ENGR 102 PROBLEM SOLVING FOR ENGINEERS

Transcription

1 PRACTICE EXAM 1. Problem statement 2. Diagram 3. Theory 4. Simplifying assumptions 5. Solution steps 6. Results & precision 7. Conclusions ENGR 102 PROBLEM SOLVING FOR ENGINEERS I N T O / C S U P A R T N E R S H I P Lecture # 8 February 08, 2018

2 OBJECTIVES FOR ENGR 102 Source: athenadr.files.wordpress.com 1. Work in a typical US university environment 2. Understand and solve engineering word problems 3. Analyze data and present engineering information 4. Understand several engineering concepts 5. Ability to use an engineering problem solving process 6. Use software tools: Microsoft Excel and MATLAB 7. Describe jobs in different engineering disciplines 8. Describe courses needed to graduate as an engineer 2

3 ASSIGNMENT 7 - PRACTICE EXAM (Chapters 1-2, 4-6, and 17) Chapters 1-2: The engineering profession Chapter 4: Use the problem solving process Chapter 5: Know Excel and graphing techniques Chapter 6: Significant digits, accuracy, and precision for estimation. Chapter 17: Electrical circuits + Need the vocabulary to understand all sections 3

4 ASSIGNMENT 7 (Due before 12 noon on Thursday, February 14) 1. Number of students in this class = 8 2. Students with homework on time = 7 3. Number of students with full credit = 7 4. Students with all answers correct = 0 4

5 Correct Answers on ASSIGNMENT 7 Question Points Students who had this 100% right 1. Word definition & usage 20 0 (1x15, 1x14) 2. Engineering functions & disciplines Ethics Electrical circuits Excel formulas and functions Graphing Solving functions Solving a flow rate problem (7-step process, digits, right answer)

6 ASSIGNMENT 7 Approximate distribution of student grades 6

7 STUDYING WORDS (VOCABULARY) Use flash cards or Quizlet to study new words Study how words are used in the context Focus on verbs and nouns When reading new text, look up only the words needed to understand the main ideas Infer meaning based on context before looking the word up in the dictionary What s your technique for learning the words? 7

8 STUDYING WORDS (VOCABULARY) Bert s technique: Write a 6-word maximum definition Find a synonym or synonyms. Think of a simple useful sentence Example: Syntax Simple definition: word arrangement Synonym: structure Simple sentence: Excel formulas give incorrect results if there are syntax errors. 8

9 Examples of vocabulary errors (Need definition and sample sentence) a. Preponderance bigger number or more important A preponderance of students did not provide sample sentences. b. Precision repeatability of result For engineers, precision is not the same as accuracy. 9

10 Examples of vocabulary errors (Need definition and sample sentence) c. Natural logarithm inverse of e x A natural logarithm is a mathematical function related to growth. d. Power law y=bx b A power law function is a straight line on a log-log graph. 10

11 Examples of vocabulary errors (Need definition and sample sentence) e. Magnitude - size of something That earthquake had a magnitude of 8. 11

12 Assignment 7: Vocabulary (Need definition and sample sentence) f. Syllabus summary of course content Every college class has a syllabus. g. Potential difference (electrical) voltage The potential difference is 9 volts. h. Network interconnected people or things This electrical circuit is a network of resistors. i. Operations job function related to running things He manages the operations of the factory. j. Sanction penalty or official permission You are sanctioned to use your calculator for the exam. 12

13 A7: Engineering Functions & Disciplines _e_ Electrical/Computer engineer (Most popular engineering discipline in US) _f d b c a_ Environmental engineer (Works with natural resources) Civil engineer (Oldest engineering profession) Research engineer (Most similar to a scientist) Consulting engineer (Most likely to have own business) Design engineer (Draws devices, processes, and structures) 13

