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Statics Handout

General principles of rigid body mechanics, problems solving, statics terminology, and resolving resultant forces
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  EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1 DFiller Chap. 1 General Principles   What is Mechanics? What is Statics ?  Mechanics  RRiiggiidd--bbooddyy   MMeecchhaanniiccss   Deformable-body   Mechanics  Fluid Mechanics SSttaattiiccss   Deals with equilibrium of bodies at rest or at constant velocity   Dynamics Deals with bodies under accelerated motion   Design & Analysis of:   Structural systems   Mechanical systems   Electrical systems   Rigid-body mechanics is based on Newton’s 3 Laws of Motion:   Law   Name   Description   1 st   Law of Equilibrium  A particle at rest or at constant velocity will remain so unless subjected to an unbalanced force. 2 nd  Law of Acceleration A particle subjected to an unbalanced force accelerates. 3 rd  Law of Mutual Attraction Mutual action-reaction forces between two particles are equal, opposite and collinear. Steps to Effective Problem Solving:   1. Understand the problem 2. Tabulate the known data and draw a free-body diagram (FBD) 3. Apply mathematical principles 4. Solve the problem with units check 5. Evaluate your result (Make sense of your solution – is it reasonable?)  Problem Formatting is an organizational skill! On engineering paper…… 1. D efine problem (in your own words is best) 2. Diagram (if appropriate) – FBD 3. Analysis (step-by-step method) 4. Solution (report to 2-3 significant figures and underline or box)  EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1 DFiller  EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1 DFiller Chap. 2 Force Vectors Terminology - Learn the lingo! Stick with convention! Scalar (number) Vector (→ magnitude, direction, and sense)  Collinear (forces or vectors) (sharing the same line, or alignment) Orthogonal axes (form right angles) Parallelogram Law (parallel sides of equal length, with equal opposite angles; used with orthogonal and non-orthogonal axes) Free Body Diagram (FBD) Drawing/illustration Resultant force (or vector) (2 force vectors added together form a resultant force vector) Force triangle (Triangle Rule, Law of Sines, Law of Cosines) Rectangular components (2D, rectify force as xy components using trig.) Cartesian vector (3D, xyz  axes; rectify force as ijk  components) Unit vector (u) (specifies direction) Position vector (r) (orients force between two points) Coordinate direction angles ( α, β, γ   orients force wrt xyz axes) Concurrent force system (multiple forces acting at/from the same point) Dot product Multiplication of two vectors together yields a scalar Conventions: x z + + +  EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1 DFiller Finding and resolving resultant forces. 2-4. Determine the magnitude of the resultant forc e F R = F 1 + F 2 and its direction, measured clockwise from the positive u axis.  2-5 .  Resolve the force F 1 into components acting along the u   and v    axes and determine the magnitudes of the components.   2-6. Resolve the force F 2 into components acting a long the u   and v axes and determine the magnitudes of t h   e compo n ents.  
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