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ME 201 Engineering Mechanics: Statics

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A particle is in equilibrium provided it is at rest if ... Solving simultaneously. FBD #2: Questions for Thought. How are pulleys represented in a FBD? ... – PowerPoint PPT presentation

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Title: ME 201 Engineering Mechanics: Statics


1
ME 201Engineering Mechanics Statics
  • Chapter 3 Part A
  • Equilibrium of a Particle
  • Free-Body Diagram
  • Co-Planar Force Systems

2
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

3
Equilibrium of a Particle
  • In vector notation
  • ? Fxi ? Fyj 0
  • Or, for this equation to be satisfied
  • ? Fx 0
  • ? Fy 0

4
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)

5
Example Problem
  • Given
  • m 10 kg
  • ? 30º
  • Find
  • TAB
  • TAC

B
A
C
?
m
6
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

7
Example Problem
  • Given
  • m 8 kg
  • ? 30º
  • kAB 300 N/m
  • lAB0.4 m (unstretched)
  • Find
  • lAC

2 m
C
A
B
?
m
8
Example Problem Solution
2 m
C
A
B
?
  • Solution
  • 1-FBD
  • 2-Equilibrium Equations

m
9
Example Problem Solution
2 m
C
A
B
?
  • Solution
  • 1-FBD
  • 2-Equilibrium Equations
  • 3-Spring
  • Fks

m
10
Example Problem
  • Given
  • m 20 lb
  • a 30º
  • ? 45º
  • Find
  • W

F
a
E
D
3
C
?
m
4
W
11
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
12
Example Problem Solution
  • FBD 1

FBD 2
Solving simultaneously
13
Questions for Thought
  • How are pulleys represented in a FBD?
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