14 Assignment 7: Ethics (True or False) 14

15 Assignment 7: Electrical Circuits V A Theory: Ohm s law: V=IR Kirchhoff s voltage law: Sum of voltages in loop is 0 Kirchhoff s current law: Sum of currents at a node is 0 Eq 1: 12V - R(0.2A) = (i 1 )18Ω (Ohm s + Voltage Law) Eq 2: 12V - R(0.2A) = (i 2 )21Ω -15V (Ohm s + Voltage Law) Eq 3: (i 2 ) + (i 1 ) = 0.2A (Kirchhoff s Current Law) i 1 i 2 Solve Eq 1 for i 1 : i 1 = (1/18)(12 - R(0.2)) i 1 = (2/3) - R/90 Solve Eq 2 for i 2 : i 2 = (1/21)(27 - R(0.2)) i 2 = (9/7) - R/105 Sub i 1 and i 2 in Eq3: (2/3) - R/90 + (9/7) - R/105 = 0.2 R(1/90+1/105) = (2/3) + (9/7) 0.2 R = ((2/3) + (9/7) 0.2)/(1/90+1/105) = = 85Ω (2 sig digits) Power = (Volts)(Amps) for each resistor Volts = (Amps)(Ohms) for each resistor Power is therefore: (Amps) 2 (Ohms) for each resistor i 1 = (2/3) - R/90 = (2/3)-(85/90) = i 2 = (9/7) - R/105 = (9/7)-(85/105) = Power = (0.2) 2 (R)+(i 1 ) 2 (18)+(i 2 ) 2 (21) = (0.2) 2 (84.923)+( ) 2 (18)+( ) 2 (21) = = = 9.6 W (2 sig digits) 15

16 ASSIGNMENT 7 Question 5: Excel Formulas, Operators, and Functions In Excel, a formula is written in the following format (syntax): =(A1*$A2)+(A$3/2) $A$5 A function in Excel is defined as: a programmed relationship between an input variable or variables and an output variable. You need the following Excel functions and operators in this class: ABS() ACOS() ASIN() ATAN() AVERAGE() CONVERT() COS() COUNT() DEGREES() EXP() INT() LN() LOG() MAX() MEDIAN() MIN() PI() POWER() RADIANS() ROUND() SIN() SQRT() STDEV() SUM() TAN() Operators: + - * / ^ ( ) 16

17 ASSIGNMENT 7 Question 5: Excel Formulas, Operators, and Functions 17

18 ASSIGNMENT 7 Question 8 Problem Solving Process The seven steps in the problem-solving process are: On the exam (and homework) you must apply this process 18

19 ASSIGNMENT 7 Question 8 Problem Solving Process The seven steps in the problem-solving process are: 1. Problem statement 2. Diagram 3. Theory 4. Assumptions 5. Solution steps 6. Identify results & verify accuracy 7. Discussion / conclusion On the exam (and homework) you must show and apply this process 19

20 ASSIGNMENT 7 Question 8 Problem Solving Process 2. Diagram 3. Theory d = 100 m h = 10 cm a. Volume of a cylinder: V = πd 2 h/4 4. Assumptions: Lake is in the shape of a cylinder Does 100m circular mean circumference or diameter? 20

21 ASSIGNMENT 7 Question 8 Problem Solving Process 5. Solution step and 6. Result: 7. Conclusion: Must be careful about significant digits 21

22 SIGNIFICANT DIGITS The columns in a number that that can be used to express the precision of a number, starting with the left-most nonzero column and extending to the right-most non-zero column. The number of significant digits for your answers in this class must be consistent with the precision of the inputs. I will allow 1 more significant digit, but you should identify that you added one digit and are uncertain. 1 significant digit: 400, 3, significant digits: 410, 3.1, significant digits: 5280, 3.14, To avoid confusion, use scientific notation: 4.00 x 10 2 (3 sig digits) 400 (probably 1 sig digit) 22

23 ASSIGNMENT 7 Question 6: Graphing and Functions 23

24 ASSIGNMENT 7 Excel and Graphing- XY Scatter Diagrams with Linear & Log Scales 24

25 RECTANGULAR, SEMI-LOG AND LOG-LOG CHARTS On a linear scale, a given addition to a value is always the same distance On a logarithmic scale a given multiplier (for example 10) is always the same distance: Rectangular chart: two linear axes Semi-log chart: one linear axis and one logarithmic axis Log-log chart: two logarithmic axes

