chapter 6 problem solving. chapter 5 summary types of problems analytical problem solving...
Post on 25-Dec-2015
238 Views
Preview:
TRANSCRIPT
Chapter 6
Problem Solving
Chapter 5 Summary
Types of ProblemsAnalytical Problem Solving Estimations
Creative Problem Solving Brainstorming
Recall “Engineering” DefinitionFunctional Description: Short Answer = Technical PROBLEM
SOLVING The Output of ALL Engineering is
The Solution to a Practical Problem Fulfillment of a Practical Need
Long Answer = PRACTICAL-PROBLEM SOLVING Through the Application of the Quantitative (Number-Based) Disciplines Mathematics Sciences; e.g., Physics, Chemistry, Biology Empiricism (Experiments and Tests)
Class Exercise
What IS a Problem? i.e., DEFINE “Problem”
1. ?2. ?3. ?4. ?5. ?6. ?
What is a “Problem”
A Problem Short Definition: is Any Question or
Matter Involving Doubt, Uncertainty or Difficulty
Long Definition: is a situation, quantitative or qualitative, that confronts an individual or team, that requires resolution, and for which the individual/team sees NO APPARENT PATH TO THE SOLUTION
Types of Problems
ResearchKnowledge/UnderstandingTroubleshootingMathematicsResourceSocialDesign
Classes of Problems…detail
Scientific Research Prove/Disprove a hypothesis (explanation)
Example: A scientific hypothesis may be that Room Temperature Superconductivity is Produced by a Specific Molecular-Electronic Configuration of Rare-Earth Ceramic Materials
Understanding Example: an engineer notices That a CVD
Machine Behaves Differently In Denver Than in Kyushu
Classes of Problems cont.Trouble Shooting The Video Output of an Inspection
MicroScope Works Fine With “composite” (single-cable) Video Signals, but “S” (Super VHS or 2-cable) Video Signals Produce a BLACK Screen
Math Problems Find Pv that Satisfies This
Equationt
P
Dr
Pr
rrv
v
v
11 2
2
Digression – Soln to Math Prob
Liquid Source Vapor Bubble Saturation Transient
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0 2.3 2.5
Radial Position Inside Bubble, r (mm)
Va
po
r S
atu
rati
on
Fra
cti
on
, v
Pv(r,t) (t=0.01 s)Pv(r,t) (t=0.04 s)Pv(r,t) (t=0.10 s)Pv(r,t) (t=0.15 s)Pv(r,t) (t=0.25 s)Pv(r,t) (t=0.35 s)Pv(r,t) (t=0.50 s)
file = BubPv(t)1.xls
• Bubble Diameter = 5 mm
• D for TEOS in N2 = 0.05 cm2/s Increasing Time
P r t
n r rn r r
evn o
o
n Dt r
n
o,sin
1 2 1 1
1
2 2 2
Classes of Problems cont.$-Resource Problems e.g.; How Will We Get The Money to
Fund our Start-Up Company?
Social Problems Example: How to Reduce Crime
Rates?
Design Problems e.g.; Design a New, Inexpensive,
Easy-to-Use, Attractive, Lightweight, Wireless Headset for Cell Phones
11
Common Engineering ProblemsCommon Engineering Problems Engineering Problems Generally Fall
into Two Broad Categories• Analytic• Creative
Analytic Problems (bridge failure load)• There is one correct answer• Involves math, number crunching,etc• Your toolbox
Creative Problems (design a bridge)• No one right answer• How you use your tools
12
Design ProblemsDesign Problems
Require The Maximum Application of Engineering Capability• Creativity
• Quantitative & Graphical Skill
• Teamwork
• Technical Knowledge
See also: http://www.asa3.org/ASA/education/think/intro.htm
13
Creative Problem Solving Creative Problem Solving 1. Identify problem2. Define goals3. Research similar attempts4. Brainstorm (team or individual)5. Analyze analytic problem solving here6. Develop models and test7. Make decision8. Communicate with team, specify9. Implement, commercialize10. Prepare post-implementation review and
assessment
Analytic Problem Solving
1. Drawing2. List Known Parameters3. Label Unknowns4. Equations5. Answer with Units
Example Problem
1. Drawing2. List Known Parameters3. Label Unknowns4. Equations V = Vo - gt ( g = 9.8
m/sec2 )5. Answer with Units
How long will a 0.058kg tennis ball be in the air if it is thrown upward at 45.7m/s?
