ME 201 Engineering Mechanics: Statics

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ME 201Engineering Mechanics Statics

• Chapter 3 Part A
• Equilibrium of a Particle
• Free-Body Diagram
• Co-Planar Force Systems

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Equilibrium of a Particle

• A particle is in equilibrium provided it is at
  rest if originally at rest, or has a constant
  velocity if originally in motion
• Static equilibrium
• Object at rest
• Then to satisfy Newtons first law, the resultant
  force acting on a particle is zero, or

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Equilibrium of a Particle

• In vector notation
• ? Fxi ? Fyj 0
• Or, for this equation to be satisfied
• ? Fx 0
• ? Fy 0

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Steps to Problem Solving

• Draw a Free Body Diagram (FBD), label known and
  unknowns
• Simple sketch of isolated particle
• Sketch all forces that act on the particle
• Active forces
• Reactive forces
• Label known forces with proper magnitude
  direction
• Watch signs negative means opposite sense from
  as drawn in FBD
• Apply equations of equilibrium
• Any suitable direction
• 2 equations, 2 unknowns (n equations, n unknowns)

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Example Problem

• Given
• m 10 kg
• ? 30º
• Find
• TAB
• TAC

B
A
C
?
m
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Example Problem Solution
B
A
C
?
m

• Solution
• 1-FBD
• Assume sense if unknown
• (magnitude will turn out negative if incorrect)
• Cord can only support tension
• 2-Apply Equations of Equilibrium
• look for an equation with a single unknown to
  simplify problem solving

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Example Problem

• Given
• m 8 kg
• ? 30º
• kAB 300 N/m
• lAB0.4 m (unstretched)
• Find
• lAC

2 m
C
A
B
?
m
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Example Problem Solution
2 m
C
A
B
?

• Solution
• 1-FBD
• 2-Equilibrium Equations

m
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Example Problem Solution
2 m
C
A
B
?

• Solution
• 1-FBD
• 2-Equilibrium Equations
• 3-Spring
• Fks

m
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Example Problem

• Given
• m 20 lb
• a 30º
• ? 45º
• Find
• W

F
a
E
D
3
C
?
m
4
W
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Example Problem Solution
F
a
E
D
3
C
?
m
4

• Solution

W
Can only solve for 2 unknowns with a single FBD
Create a second FBD of point E
3 unknowns 2 equations
2 unknowns 2 equations
Solve for W by using the FBDs in succession
through TCE
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Example Problem Solution

• FBD 1

FBD 2
Solving simultaneously
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Questions for Thought

• How are pulleys represented in a FBD?