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
[email protected]
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

2
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Lecture 10 Objectives

3
to examine and apply Chapter 3 objectives
in 2D space
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Particle Equilibrium

Newton’s 1st Law – Inertia

+Y
V = 0, v
F1
Particle equilibrium
+X
• Rest (Static)
• Constant velocity
F3
F  0
F2
 Scalar components = 0
2 Equations
 Solve for at most 2 Unknowns
4
© 2007 S. Kenny, Ph.D., P.Eng.
 


 F  F1  F2  F3  0


 Fx î   Fy ĵ  0
F  0
F  0


x
y
ENGI 1313 Statics I – Lecture 10
Free-Body Diagram (FBD)

What is it?


Purpose?


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?



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

FBD Procedure
Draw isolated
or “free”
outlined shape
 Show all forces
 Characterize
each force

+X
• Magnitude
• Sense
• Direction
6
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Comprehension Quiz 10-01

Select the Correct FBD
of Particle A

Answer: D
Hibbeler (2007)
7
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Applications
Hibbeler (2007)
8
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-01

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

Draw FBD
+Y
FAB
A
 = 30
FAD
+X
W = FAC = mg
W = (255 kg)(9.806m/s2) = 2.5kN
10
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-01

State Equilibrium
Equation
 F  0
+Y
FAB
A
 = 30
FAD

x
 FAD  FAB cos 30   0
W = FAC = 2.5kN
FAD  5 kN cos 30   4.33 kN

F
y
0
 FAC  FAB sin 30   0
11
© 2007 S. Kenny, Ph.D., P.Eng.
FAB 
2.5 kN
 5 kN

sin 30
ENGI 1313 Statics I – Lecture 10
+X
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.
12
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-02 (cont.)

FBD at Point A
600 lb
A
25

F
x
0
FAB
30
FAC
FAC cos 30   FAB cos 25   0

F
y
0
 FAC sin 30   FAB sin 25   600 lb  0
2 Equations
2 Unknowns
13
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-03 (cont.)

600 lb
Equilibrium at Point A

Rearrange

F
x
0
A
FAC cos 30   FAB cos 25   0
25
FAC  1.047 FAB
FAB

Substitute

F
y
0
 FAC sin 30   FAB sin 25   600 lb  0
 1.047 FAB sin 30   FAB sin 25   600 lb  0
FAB  634.2 lb  634lb
 FAC  1.047 FAB  664 lb
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
30
FAC
Example 10-03

Find the forces in the
cables and weight
of sack B.

What point is first selected for the FBD?
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-03 (cont.)
Unknown force
magnitudes at Point C
  FBD at Point E
 F  0


x
TEG sin 30   TEC cos 45   0

F
y
0
TEG cos 30   TEC sin 45   20 lb  0
2 Equations
2 Unknowns
16
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Example 10-03 (cont.)

Equilibrium at Point E

Rearrange

F
x
0
TEG sin 30   TEC cos 45   0
TEG  2 TEC

Substitute

F
y
0
TEG cos 30   TEC sin 45   20 lb  0
2 TEC cos 30   TEC sin 45   20 lb  0
TEC  38.64 lb  38.6 lb
 TEG  2TEC  54.6 lb
17
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
TEG  54.6 lb
Example 10-03 (cont.)

18
FBD at Point E and
Point C
© 2007 S. Kenny, Ph.D., P.Eng.
TEC  38.6 lb
ENGI 1313 Statics I – Lecture 10
Example 10-03 (cont.)

Equilibrium at Point C
 F  0

x
 TCD
TCD

4
 TCE cos 45   0
5
5
 38.64 lbcos 45   34.2 lb
4
F
y
0
3
TCD  TCE sin 45   WB  0
5
3
WB  34.15 lb  38.64 lbcos 45   47.8 lb
5
19
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Homework Problem

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
 Only approved calculators allowed
 Any formulae, conversion factors will be
provided
 Ancillary information may also be provided

21
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
Classification of Textbook Problems
Hibbeler (2007)
22
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10