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# TAMU MEEN 221 - Module 2 Chapter 2 – Force Vectors in 2D

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Module 2Chapter 2 – Force Vectors in 2D▪ Forces and Vectors▪ Force characteristics▪ Vector Review▪ Concurrent Force SystemsForce and Vector ReviewForce –directindirectForce has 1) Internal Effect2) External EffectCharacteristics of a Force1. Magnitude:2. Direction:3. Point of Application:4. Line of Action:Review of Vector Operations1) Scalar:examples: 2) Vector: examples:If r= 10 ft and θ=50o , write position vector rin Cartesian vector formWrite position vector from Ato Bin Cartesian vector form. θ=60oWrite force vector from in Cartesian vector form. Direction Cosines for components:Component = magnitude*cosine of angle between vector and positive coordinate axis (x or y)Types of Vectors1. Free – does not pass through a unique point2. Sliding – does pass through a unique point and can slide along the line of action3. Bound- fixed to the point of applicationPrinciple of Transmissibility – force can be applied at any point along the line of action without changing the external effect of the force.◼ The lines of actions of all forces intersect at a common point.Replace concurrent forces with a single resultant force R1. Graphically2. Use Law of Sines and Law of Cosines3. Add components in common coordinate systemF2F1Concurrent Force SystemsFind Resultant R1. GraphicallyFind Resultant R2. Law of SinesFind Resultant RF2F13. Add components in common coordinate systemFind Resultant of 2 forcesFind Resultant of 2 forcesComponents using measurementsFind Resultant of 2 forces210 N170 Nxy52512Inverse Problem: Two ropes are used to tow a boat upstream. The resultant R of the rope forces Fuand Fvhas a magnitude of 400 lb and a direction as shown. Determine the magnitudes of forces Fuand FvDetermine the magnitude of F1and its direction θ so that the resultant force is directed vertically upward and has a magnitude of 800 N.Items to complete◼ Submit the classwork ICW #2: 6/3 to the submission box on Canvas by midnight, Saturday, 6/4◼ Complete Homework #2 in Pearson by midnight, Saturday, 6/4◼ Complete Quiz #1 over the syllabus by midnight, Sunday, 6/5. This will be taken un-proctored and you can take the quiz twice using open notes. There is feedback, so read it if you miss a question. The password

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