Lecture 08 sect 2.9 - 1 2 3 4 x x x x F F F F =...

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ME 221 Lecture 8 1 ME 221 Statics Lecture #8 Sections 2.9 & 2.10
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ME 221 Lecture 8 2 Homework HW #3 Due Monday, September 15 Chapter 2 problems: 61, 64, 70, 71, 72, 82, 86, 94, 105 & 113 Grades posted in Angel HW #1 & Quiz #1 (and solutions) HW #2 & Quiz #2 soon (solutions posted) HW #3 solutions to be posted late Monday No late homework will be accepted once posted
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ME 221 Lecture 8 3 Exam 1 Wednesday, September 17 Details on Monday
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ME 221 Lecture 8 4 Particle Equilibrium For a particle to be in equilibrium, the resultant of the forces acting on it must sum to zero. This is essentially Newton’s second law with the acceleration being zero. In equation form: Σ F = 0
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ME 221 Lecture 8 5 Representing Equilibrium m i Vector Diagram R = F 1 + F 2 + F 3 + F 4 = 0 Vector Equation F 1 F 2 F 3 F 4 F 1 F 2 F 3 F 4
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ME 221 Lecture 8 6 Representing Equilibrium Matrix Form 1 2 3 4 1 2 3 4 1 2 3 4 0 0 0 x x x x y y y y z z z z F F F F F F F F F F F F     + + + =
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Unformatted text preview: 1 2 3 4 x x x x F F F F + + + = x-components 1 2 3 4 y y y y F F F F + + + = y-components 1 2 3 4 z z z z F F F F + + + = z-components Component Form ME 221 Lecture 8 7 Statically Determinate • For 3-D equilibrium, there are three scalar equations: Σ F x = 0 , Σ F y = 0 , Σ F z = 0 • Problems with more than three unknowns cannot be solved without more information, and such problems are called statically indeterminate. ME 221 Lecture 8 8 Free-body Diagram A free-body diagram is a pictorial representation of the equation Σ F = 0 and has: – all of the forces represented in their proper sense and location – indication of the coordinate axes used in applying Σ F = 0 ME 221 Lecture 8 9...
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