MEM202-Chapter-3

# MEM202-Chapter-3 - CHAPTER3 EquilibriumofaParticle...

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CHAPTER 3 Equilibrium of a Particle t F St ) (Concurrent Force Systems) In a concurrent force system, all forces pass through a common point. Whenever cables are used for hoisting loads, their sizes and oints of attachment must be points of attachment must be selected carefully to prevent cable failure and to ensure a MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 1 proper handling of the load.

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Examples of Concurrent Force Systems MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 2
3.1 EQUILIBRIUM OF A PARTICLE 3.2 THE FREE BODY DIAGRAM 3.3 COPLANAR (2 D) FORCE SYSTEMS bjectives Objectives : Students will be able to : D f bd di (FBD) d a) Draw a free body diagram (FBD) , and, b) Apply equations of equilibrium to solve a 2 D bl problem. MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 3

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SPRINGS, CABLES AND PULLEYS Spring k k : Spring constant Spring elongation (or compression) s : Spring elongation (or compression) F : Force applied on the spring •Cables are assumed to be weightless and cannot e stretched s k F Cable and Pulley be stretched •Pulleys are assumed to be frictionless •Cables can only transmit tensile forces •The force in a continuous cable that passes over frictionless pulleys must have a constant it d dl f ht di ti th MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 4 magnitude regardless of what direction the cable is being pulled
THE FREE BODY DIAGRAM Procedure for Drawing a Free Body Diagram Example: Draw the free body diagram for knot C CB F CD F Isolate the body from its surroundings CE F 1. Isolate the body from its surroundings. 2. Show all forces (active and reactive) acting on the body. Label each force with its proper magnitude and direction MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 5 3. Label each force with its proper magnitude and direction.

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THE FREE BODY DIAGRAM Non concurrent Force System hapter 4) Draw free body diagrams for the (Chapter 4) sphere, cord CE , spring CD , knot C , and pulley B . Concurrent Force Systems (Chapter 3) MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 6
EQUATIONS OF EQUILIBRIUM (For 2 D Concurrent Force Systems) Since particle C is in equilibrium, t f t t b B F the net force at C must be zero. 0 CE CD CB F F F F CD F CB 0 , 0 or, y x F F CE F For 2 D equilibrium of a particle (hence a concurrent force system), there are two scalar equations, which can be used to solve for at most two unknowns . The unknowns could be the magnitudes of two forces, one magnitude and one direction (angle), or two MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 3 EQUILIBRIUM OF A PARTICLE 7 directions (angles).

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EXAMPLE Free body diagrams CB F Determine the forces in cables AB and CE and spring CD if the CD F CD F E F DC F sphere has a mass of 6 kg .
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## This note was uploaded on 10/07/2011 for the course MEM 202 taught by Professor Cook during the Fall '08 term at Drexel.

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MEM202-Chapter-3 - CHAPTER3 EquilibriumofaParticle...

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