

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

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

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

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

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

Applications Hibbeler (2007)

Example 10-01 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.

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

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

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.

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

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

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

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

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

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

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

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.

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

Classification of Textbook Problems Hibbeler (2007)

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