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Engineering 36 Chp 1 Introduction Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected] Engineering-36: Vector Mechanics - Statics 1 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Learning Statics There is ONLY ONE WAY to Learn Statics Work LOTS of Problems • Work Thru, and UNDERSTAND, all Sample Problems • Work Chp Problems for Which the Book Provides Answers – Handily Located in the Back of the Book; See “ANSWERS TO SELECTED PROBLEMS” Engineering-36: Vector Mechanics - Statics 2 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Class Structure – ENGR36 Lecture TTh 1:00-1:50p • PowerPoint Instruction-Presentation on The Interactions of Forces (Push/Pull) and Moments (Twists) on NONmoving structures Lab – TTh 2:00-3:15p • Tu: WhiteBoard Example Solutions to Problems Similar to the LPS (HomeWork) Problems • Th: Work in Computer Lab 3906A on the Mastering Engineering LPS Problems Engineering-36: Vector Mechanics - Statics 3 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt If you can’t Make the Lab Every time... Don’t Worry I will post my solved Examples on the ENGR36 Course WebPage Any Student can Work at his/her own Time & Location in place of the lab AS LONG AS the LPS are Submitted to Mastering Engineering ON TIME If a student can not make the Lab Session, I suggest forming an ENGR36 study Group outside of class times Engineering-36: Vector Mechanics - Statics 4 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Mastering Engineering http://www.masteringengineering.com/ Engineering-36: Vector Mechanics - Statics 5 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Mastering Engineering http://www.masteringengineering.com/site/register/new-students.html Pick One, then Continue Engineering-36: Vector Mechanics - Statics 6 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Mastering Engineering: $60.50 http://www.mypearsonstore.com/bookstore/product.asp?isbn=0132915545&xid=PSED An Access Code is provided with the TextBook Available in the BookStore Students who purchased the book from another source can purchase Stand-Alone Mastering Engineering for $60.50 Engineering-36: Vector Mechanics - Statics 7 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt If you received a Course ID from your instructor, click Yes, enter your Course ID and click Continue. CHABOTENGR36FA12 Engineering-36: Vector Mechanics - Statics 8 If you DO NOT have a Course ID, follow the instructions on the NEXT slide. Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt W12345678 Your instructor may provide specific instructions for completing this field. If so, enter the appropriate information and click Continue. Use “W” Number as Student ID Engineering-36: Vector Mechanics - Statics 9 If you are not sure what to enter, contact your instructor or click Skip This Step. (You can enter your Student ID later.) Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Registering Tips Video http://www.masteringsupport.com/video s/registration_tips/registration_tips.html Engineering-36: Vector Mechanics - Statics 10 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Product Design Engineering-36: Vector Mechanics - Statics 11 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Product Design Requirements/Goals • The goal of this phase is to figure out exactly what the customer wants Specification • describe exactly what the product will do and how it will perform Engineering-36: Vector Mechanics - Statics 12 • focus on WHAT the product is supposed to do, not HOW it is supposed to do it Design • Conceptual → Generate Broad Concept Solutions • Preliminary → Choose 2-3 Concepts for Testing Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Product Design Design • Detailed → Select “winning” solution • Sweat details → select materials, Perform engineering analyses, make Engineering DWGs, determine production and test methods Implement • Make a PHYSICAL Prototype unit Engineering-36: Vector Mechanics - Statics 13 Test • Test every item in the performance specification → Possible OutComes – The product does NOT meet the spec – The product meets the spec but the spec was WRONG – customer CHANGED his/her mind – product MEETS the spec and customer is