Chapter 3 - ENGI 1400 Engineering Mechanics I STATICS...

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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 3-P1 Chapter 3 Equilibrium of a Particle ; WHAT YOU SHOULD LEARN & UNDERSTAND FROM THIS CHAPTER? ¾ How to draw the Free-Body Diagram (FBD) for a particle (in 2-D and 3-D force systems) ¾ How to solve particle equilibrium problems (2-D and 3-D) using the equations of equilibrium ; READING MATERIALS IN TEXTBOOK – CHAPTER 3 (All Sections 3.1 – 3.4) ; Fundamental RINCIPLES and APPLICATION EXAMPLES – throughout the whole course APPLICATIONS For a spool of given weight, what are the forces in cables AB, AC, and AD? For a given cable strength, what is the maximum weight that can be lifted? For a given weight of the lights, what are the forces in the cables? What size of cable must you use?
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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 3-P2 3.1. Coplanar (2-D) Force Systems (Section 3.3) This is an example of a 2-D or coplanar force system. If the whole assembly is in equilibrium , then particle A is also in equilibrium. To determine the tensions in the cables for a given weight of the engine (Engine Mass = 250 kg), we need to learn how to draw a free body diagram and apply equations of equilibrium. !!! Free Body Diagrams are one of the most important things for you to know how to draw and use !!! 1. WHAT, WHY AND HOW OF A Free-Body Diagram (FBD) What a FBD is ? It is a drawing that shows all external forces acting on the particle . Questions: (1) external forces, internal forces? (2) what is a particle? A is a particle, what about others (e.g., engine)? Why need it? It helps you write the equations of equilibrium used to solve for the unknowns (usually forces or angles).
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Winter 2009 L. Liu, Civil and Resource Engineering Chapter 3-P3 How to draw it ? (1) Imagine the particle to be isolated or cut “free” from its surroundings. (2) Show all the forces (from external sources) that act on the particle. Active forces: they want to move the particle. Reactive forces: they tend to resist the motion. (3) Identify each force: forces with known magnitudes and directions – given conditions; all unknowns as variables (force magnitudes and/or directions). FBD at the particle A
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Chapter 3 - ENGI 1400 Engineering Mechanics I STATICS...

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