Transcript ENGR-36_Lec-01_Intro_General_Principles_H13ex

Engineering 36
Chp 1
Introduction
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
[email protected]
Engineering-36: Vector Mechanics - Statics
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Bruce Mayer, PE
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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”
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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If you can’t Make the Lab Every
time... Don’t Worry
 I 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
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Mastering Engineering
http://www.masteringengineering.com/
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Bruce Mayer, PE
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Mastering ENGR↔PHYS
 Mastering Engineering is VERY Similar
in “Look & Feel” to Mastering Physics
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Mastering Engineering
http://www.masteringengineering.com/
 Course ID
 Student ID
• Please use Chabot Student “W” Number
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Bruce Mayer, PE
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Use BookStore Version
 This Term we will use The Special
“California (13th) Edition” of the text
• Comes bundled with Mastering
Engineering
• Available in Bookstore
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
[email protected] • ENGR-36_Lec-01_Introduction.ppt
Engineering Analysis
 Goal
• What EXACTLY do we want to determine?
– MUST 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
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Assumption Digression
 BMayer 2001 JVST Paper
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Bruce Mayer, PE
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Assumption Digression
 PARTIAL
Assumption List
• 100% Vapor
Saturation at Bubble
Edge
• Gases in bubble
behave as perfect
gases
• Bubbles are
Spherical
– Radial Symmetry
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• Diffusion CoEfficient
is Constant
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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
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Bruce Mayer, PE
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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”
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Bruce Mayer, PE
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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
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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).
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Bruce Mayer, PE
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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
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Sir Issac Newton
Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
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NO → 789,321 s
Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
 SI
1hr = 3600s
mi   5280 ft   1hr 
ft



88
 
 

hr   mi   3600s 
s
m
 ft   1m 
  26.82
  88   
s
 s   3.281 ft 
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and
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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CoOrdinate Systems
 The CoOrd TriAd is Defined by Your
RIGHT Hand → Right-Hand Rule
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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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
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Bruce Mayer, PE
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Vector Representations
 MagAngle
 Unit Vectors
• Length of “Unit”
Vectors (i, j, k) = 1
• Magnitude ≡ ||V||
= Geometric Length
• Space Angles:
θx, θy, θz
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 More on Vector
“DeComposition” in
future lectures
Bruce Mayer, PE
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Engineering Drawings
 Formal Drawing
 Informal Drawing
• Contains all
information needed
for FABRICATION or
ASSEMBLY
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Bruce Mayer, PE
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Free-Body Diagrams
 SPACE DIAGRAM 
A (hopefully good)
Sketch Showing
The Physical
Conditions Of The
Problem
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 FREE-BODY
DIAGRAM  A
Sketch Showing
ONLY The Forces
Acting On The
Selected Body
Bruce Mayer, PE
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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, b=24, B=43°
 a=11, b=19, C=101°
• A=21.7° → C = 115.3°
• c = 23.7
• c = 31.8
• Then Find A & B
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Bruce Mayer, PE
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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 (calc 3rd Angle First)
• 2-SIDES & NonIncluded Angle
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Bruce Mayer, PE
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Done for 1st Meeting
 Please see
me if you
would like to
ADD
Static Loading
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Bruce Mayer, PE
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Engineering 36
Appendix
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
[email protected]
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Bruce Mayer, PE
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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 2
( F a SCALAR)
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
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Bruce Mayer, PE
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-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
R  h 2
GM
but R  h  F  m 2  mg
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
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W  mg
Bruce Mayer, PE
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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
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Bruce Mayer, PE
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Engineering Product Design
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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
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• 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
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 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