HAPPY Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Analysis Goal • What EXACTLY do we want to determine? – Suggest including the UNITS for the “answer” Given • Summarize KNOWN conditions and previously collected DATA Assume (this HAS to be done) • Make an analytical MODEL • List Important assumptions Engineering-36: Vector Mechanics - Statics 14 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Assumption Digression BMayer 2001 JVST Paper • See ENGR45 for More Details Engineering-36: Vector Mechanics - Statics 15 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Assumption Digression PARTIAL Assumption List • 100% Vapor Saturation at Bubble Edge • Gases in bubble behave as perfect gases • Bubbles are Spherical – Radial Symmetry Engineering-36: Vector Mechanics - Statics 16 • Diffusion Coefficient is Constant Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Analysis Draw Diagram if Possible • Sketching a Diagram is critical • Take time to make a Sketch that is Clear and in Proportion (roughly to scale) Create Math Model • Make equations based on known scientific (physics, chem) or engineering principles Solve Math Model • Math Processors (MATLAB, Excel) helpful Engineering-36: Vector Mechanics - Statics 17 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Analysis Check Results • Make a “Reality Check” on Results • Test with KNOWN inputs and compare to the KNOWN result • Test with a WIDE range of inputs to test “robustness” Engineering-36: Vector Mechanics - Statics 18 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Mechanics – General Mechanics The Physical Science Which Describes Or Predicts The Conditions Of REST Or MOTION For BODIES Under The Action Of FORCES and/or MOMENTS • Some Classes of Mechanics Analysis – Rigid Bodies Statics → NO Motion Dynamics → Moving in General – Deformable Bodies → Forces Interact with MATERIAL Properties 3rd yr course at the University Level – Fluid Mechanics → almost always deforming materials Compressible → gas Incompressible → liquids Engineering-36: Vector Mechanics - Statics 19 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Rigid Body – Special Case Rigid-Body Analysis Considers All Bodies To Be Perfectly Stiff → NO Deformation • Not Strictly True In Practical Situations as All Physical Structures Deform (However Slightly) When Subjected to Force-Loading. – Rigid Body Analysis Applies When Deformations Are “Small” and so Do Not “Significantly” Affect The Conditions Of Equilibrium Or Motion i.e., Can Neglect Deformation For Equil/Motion Analysis Rigid Body ≡ A Body is Considered Rigid When The Relative Movement Between Its Parts is Negligible Engineering-36: Vector Mechanics - Statics 20 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Statics – Further Special Case Statics Is A SubClass of Rigid Body Mechanics Analysis Statics ≡ Study Of Equilibria Of A System Without Regard To Inertia Forces Or Velocity Dependent Forces → No or Const. Motion • Apply Newton’s 2nd Law Using Vector Notation F ma but a 0 F 0! • Consequences of Static Rigid-Body Conditions – System Accelerations Are ZERO – Force InterActs with CONFIGURATION Only – governing equations are ALGEBRAIC In Nature Engineering-36: Vector Mechanics - Statics 21 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Statics - Fundamental Concepts Static Analysis is Based on Incompletely Defined, But Thoroughly Familiar Concepts 1. SPACE ≈ The Geometric Region Occupied By Bodies Whose Positions Are Described By Linear and Angular Measurements Cartesian Relative to a Coordinate System Space 2. TIME ≈ The Measure Of The Succession Of Events 3. MASS ≈ The Measure of the Body’s Inertia, Which Is Its Resistance to a Change Of Motion. Sometimes Called "Quantity Of Matter“ 4. FORCE ≈ The Action Of One Body On Another Engineering-36: Vector Mechanics - Statics 22 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Newtonian Mechanics Sir Isaac Newton (1642-1727) Was the First Person To Mathematically Describe the Physical Relationship Between the Fundamentals • In Newtonian Mechanics Space, Time, And Mass Are Absolute, And Independent Of Each Other Newton’s Laws 1. Objects At Rest Will Stay At Rest, and Objects In Motion Will Stay In Motion In A Straight Line Unless Acted Upon By An Unbalanced Force (Resultant