ME 221 Statics
Lecture #4
Sections 2.9 & 2.10
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Lecture 4
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Announcements
• Quiz #2 - 15 minutes before the end of the lecture
• HW #2 due Friday 5/28
Ch 2: 23, 29, 32, 37, 47, 50, 61, 82, 105, 113
Ch 3: 1, 8, 11, 25, 35
• Quiz #3 on Friday, May 28
• Exam # 1 will be on Wednesday, June 2
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Vector Dot Product
Section 2.8
• Determining the angle between 2 vectors
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Dot Product
Consider two vectors A and B with included
angle q
A
q
B
By definition, the dot product is
A • B = |A| |B| cos q
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Applications
• Determine the angle between two arbitrary
vectors
·
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Free-Body Diagrams; Equilibrium
Sections 2.9 & 2.10
• These two topics will tie Chapter 2 together.
• This material is the most important of the
topics covered in class thus far.
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Particle Equilibrium
• For a particle to be in equilibrium, the
resultant of the forces acting on it must sum
to zero.
• This is essentially Newton’s second law
with the acceleration being zero.
• In equation form: SF = 0
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Representing Equilibrium
F3
F2
F3
F4
mi
F1
F1
F4
R = F1 + F2 + F3 + F4 = 0
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F2
Vector Diagram
Lecture 4
Vector Equation
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Representing Equilibrium
 F1x   F2 x   F3 x   F4 x  0
          Matrix Form
 F1 y    F2 y    F3 y    F4 y   0
 F   F   F   F  0 
 1z   2 z   3 z   4 z   
F1x  F2 x  F3 x  F4 x  0
x-components
F1 y  F2 y  F3 y  F4 y  0
y-components
F1z  F2 z  F3 z  F4 z  0
z-components
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Component
Form
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Statically Determinate
• For 3-D equilibrium, there are three scalar
equations: SFx = 0 , SFy = 0 , SFz = 0
• Problems with more than three unknowns
cannot be solved without more information,
and such problems are called statically
indeterminate.
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Free-Body Diagram
A free-body diagram is a pictorial representation
of the equation SF = 0 and has:
– all of the forces represented in their proper
sense and location
– indication of the coordinate axes used in
applying SF = 0
(Even though this is covered on a single slide, free-body
diagrams are arguably the most important topic of the
entire course.)
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Quiz #2
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