‫معهد اإلسكندرية العالى للهندسة والتكنولوجيا‬
‫‪Alexandria Higher Institute of Engineering and Technology‬‬
‫‪STATICS‬‬
‫‪ME001‬‬
‫دكتورمهندس استشارى‪ /‬سامح توفيق عبد الفتاح‬
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‫‪Dr\ Sameh Tawfik‬‬
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‫المحاضرة الثانية‬
Lecture (2)
Force Vectors
(Scalars and Vectors(
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Lecture 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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Scalars and Vectors
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Scalars
A scalar Is any positive or negative physical quantity that can be completely
specified by its magnitude .
Examples of scalar quantities:
length, mass, and time
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Vectors
A vector is any physical quantity that requires both a magnitude and a
direction for its complete description.
Examples of vectors encountered in statics are:
position, force, and moment
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Vector Graphical Representation
-
A vector is shown graphically by an arrow.
The length of the arrow represents the magnitude of the vector.
The angle between the vector and a fixed axis defines the direction of its
line of action .
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Scalars &Vector Writing Representation
In print
,
vector quantities are represented by boldface letters such as
A , and the magnitude of a vector is italicized, A .
A
A
Vector Quantity
Scalar Quantity
For handwritten
work it is often convenient to denote a vector quantity by simply drawing an
arrow on it
𝐴
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Vector Operations
1- Multiplication and Division of a Vector by a Scalar.
- If a vector is multiplied by a positive scalar, its magnitude is increased
by that amount.
- Multiplying by a negative scalar will also change the directional sense
of the vector.
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Graphic examples
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Vector Operations
2-Vector Addition
All vector quantities obey the parallelogram law of addition
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Vector Operations
2-1 Special case of Vector Addition
If the two vectors A and B are collinear
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Vector Operations
3-Vector Subtraction
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Practical Examples
Vector Addition of Forces
The parallelogram law must be used to determine
the resultant of the two forces acting on the hook.
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Using the parallelogram law the supporting force (F)
can be resolved into components acting along the
(u)
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and
(v)axes .
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- The magnitude of the resultant force can be determined using the law of (cosine)
- The direction is determined from the law of (sine).
- The magnitudes of two force components are determined from the law of (sine)
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Solved Example
The screw eye in the shown figure is subjected to
two forces, (F1) and (F2). Determine the magnitude
and direction of the resultant force (FR).
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Given:F1 = 100 N , 15O with (X) axis
F2 = 50 N , 10O with (Y) axis
Required
The magnitude & direction of
(FR)
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Solution
The two unknowns are the magnitude of (FR ) and the angle (θ)
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Then the final required is of (FR ) & (ϕ)
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Assignment
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Solve all problems of
sheet (2)
Dr\ Sameh Tawfik
‫مع أطيب تمنياتي بالتوفيق‬
‫دكتورمهندس استشارى‪ /‬سامح توفيق عبد الفتاح‬
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‫‪Dr\ Sameh Tawfik‬‬
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