26 METHOD OF SELECTED POINTS (SEE TEXTBOOK 5.6) The method of selected points can find a y=mx+b equation to fit data that has a linear relationship. Once the data is plotted and you decide that a linear (y=mx+b) equation is good, place a line that appears to best fit the data by going through as many data points as possible and having the same number of data points on either side. A similar method can also be used for exponential, logarithmic and power law functions using y=(b)e mx or y=(b)10 mx for an exponential function y=m+(b)ln(x) or m+(b)log 10 (x) logarithmic function y=bx m for a power law function 26

27 WHICH FUNCTIONS PRODUCE A STRAIGHT LINE ON WHICH CHART (function) y = mx + b (linear relationship) y = m+(b)ln(x) Y= m+(b)log 10 (x) (logarithmic) y = (b)e mx y = (b)10 mx (exponential) y = bx m (power law) RECTANGULAR CHART Linear Linear SEMI-LOG CHART X is logarithmic SEMI-LOG CHART Y is logarithmic LOG-LOG CHART Straight line Curved line Curved line Curved line Curved line Straight line Curved line Curved line Curved line Curved line Straight line Curved line Curved line Curved line Curved line Straight line Note: In an Excel formula, log(a1) means: log 10 (x) In an Excel formula, ln(a1) means: ln(x) In an Excel formula, exp(a1) means: e x In an Excel formula, 10^(A1) means: 10 x 27

28 GENERAL APPROACH TO CURVE FITTING USING TWO POINTS The equation for a straight line (linear) relationship: y = m x + b Find x and y values for two points: y 1 = m x 1 + b y 2 = m x 2 + b (X 1,Y 1 ) Solve the two simultaneous equations for a and b: m = (y 2 - y 1 ) / (x 2 - x 1 ) b = (x 2 y 1 - x 1 y 2 ) / (x 2 - x 1 ) 2 1 (X 2,Y 2 ) 28

29 IF YOU SEE A STRAIGHT LINE ON A GRAPH, YOU CAN CALCULATE m AND b Equation Straight line on this type of graph Solve using y = mx + b Linear-Linear y 1 = m x 1 + b y 2 = m x 2 + b y = m+(b)ln(x) y = (b)e mx Semi-Log (X is logarithmic) Semi-Log (Y is logarithmic) y 1 = m + b ln(x 1 ) y 2 = m + b ln(x 2 ) ln(y 1 )= m x 1 + ln(b) ln(y 2 )= m x 2 + ln(b) y = bx m Log-Log log(y 1 )= m log(x 1 ) + log(b) log(y 2 )= m log(x 2 ) + log(b) 29

30 ASSIGNMENT 6 BEST ANSWERS: y = (0.0202)x y = (49.14)x y = (0.0434)x (0.696) y = (90.27)x (1.433) Linear (y = mx + b) x is Q, y is H Linear (y = mx + b) x is H, y is Q Power Law (y = bx a ) x is Q, y is H Power Law (y = bx a ) x is H, y is Q 30

31 Linear regression on TI-84 calculator 1. Enter data into L1 and L2 (STAT -> EDIT -> ENTER) L1 is for X values, L2 is for Y values 2. To get y = ax + b best fit: STAT -> CALC -> 4 (LinReg) -> ENTER 3. To get a plot: STAT -> CALC -> 4 (LinReg) -> L1 -> L2 -> GRAPH Make sure that the screen is clear before doing this Enter equation using Y= to show data and line 4. To learn more: 31

32 Power law regression on TI-84 calculator 1. Enter data into L1 and L2 (STAT -> EDIT -> ENTER) L1 is for X values, L2 is for Y values 2. To get y = ax + b best fit: STAT -> CALC -> A (PwrReg) -> ENTER 3. To get a plot: STAT -> CALC -> A (PwrReg) -> L1 -> L2 -> GRAPH 4. Logarithmic (LnReg) and Exponential (ExpReg) regression work similarly 5. Go to Catalog and set DiagnosticOn to see correlation coefficients 32

33 ASSIGNMENT 7 Question 7 This is an exponential function 33

34 WHAT S NEXT (See First exam is Tuesday, 19 February Make sure you bring your calculator Assignment 8: due noon Thursday, 21 February Units and dimensions Assignment 9: due noon Tuesday, 26 February Matlab, gas law, and energy Project part 1 is due noon, Tuesday, 5 March 34