CE 201 Statics

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CE 201 - Statics

• Lecture 3

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ADDITION OF A SYSTEM OF COPLANNAR FORCES

• If we have more than two forces, the resultant
  can be determined by successive applications of
  the parallelogram law.

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How about finding the components of each force
along certain axe?
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• The forces can then be added algebraically and
  the resultant can be determined. Which method is
  EASIER?
• The main objective of this SECTION is to resolve
  each force into its rectangular components, Fx
  and Fy along x and y axes, respectively, where x
  and y must be perpendicular

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Directional Sense of Rectangular Components

• There are two ways to do that
• 1. Scalar Notation
• The components can be represented by algebraic
  scalar (ve and ve).
• If the component is in the positive direction of
  x or y, then it is positive.
• If the component is in the negative direction of
  x or y, then it is negative.

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Fx and Fy are ve
Fx is ve and Fy is ve
Fx is ve and Fy is ve
Fx and Fy are -ve
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• 2. Cartesian Vector Notation
• The component forces can also be represented in
  terms of Cartesian Unit Vector.
• In two dimensions, the Cartesian unit vector i
  and j are used to represent x and y, respectively.

F Fx i Fy j
F Fx i Fy j
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• As can be seen, the sense of the Cartesian unit
  vectors are represented by plus or minus signs
  depending on if they are pointing along the ve
  or ve x and y axes.

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Resultant of Coplanar Forces
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• - By Scalar Notation
• FRx F1x F2x F3x
• FRy F1y F2y F3y
• - By Cartesian Vector Notation
• FR F1 F2 F3
• F1x i F1y j F2x i F2y j F3x i F3y j
• (F1x F2x F3x) i (F1y F2y F3y) j
• (FRx) i (FRy) j
• (?Fx) i (?Fy) j

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• In general,
• FRx ?Fx
• FRy ?Fy
• Components along positive x and y axes are
  positive.
• Components along negative x and y axes are
  negative.
• After finding FRx and FRy, the magnitude of yhe
  resultant force (FR) can be determined using
  Pythagorean Theorem, where
• FR ? F2Rx F2Ry
• and the direction of FR can be found from
• ? tan-1 ( FRy / FRx )

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Examples

• Example 2.5
• Example 2.6
• Example 2.7
• Problem 2-31
• Problem 2-34
• Problem 2-38

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