Static of Mechanic

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FUNDAMENTAL of
AEROSPACE ENGINEERING
MUHAMMAD ASYRAF BIN ABDULLAH

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Mid Sem. Exam- CO1 & CO2, 30% (1 1/2hrs –2 questions 14 OCT 8-9.30pm , Selasa)
Assignment - All students Submit the assignment in Group the
following week. 20% (Tutorial Session)
Quiz – Submit in Group 10%
Exam – CO1- CO4, 10%+ 10% + 30% + 20% = 40% (3 hours – three questions)

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Contact Details
• Email: asyrafabdullah484@gmail.com
• Contact Number: 014-516 6521
• Chamber: 203-G, 2nd floor, Bloc B, Faculty of Mechanical And Automotive
Engineering Technology, Universiti Malaysia Pahang.
• Laboratory: Joining & welding Laboratory, Ground Floor, Faculty of
Mechanical And Automotive Engineering Technology.
4

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Assignment/ Quizzes
• Need to form a group by the second week. Not more than 5
students per group.
• Every student submits Assignments and Quizzes in groups.
• Late submissions will be rejected.

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1.1 Mechanics (Chapter 1)
Statics – Equilibrium of bodies
 At rest
 Move with constant velocity
Dynamics – Accelerated motion of bodies

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Engineering Mechanics: Statics
Chapter 2:
Force Vectors

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2.1 Objectives
• To show how to add forces and resolve them into components
using the Parallelogram Law.
• To express force and position in Cartesian vector form and
explain how to determine the vector’s magnitude and direction.
• To introduce the dot product in order to determine the angle
between two vectors or the projection of one vector onto
another.

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2.3 Chapter Outline
• Scalars and Vectors
• Vector Operations
• Vector Addition of Forces
• Addition of a System of Coplanar Forces
• Cartesian Vectors

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2.3 Addition of a System of Coplanar Forces
For resultant of two or more forces:
• Find the components of the forces in the specified
axes
• Add them algebraically
• Form the resultant
In this subject, we resolve each force into rectangular
forces along the x and y axes.
y
x F
F
F 


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2.3 Addition of a System of Coplanar Forces
(Cont.)
• Scalar Notation
- x and y axes are designated positive and negative
- Components of forces expressed as algebraic scalars
Eg:
Sense of direction
along positive x and
y axes y
x F
F
F 


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• Scalar Notation
Eg:
Sense of direction
along positive x and
negative y axes
y
x F
F
F '
'
' 

2.3 Addition of a System of Coplanar Forces
(Cont.)

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….REMINDER … THINK LOGIC
• Always check the unit …

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• Cartesian Vector Notation
- Cartesian unit vectors i and j are used to designate
the x and y directions
- Unit vectors i and j have dimensionless magnitude of
unity ( = 1 )
- Their sense are indicated by a positive or negative
sign (pointing in the positive or negative x or y axis)
- Magnitude is always a positive quantity, represented
by scalars Fx and Fy
2.3 Addition of a System of Coplanar Forces
(Cont.)

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• Cartesian Vector Notation
F = Fx i + Fy j kN
(positive direction)
Point F (Fx,Fy)
2.3 Addition of a System of Coplanar Forces (Cont.)

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 Cartesian Vector Notation
F’ = F’x i + F’y (-j) kN
F’ = F’x i – F’y j

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• Coplanar Force Resultants
Example: Consider three coplanar forces
Cartesian vector notation
F1 = F1x i + F1y j
F2 = - F2x i + F2y j
F3 = F3x i – F3y j
2.3 Addition of a System of Coplanar Forces (Cont.)

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• Coplanar Force Resultants
Vector resultant is therefore
FR = F1 + F2 + F3
= F1xi + F1yj - F2xi + F2yj + F3xi – F3yj
= (F1x - F2x + F3x)i + (F1y + F2y – F3y)j
= (FRx)i + (FRy)j
2.3 Addition of a System of Coplanar Forces (Cont.)

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• Coplanar Force Resultants
If scalar notation are used
FRx = (F1x - F2x + F3x)
FRy = (F1y + F2y – F3y)
In all cases,
FRx = ∑Fx
FRy = ∑Fy
2.3 Addition of a System of Coplanar Forces (Cont.)

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2.4 Comparison between Resultant and Equilibrium force
Resultant force:
∑Fy =FRx = (F1x - F2x + F3x)
∑Fy =FRy = (F1y + F2y – F3y)
If Point A is at Equilibrium.
∑Fx =0= (F1x - F2x + F3x)
∑Fy =0= (F1y + F2y – F3y)

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Assignment 1
Assignment 1.1
The end of the boom O is subjected to three
concurrent and coplanar forces. Determine
the magnitude and orientation of the
resultant force.