Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege
Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege
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Transcript of Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege
[email protected] • ENGR-36_Lec-01_Introduction.ppt1
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engineering 36
Chp 1Introductio
n
[email protected] • ENGR-36_Lec-01_Introduction.ppt2
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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”
[email protected] • ENGR-36_Lec-01_Introduction.ppt3
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 Math & Science Center 3906 on the Mastering Engineering LPS Problems
[email protected] • ENGR-36_Lec-01_Introduction.ppt4
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt5
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Mastering Engineeringhttp://www.masteringengineering.com/
[email protected] • ENGR-36_Lec-01_Introduction.ppt6
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Mastering Engineeringhttp://www.masteringengineering.com/site/register/new-students.html
Pick One, then Continue
[email protected] • ENGR-36_Lec-01_Introduction.ppt7
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt8
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
If you received a Course ID from your instructor, click Yes, enter your Course ID and click
Continue.
If you DO NOT have a Course ID, follow the instructions on
the NEXT slide.CHABOTENGR36FA13
[email protected] • ENGR-36_Lec-01_Introduction.ppt9
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Your instructor may provide specific instructions for completing this field.
If so, enter the appropriate information and click Continue.
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[email protected] • ENGR-36_Lec-01_Introduction.ppt10
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Registering Tips Video http://www.masteringsupport.com/
videos/registration_tips/registration_tips.html
[email protected] • ENGR-36_Lec-01_Introduction.ppt11
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Engineering Product Design
[email protected] • ENGR-36_Lec-01_Introduction.ppt12
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
• 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
[email protected] • ENGR-36_Lec-01_Introduction.ppt13
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt14
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt15
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Assumption Digression BMayer 2001 JVST Paper
• See ENGR45 for More Details
[email protected] • ENGR-36_Lec-01_Introduction.ppt16
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Assumption Digression PARTIAL Assumption List
• 100% Vapor Saturation at Bubble Edge• Gases in bubble behave as perfect gases• Bubbles are Spherical
– Radial Symmetry
• Diffusion Coefficient is Constant
[email protected] • ENGR-36_Lec-01_Introduction.ppt17
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt18
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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”
[email protected] • ENGR-36_Lec-01_Introduction.ppt19
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 BodiesStatics → NO MotionDynamics → Moving in General
– Deformable Bodies → Forces Interact with MATERIAL Properties 3rd yr course at the University Level
– Fluid Mechanics → almost always deforming materialsCompressible → gas Incompressible → liquids
[email protected] • ENGR-36_Lec-01_Introduction.ppt20
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt21
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
!00but FaaF m• Consequences of Static Rigid-Body Conditions
– System Accelerations Are ZERO– Force InterActs with CONFIGURATION Only – governing equations are ALGEBRAIC In Nature
[email protected] • ENGR-36_Lec-01_Introduction.ppt22
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Statics - Fundamental Concepts Static Analysis is Based on
Incompletely Defined, But Thoroughly Familiar Concepts1. SPACE ≈ The Geometric Region
Occupied By Bodies Whose Positions Are Described By Linear and Angular MeasurementsRelative to a Coordinate System
2. TIME ≈ The Measure Of TheSuccession 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
CartesianSpace
[email protected] • ENGR-36_Lec-01_Introduction.ppt23
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 Laws1. 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).
[email protected] • ENGR-36_Lec-01_Introduction.ppt24
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Newtonian Mechanics cont.2. Force Is Equal To Body
Mass Times its Acceleration; MathematicallyaF m
3. For Every Action There Is Always An Opposite And Equal Reaction that is CoLinear
Sir Issac Newton
Note: for STATIC; i.e., NonMoving, systems a = 0
[email protected] • ENGR-36_Lec-01_Introduction.ppt25
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Systems of Units Base units For Static Analysis
System Length Mass TimeSI Units Meter (m) Kilogram (kg) Second (s)US Customary Units 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
[email protected] • ENGR-36_Lec-01_Introduction.ppt26
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 NO → 789,321 s
[email protected] • ENGR-36_Lec-01_Introduction.ppt27
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt28
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt29
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 1hr
= 3600sand 1m = 3.281ft
sft
shr
mift
hrmi
fps 8836001528060
sm
ftm
sft
SI 82.26281.3188
[email protected] • ENGR-36_Lec-01_Introduction.ppt30
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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)
(reliably)10.4calc)(by 391.103
803.79.947.13
avg
– In This Example, the Middle Value Governs Precision
[email protected] • ENGR-36_Lec-01_Introduction.ppt31
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt32
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
CoOrdinate Systems The CoOrd TriAd is Defined by Your
RIGHT Hand → Rt-Hand Rule
[email protected] • ENGR-36_Lec-01_Introduction.ppt33
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt34
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Vectors VECTOR ≡ Parameter Possessing
Magnitude And Direction, Which Add AccordingTo 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
[email protected] • ENGR-36_Lec-01_Introduction.ppt35
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt36
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Vector Representations Mag-
Angle
• Magnitude ≡ ||V|| = Geometric Length
• Space Angles: θx, θy, θz
Unit Vectors
• Length of “Unit” Vectors (i, j, k) = 1
More on Vector “DeComposition” in future lectures
[email protected] • ENGR-36_Lec-01_Introduction.ppt37
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Engineering Drawings Formal Drawing
• Contains all information needed for FABRICATION or ASSEMBLY
Informal Drawing
[email protected] • ENGR-36_Lec-01_Introduction.ppt38
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Free-Body Diagrams
SPACE DIAGRAM A Sketch Showing The Physical Conditions Of The Problem
FREE-BODY DIAGRAM A Sketch Showing ONLY The Forces Acting On The Selected Body
[email protected] • ENGR-36_Lec-01_Introduction.ppt39
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Suggested Review → Trig Solving Statics Problems Often Involves
Non-Right Triangle Geometry. Some Useful Relationships (See your Math Book)
Law of Sines
a=13, c=17, B=43°• A=31.4°, C=105.6°
b=24
a=11, b=19, C=101°• c = 23.7
Law of CoSines
[email protected] • ENGR-36_Lec-01_Introduction.ppt40
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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 theIncluded 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
[email protected] • ENGR-36_Lec-01_Introduction.ppt41
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Done for 1st MeetingPlease see
me if you would like to ADD
Static Loading
[email protected] • ENGR-36_Lec-01_Introduction.ppt42
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Bruce Mayer, PERegistered Electrical & Mechanical Engineer
Engineering 36
Appendix
[email protected] • ENGR-36_Lec-01_Introduction.ppt43
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Newtonian Mechanics cont.2. Force Is Equal To Body Mass Times its
Acceleration; Mathematically aF m
SCALAR) a (2 FrGMmF
M
m
-F
F
3. For Every Action There Is Always An Opposite And Equal Reaction
Newton’s Law of Gravitation
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt44
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
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)
mg
RGMmF
hRGMmF
22 h Rbut
mgW
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
[email protected] • ENGR-36_Lec-01_Introduction.ppt45
Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics
Earth Facts D 7 926 miles (12 756 km) M 5.98 x 1024 kg
• About 2x1015 EmpireState Buildings
Density, 5 520 kg/m3 • water 1 027 kg/m3
• steel 8 000 kg/m3
• glass 5 300 kg/m3