Lecture 10 - Faculty of Engineering and Applied Science
Download
Report
Transcript Lecture 10 - Faculty of Engineering and Applied Science
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
ˆ
Fx i Fy ˆj 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
x
+Y
FAB
A
= 30
FAD
0
FAD FAB cos 30 0
W = FAC = 2.5kN
FAD 5kN cos30 4.33kN
F
y
0
FAC FAB sin30 0
11
© 2007 S. Kenny, Ph.D., P.Eng.
FAB
2.5kN
5kN
sin30
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 cos30 FAB cos25 0
F
y
0
FAC sin30 FAB sin25 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 cos30 FAB cos25 0
25
FAC 1.047 FAB
FAB
Substitute
F
y
0
FAC sin30 FAB sin25 600 lb 0
1.047 FAB sin30 FAB sin25 600 lb 0
FAB 634.2 lb 634lb
FAC 1.047FAB 664 lb
14
© 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?
15
© 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
x
0
TEG sin30 TEC cos45 0
F
y
0
TEG cos30 TEC sin45 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 sin30 TEC cos45 0
TEG 2 TEC
Substitute
F
y
0
TEG cos30 TEC sin45 20 lb 0
2 TEC cos 30 TEC sin45 20 lb 0
TEC 38.64 lb 38.6lb
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 38.6lb
ENGI 1313 Statics I – Lecture 10
Example 10-03 (cont.)
Equilibrium at Point C
F
x
0
4
TCE cos45 0
5
5
TCD 38.64lbcos 45 34.2lb
4
TCD
F
y
0
3
TCD TCE sin45 WB 0
5
3
WB 34.15lb 38.64lbcos45 47.8lb
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
23
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 10