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TAMU MEEN 221 - Topic 4 Chapter 3: Equilibrium of a Particle (2D)

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A spool of given weight W is suspended from a crane. When designing the spreader bar, we need to know the cable forces AB and AC to make sure the rigging doesn’t fail. Topic 4Chapter 3: Equilibrium of a Particle (2D)Newton’s 1stlaw governs statics: Resultant of forces in Cartesian coordinate systemSteps to solve Equilibrium Problems:▪ Draw Free Body Diagram▪ Apply Equilibrium ConditionsEquilibrium of a ParticleNotes about forces▪ Gravity: W, place at center of gravity of body▪ Contact forces: forces that arise between bodies that physically touch. They are perpendicular to contact surfaces.Notes about forces –cont-▪ Flexible rope or cables: always in tension▪ Spring Forces: length of spring changes in proportional to the force acting on itWhat, Why and How of a Free Body DiagramFree Body Diagrams (FBD) are one of the most important things for you to know how to draw and use.What ? - It is a drawing that shows all external forces acting on the body.Why ? - It is essential for writing the equations of equilibrium used to solve for unknowns (usually forces or angles).How? Steps:1. Decide on body (or bodies) to isolate2. Draw outline of isolated body, free of surroundings3. Draw all forces applied by other bodies:Active forces: want to move bodyReactive forces: tend to resist motionShow all known and unknown forces magnitudes and directions.4. Indicate set of coordinate axes on FBDA B C100 lbDraw FBD of sphereDraw FBD of knot at point CDraw FBD of cord CEThe sphere has a mass of 6 kg and is supported as shownDraw a FBD for use when solving for the cable forces when the system is in equilibriumThe sphere has a mass of 6 kg and is supported as shownDetermine the force in the spring and in the cable ABC.Determine the forces in cables AB and AD when the system is in equilibriumDetermine the unstretched length of DBto hold the40-kg crate in the position shown. Take k= 180 N/m.Determine the tension in the cables AB, BC, and CD, necessary to support the 10 kg light at B and the 15 kg light at C. Also find the angle θ.Determine the maximum weight W of bucket F that can be supported in the position shown if each cable can support a maximum tension of 600 N before it fails.Items to complete◼ Submit the classwork ICW #3: 6/8 to the submission box on Canvas by midnight, Thursday, 6/9◼ Complete Homework #4a in Pearson by midnight, Thursday, 6/9◼ Scan and upload a pdf of your FBD’s needed forHomework #4 (called “Hwk #4b Paper with FBD’s for 2D particle equilibrium”) in Canvas by midnight, Thursday, 6/9◼ Read the MEEN 221 Quiz Instructions with Honorlockbefore class on Friday

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