[email protected] ENGR-36_Lec-01_Introduction.ppt 1 Bruce Mayer, PE Engineering-36: Vector...

[email protected] • ENGR-36_Lec-01_Introduction.ppt1

Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 36

Chp 1Introductio

n



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”



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



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



Mastering Engineeringhttp://www.masteringengineering.com/



Mastering Engineeringhttp://www.masteringengineering.com/site/register/new-students.html

Pick One, then Continue



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



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



Your instructor may provide specific instructions for completing this field.

If so, enter the appropriate information and click Continue.

If you are not sure what to enter, contact your instructor or click Skip

This Step.

(You can enter your Student ID later.)

W12345678

Use “W” Number as Student ID



Registering Tips Video

http://www.masteringsupport.com/videos/registration_tips/registration_tips.html



Engineering Product Design



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



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



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



Assumption Digression

BMayer 2001 JVST Paper• See

ENGR45 for More Details



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




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




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”



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



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



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



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



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).



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



Systems of Units

Base units For Static AnalysisSystem Length Mass Time

SI 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



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



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



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



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

s

ft

s

hr

mi

ft

hr

mifps 88

3600

1528060

s

m

ft

m

s

ftSI 82.26

281.3

188



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



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



CoOrdinate Systems

The CoOrd TriAd is Defined by Your RIGHT Hand → Rt-Hand Rule



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



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



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



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



Engineering Drawings

Formal Drawing

• Contains all information needed for FABRICATION or ASSEMBLY

Informal Drawing



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



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



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



Done for 1st Meeting

Please see me if you would like to ADD

Static Loading



Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 36

Appendix



Newtonian Mechanics cont.2. Force Is Equal To Body Mass Times its

Acceleration; Mathematically aF m

SCALAR) a (2

Fr

GMmF

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



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

R

GMmF

hR

GMmF

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



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

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