Force = 0). Engineering-36: Vector Mechanics - Statics 23 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Newtonian Mechanics cont. 2. Force Is Equal To Body Mass Times its Acceleration; Mathematically F ma Note: for STATIC; i.e., NonMoving, systems a = 0 3. For Every Action There Is Always An Opposite And Equal Reaction that is CoLinear Engineering-36: Vector Mechanics - Statics 24 Sir Issac Newton Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Systems of Units Base units For Static Analysis System SI Units US Customary Units Length Mass Time Meter (m) Kilogram (kg) Second (s) Foot (ft) Slug (slug) Second (s) FORCE is the Most Important Derived Unit • Find the SI Consistent Force Unit by Applying a Unitary Acceleration, a, of 1 m/s2 – Funit = (1 kg)•(1 m/s2) = 1 N (newton) • Recall for a Weight, the Acceleration is g. One kg “weighs”: – W = mg = (1 kg)•(9.81 m/s2) = 9.81 N Engineering-36: Vector Mechanics - Statics 25 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Tips on Units Maintain Units Through ALL Calculations • Serves as A Consistency Check Use SI Prefixes (Next Slide) to Avoid Scientific Notation • But for Complex Calculations, Convert back to Non-Prefixed SI Units to Avoid Order-of Magnitude Errors Separate 3-Digit Groups with a Space, NOT a Comma • YES → 45 611 m Engineering-36: Vector Mechanics - Statics 26 NO → 789,321 s Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt SI prefixes Factor Name Symbol Factor Name Symbol 1024 yotta Y 10-1 Deci d 1021 zetta Z 10-2 Centi c 1018 exa E 10-3 milli m 1015 peta P 10-6 micro µ 1012 tera T 10-9 nano n 109 giga G 10-12 pico p 106 mega M 10-15 femto f 103 kilo k 10-18 atto a 102 hecto h 10-21 zepto z 101 deka da 10-24 yocto y Engineering-36: Vector Mechanics - Statics 27 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt US Units lbs vs. slugs In The US Customary System the Unit of FORCE Pound (lb) • F = ma and 1 lb = m•(1 ft/s2) • Thus m = 1 lb•s2/ft = 1 slug Weight of 1 slug by gravity? • W = mg Where g = 32.2 ft/s2 • Thus Wslug = 32.2 slug•ft/s2 = 32.2 lb Summary • 1 lb Is The Force Required To Give A Mass Of 1 Slug An Acceleration Of 1 ft/s² • 1 lb Is The Force Required To Give A Mass Of 1/32.2 Slug An Acceleration Of 32.2 ft/s² Engineering-36: Vector Mechanics - Statics 28 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Unit Conversion As Noted Before Unit-Consistency Is Critical for Arriving at a Proper Answer To Convert From One Set of Units to Another use the “Cross-Out” Division Method • e.g. Given a Speed, , of 60 mph; find ft/s & m/s – Given From ref Bk: 1mi = 5280ft and 1m = 3.281ft fps 60 and 1hr = 3600s m i 5280ft 1hr ft 88 hr m i 3600s s m ft 1m 26.82 SI 88 s s 3.281ft Engineering-36: Vector Mechanics - Statics 29 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Numerical Precision Precision is Determined by The PHYSICAL Situation, NOT the CALCULATOR • In Particular, A Computed Result Can be NO MORE Precise Than The LEAST Accurate of – Physically Measured (or Derived from Measured) DATA – The Precision of the Calculation This Was Issue in the SlideRule Days, But Rarely Now • Example: Find the Average of this Physically Reliable Data Set (13.47, 9.9, 7.803) avg 13.47 9.9 7.803 10.391 (by calc) 3 10.4 (reliably) – In This Example, the Middle Value Governs Precision Engineering-36: Vector Mechanics - Statics 30 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Numerical Precision, cont. It is Physically difficult to Make Precise and Reliably-Accurate Measurements to Better Than 1 part per 1 000 (1 ppt); or about 0.1% • Most Practicing Engineers are Very Skeptical of Any Data/Calculations Presented at 1 part in 10 000 (or more) Good “Rule of Thumb” • 4 Figures For Values Starting With No. 1 – Called “3½” Significant Figures • 3 Figures In All Other Cases Engineering-36: Vector Mechanics - Statics 31 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt CoOrdinate Systems The CoOrd TriAd is Defined by Your RIGHT Hand → Rt-Hand Rule Engineering-36: Vector Mechanics - Statics 32 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Right-Hand Rule Thumb points in the positive x direction Index finger points in the positive y direction Middle finger points in the positive z direction Used to define positive