Some Helpful Equations
Radius of a Circle or Sphere: rDiameter of a Circle or Sphere: d=2r Circumference of a Circle: S = 2r = dArea of a Circle: A= r2
Volume of a Sphere: V = (4/3) r3
Surface Area of a Sphere: A = 4r2
Volume of a Cylinder: V = hr2
Surface Area of a Cylinder: A= 2r2 + 2hrPythagorean Theorem: c2 = a2 + b2
Engineering Exercise
You are asked to build a storage tank for 22 cubic meters of gasoline.You want to use the least amount of metal to keep your construction costs low. Suppose that you use 1-centimeter thick steel sheets to create storage tanks.
Engineering Exercise (con’t)
If you had a tank in the shape of a cube, then how long would each side be?What would be the inner surface area of the tank?How much metal would you need (volume)?
Engineering Exercise (con’t)
If you had a tank in the shape of a sphere, then what would its radius be?What would be the inner surface area of the tank?How much metal would you need (volume)?
Engineering Exercise
If you had a tank in the shape of a cylinder, then what would its radius be?What would be the inner surface area of the tank?How much metal would you need (volume)?
Aha! We will need to make some assumptions.
TEAMWORK
Each team will now make a different assumption and record their results on the table on the chalkboard.
Who uses the least metal for the cylindrical tanks?
Team h r A Vmetal
1 h=0.5r2 h=1r
3 h=1.5r
4 h=2r
5 h=2.5r
6 h=3r
7 h=3.5r
8 h=4r
Recorders: To the chalk board…
Write down your team name.Write down your assumption about the connection between h and r.Write down the equation for the volume of a cylinder.Substitute.Solve for r.Find A.Find the volume of the metal. Vmetal
Optimization?Height=2 Radius
0
0.1
0.2
0.3
0.4
0.5
0.6
Vo
lum
e (
Cu
bic
Me
ters
)
0.5 1 2 3 4 5 6 7
Height to Radius Ratio
Cylindrical Tanks
How do we know that h=2r is the best?
1. We can use trial-and-error.2. We can prove it using calculus.
Estimation – a subset of analytical problems
Quick answers, when quick decisions needed (out in the field)Verify complicated analysisGain insight into issues involvedHow to “break in” young engineers!Ben Franklin estimated size of a molecule In the 18th century!
Estimation #1
Team Exercise Estimate How many Ping Pong balls can fill
this room (3 minutes)1. Drawing2. List Known Parameters3. Assumptions important!4. Label Unknowns5. Equations6. Answer with Units
Estimation #2
Team Exercise Estimate the speed of hair growth in
miles per hour. (3 minutes) What would be a more appropriate
unit for the speed of hair growth? Design an experiment that could
better estimate the speed of hair growth. (1 minute)
Back of the Envelope Calculations
A crude but educated guessWe estimate not only the values of numbers we need, but which numbers are appropriate, and how to perform the calculation the emphasis here is on “order of
magnitude” estimates – to the nearest factor of 10
it is also important to remember that these are rough estimates and to place only appropriate reliance on the results
Accuracy of calculationsA well-known curve of a calculation’s accuracy versus mental effort goes like:
% error
effort
errors in various assumptions cancel out so rapid apparent improvement is made
better understanding may actually make things worse
hard work means that the model yields improved results
R. HornseyBOTE 31
How many piano tuners live in NYC? Approximately how many people are in New York City?
10,000,000 Does every individual own a piano?
No Would it be reasonable to assert that "individuals don't tend to
own pianos; families do? Yes.
About how many families are there in a city of 10 million people?
Perhaps there are 2,000,000 families in NYC. Does every family own a piano?
No. Perhaps one out of every five does.
That would mean there are about 400,000 pianos in NYC.
R. HornseyBOTE 32
How many piano tuners are needed for 400,000 pianos? Some people never get around to tuning their piano; some people tune
their piano every month. If we assume that "on the average" every piano gets tuned once a year, then there are 400,000 "piano tunings" every year.
How many piano tunings can one piano tuner do? Let's assume that the average piano tuner can tune four pianos a day.
Also assume that there are 200 working days per year. That means that every tuner can tune about 800 pianos per year.
How many piano tuners are needed in NYC? The number of tuners is approximately 400,000/800 or 500 piano
tuners.
