ch03 - Chapter3 :Statics ChapterObjectives...

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Engineering Mechanics: Statics Chapter 3:  Equilibrium of a Particle 
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Chapter Objectives To introduce the concept of the free-body  diagram for a particle. To show how to solve particle equilibrium  problems using the equations of equilibrium.
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Chapter Outline Condition for the Equilibrium of a  Particle  The Free-Body Diagram Coplanar Systems Three-Dimensional Force Systems
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3.1 Condition for the  Equilibrium of a Particle  Particle at  equilibrium  if - At rest - Moving at constant a constant velocity Newton’s first law of motion F  = 0 where ∑ F  is the vector sum of all the  forces acting on the particle 
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3.1 Condition for the  Equilibrium of a Particle  Newton’s second law of motion F  = m a When the force fulfill Newton's first law  of motion,  m = 0   = 0 therefore, the particle is moving in  constant velocity or at rest
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3.2 The Free-Body Diagram Best representation of all the unknown  forces (∑ F ) which acts on a body A sketch showing the particle “free” from  the surroundings with all the forces acting  on it Consider two common connections in this  subject –  Spring        –  Cables and Pulleys
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3.2 The Free-Body Diagram Spring - Linear elastic spring: change in length is  directly proportional to the force acting on it spring constant or stiffness k defines the elasticity of  the spring - Magnitude of force when spring  is elongated or compressed F  =  k s  
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3.2 The Free-Body Diagram Spring where s is determined from the difference in  spring’s deformed length l and its  undeformed length l o s = l - l o   - If s is positive,  F  “pull” onto the spring - If s is negative,  F  “push” onto the spring  
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3.2 The Free-Body Diagram Example  Given l o  = 0.4m and  k  = 500N/m To stretch it until l = 0.6m,  A force,  F  =  k =(500N/m)(0.6m – 0.4m) = 100N is needed To compress it until l = 0.2m,   A force,  F  =  k =(500N/m)(0.2m – 0.4m) = -100N is needed
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3.2 The Free-Body Diagram Cables and Pulley - Cables (or cords) are assumed to have  negligible weight and they cannot stretch - A cable only support tension or pulling force - Tension always acts in the  direction of the cable - Tension force in a continuous cable must have a constant  magnitude for equilibrium  
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3.2 The Free-Body Diagram Cables and Pulley - For any angle  θ , the cable is  subjected to  a constant tension  T   throughout its length  
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3.2 The Free-Body Diagram Procedure for Drawing a FBD  1.  Draw outlined shape - Isolate particle from its surroundings 2. Show all the forces - Indicate all the forces
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ch03 - Chapter3 :Statics ChapterObjectives...

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