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. 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

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. 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

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 static equilibrium, using a free body diagram, solve for the force magnitudes FAD 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. Example 10-01 State Equilibrium Equation +Y +X  = 30 FAB
W = FAC = 2.5kN
FAD A
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. Example 10-02 (cont.) FBD at Point A 600 lb A 25 30 FAC FAB
2 Equations 2 Unknowns

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

18. Example (cont.)
FBD at Point E and Point C

19. Example (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)