rotation • Point thumb in the positive direction along the axis which is perpendicular to the plane of rotation • The fingers point in the direction of positive rotation Engineering-36: Vector Mechanics - Statics 33 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Vectors VECTOR ≡ Parameter Possessing Magnitude And Direction, Which Add According To The Parallelogram Law • Examples: Displacements, Velocities, Accelerations, FORCES SCALAR ≡ Parameter Possessing Magnitude But Not Direction • Examples: Mass, Volume, Temperature Vector Classifications • FIXED Or BOUND Vectors Have Well Defined Points Of Application That CanNOT Be Changed Without Affecting An Analysis Engineering-36: Vector Mechanics - Statics 34 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Vectors cont. • FREE Vectors May Be Moved In Space Without Changing Their Effect On An Analysis • SLIDING Vectors May Be Applied Anywhere Along Their Line Of Action Without Affecting the Analysis • EQUAL Vectors Have The Same Magnitude And Direction • NEGATIVE Vector Of a Given Vector Has The Same Magnitude but The Opposite Direction Equal Vectors Negative Vectors Engineering-36: Vector Mechanics - Statics 35 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Vector Representations MagAngle Unit Vectors • Length of “Unit” Vectors (i, j, k) = 1 • Magnitude ≡ ||V|| = Geometric Length • Space Angles: θx, θy, θz Engineering-36: Vector Mechanics - Statics 36 More on Vector “DeComposition” in future lectures Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering Drawings Formal Drawing Informal Drawing • Contains all information needed for FABRICATION or ASSEMBLY Engineering-36: Vector Mechanics - Statics 37 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Free-Body Diagrams SPACE DIAGRAM A Sketch Showing The Physical Conditions Of The Problem Engineering-36: Vector Mechanics - Statics 38 FREE-BODY DIAGRAM A Sketch Showing ONLY The Forces Acting On The Selected Body Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Suggested Review → Trig Solving Statics Problems Often Involves Non-Right Triangle Geometry. Some Useful Relationships (See your Math Book) Law of Sines Law of Cosines a=13, c=17, B=43° a=11, b=19, C=101° • A=31.4°, C=105.6° b=24 Engineering-36: Vector Mechanics - Statics 39 • c = 23.7 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Battle of the TriAngle If 3 SIDE-LENGHTS are known → Use Cos-Law to Find any angle • Solve Eqn at Right for cos(c) If 2 SIDE-LENGTHS and the Included Angle are known → Use Cos-Law to find the Opp Side-Length Use Sin-Law for • 2-ANGLES & 1-SIDE known • 2-SIDES & NonIncluded Angle Engineering-36: Vector Mechanics - Statics 40 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Done for 1st Meeting Please see me if you would like to ADD Static Loading Engineering-36: Vector Mechanics - Statics 41 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical Engineer [email protected] Engineering-36: Vector Mechanics - Statics 42 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Newtonian Mechanics cont. 2. Force Is Equal To Body Mass Times its Acceleration; Mathematically F ma 3. For Every Action There Is Always An Opposite And Equal Reaction Newton’s Law of Gravitation GMm F ( F a SCALAR) 2 r M F F mutual force of attraction between 2 particles G universal constant known as the constant of gravitation M, m masses of the 2 particles r distance between the 2 particles Engineering-36: Vector Mechanics - Statics 43 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt -F m Weight Consider An Object of mass, m, at Height, h, Above the Surface of the Earth, Which as Radius R • Then the Force on the Object (e.g., Yourself) GMm F 2 R h GM but R h F m 2 m g R This Force Exerted by the Earth is called Weight • While g Varies Somewhat With the Elevation & Location, to a Very Good Approximation – g 9.81 m/s2 32.2 ft/s2 Engineering-36: Vector Mechanics - Statics 44 W mg Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt Earth Facts D 7 926 miles (12 756 km) M 5.98 x 1024 kg • About 2x1015 Empire State Buildings Density, 5 520 kg/m3 • water 1 027 kg/m3 • steel 8 000 kg/m3 • glass 5 300 kg/m3 Engineering-36: Vector Mechanics - Statics 45 Bruce Mayer, PE [email protected] • ENGR-36_Lec-01_Introduction.ppt