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt33
Bruce Mayer, PE Engineering-10: Intro to Engineering
BrainstormingBrainstorming – for creative – for creative problem solvingproblem solving
Definition of Brainstorming Different types of Brain Storming Ways to create effective Brainstorming How Brainstorming can be used
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt34
Bruce Mayer, PE Engineering-10: Intro to Engineering
Importance of BrainstormingImportance of Brainstorming
Increases ability to figure out different ways in which to cure or solve a problem• Can Yield Unexpected and Elegant
Solutions
Allows opportunity for synergism within a company or organization• Whenever Possible, Make the Session
Cross-Disciplinary
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt35
Bruce Mayer, PE Engineering-10: Intro to Engineering
BrainStorm(ing) DefinedBrainStorm(ing) Defined
BrainStorm• A sudden clever Plan or idea,
violent disturbance of the mind
BrainStorming• A CONFERENCE technique of Solving
Specific Problems, Amassing information, Stimulating Creative Thinking, Developing New Ideas by Unrestrained and Spontaneous Participation In Discussion
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt36
Bruce Mayer, PE Engineering-10: Intro to Engineering
Types of BrainstormingTypes of Brainstorming Individual
• Completely Private & Open– Don’t have to worry about
any one else's opinion
Group• Builds team unity • Use Other Peoples Ideas as “Jumping Off”
Points – a “NonLinear” Process• Helps To Create “Outside The Box”
Thinking
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt37
Bruce Mayer, PE Engineering-10: Intro to Engineering
¿¿¿¿Question??Question?? Has Anyone in the Class been Involved
in a Formal “BrainStorming” Session?
If So, can you briefly describe what happened?
Thanks so Much
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt38
Bruce Mayer, PE Engineering-10: Intro to Engineering
Effective BrainstormingEffective Brainstorming
Brainstorming is “Free Form”• But Without Proper Structure It can Lose
Focus and Wander off Track
At Session-Start Present the ISSUE and outline GROUND RULES• Yields more effective use of time
• Allows Everyone in the group to start thinking about the REAL ISSUE
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt39
Bruce Mayer, PE Engineering-10: Intro to Engineering
Rules of BrainstormingRules of Brainstorming
1. Stress quantity over quality• Want the Maximum Number of Ideas
2. Freewheeling should be encouraged• Want Violent Mind Disturbances
3. Suspend judgment • Negative Comments Inhibit The
Freewheeling Atmosphere
4. Ignore seniority• Everyone’s Ideas Have Equal Value
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt40
Bruce Mayer, PE Engineering-10: Intro to Engineering
BrainStorming CheckListBrainStorming CheckList
Proposed change Description
Substitute
Combine
Adapt
Modify, magnify, minify
Other uses
Eliminate
Rearrange, reverse
What is used: material, process, person place or approach ?
Could units/systems be combined
What else is like this, what can I copy, Does it suggest other ideas
Could I change meaning, color, form or shape? Can something be subtracted?
Are there new ways to use this ?
Can a part, function, person be removed ?
Can components be interchanged, can it be transposed, turned upside down ?
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt41
Bruce Mayer, PE Engineering-10: Intro to Engineering
BrainStorming Session BrainStorming Session Start with a specific statement of problem Allow all members time to assimilate problem Ask each member in turn Build on ideas, allow wild and wacky ones Write ideas down, do not interrupt flow
• WhiteBoard or FlipChart
When group is exhausted of ideas, go back and clarify• Prioritize Ideas Only
– Avoid Negative Comments if Possible
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt42
Bruce Mayer, PE Engineering-10: Intro to Engineering
Brainstorm an idea for a Final ProjectBrainstorm an idea for a Final Project
Should take no more than 20 hours to complete
Should cost no more than $15 in materials
Open ended -- a variety of solutions Fun to do Competitive in terms of performance Examples from past classes…
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt43
Bruce Mayer, PE Engineering-10: Intro to Engineering
Motivate the BrainStromersMotivate the BrainStromers
Reward the group for coming up with solution or new idea• Money talks
• Time off
Make it an “experience”• Provide Refreshments
• No Time Limits
• Professionally Uninhibited Environment
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt44
Bruce Mayer, PE Engineering-10: Intro to Engineering
Create an Effective AtmosphereCreate an Effective Atmosphere
The Normal Work Environment can be• Unconsciously Inhibiting
• Certainly Distracting (phones, eMail, etc.)
Leave work premises – Be Creative• Manager’s Home
• Roaring Camp Small-Gage RailWay
• A Different Company Facility
Take ROUTINE away from the situation
BMayer@ChabotCollege.edu • ENGR-10_Lec-16_Problem_Solving.ppt45
Bruce Mayer, PE Engineering-10: Intro to Engineering
BrainStorming SummaryBrainStorming Summary
Brain Storming Is Effective When Done Right• Can be A WASTE OF TIME if Done Wrong
Can help to create Team/Org Unity Helps to Take Routine Away From The
Office – Encourages New Thinking New Ideas Get Generated For Possible
Solutions
top related