ENGR Fall Exam 1 PRACTICE EXAM

Transcription

1 ENGR Fall 2012 Exam 1 PRACTICE EXAM INSTRUCTIONS: Duration: 60 minutes Keep your eyes on your own work! Keep your work covered at all times! 1. Each student is responsible for following directions. Read carefully. 2. MATLAB and Excel commands are provided on the next page. 3. This exam consists of x questions on y pages (z sheets front AND back). Check to be sure that you have all of the pages. 4. Write your name, PUID, Section #, and Team # on both sides of the answer sheet. NO ANSWER SHEET IS PROVIDED FOR THE PRACTICE EXAM. 5. Closed book and notes. 6. No calculators. 7. Please make sure you return the answer sheet (you may keep this booklet). 8. Element-by-element computations are to use appropriate notation ONLY where necessary. Academic Integrity Statement I have not used material obtained from any other unauthorized source, either modified or unmodified. Neither have I provided access to my work to another. The solutions I am submitting are my own original work.

2 Exam 1 Formula Sheet ENGR Fall 2012 s 2 s Statistics Equations 1 n 1 2 n n i1 n i1 n 2 xi i n n 1 ( x i x) 1 xi 2 2 MATLAB Functions / Operators + - * / ^ = ans grid max sort.*./.^ clc help mean sqrt % clear hist median std (transpose) cos hold min subplot, csc i, j NaN sum : doc Inf ones tan ; cumsum legend pi title [ ] (null vector) exit length plot who ( ) exp linspace prod whos (ellipsis) factorial load quit xlabel abs figure log round ylabel acos format log10 sec zeros asin fprintf logspace sin atan function lookfor size Selection of MATLAB plot Special Characters Line Type Indicator Point Type Indicator Color Indicator solid - circle o blue b dotted : x-mark x green g dash-dot -. plus + red r dashed -- square s black k Excel Functions + - * / ^ = EXP MIN STDEV $ LN MODE SUM ABS LOG10 PI TAN AVERAGE MAX SIN COS MEDIAN SQRT

3 Problem 1 List the five stages of team dynamics. Problem 2 a. What is a Code of Cooperation? b. Why is a Code of Cooperation important to a team? Problem 3 Given the following equation, write out the formula as it would appear if used in Excel. A = xz 2-2z 3x 3/5 Problem 4 Using high quality research sources can help you investigate and often manage complexity in problems. Name two things that can help you determine if you are using a high quality research resource/reference

4 Problem 5 Your team has been asked by the V.P. of Operations for the BIGBROWN shipping company to develop a draft/possible solution for a logistics problem that has been plaguing the company. The solution will involve providing an aircraft loading model which will maximize the number of mail packages loaded into their 747 aircraft that deliver the packages across country. Each 747 aircraft must have a least 1,820 packages to maximize BIGBROWN s profit dollars per plane load. Your team s solution will be used by the package loading supervisors. a) Name two possible stakeholders in this problem context: 1) 2) b) Name the direct user in this problem context: Your team quickly completes a draft solution and sends it back to the V.P. of Operations to get her early feedback. She s your team the following comments: Your team s work is impressive and I was quickly able to replicate the results you provided in your memo for the 747 package loading line. Unfortunately beginning December we will need to change to a larger/different aircraft to handle the increased holiday shipping of customers, and your model does not allow me to change the type/size of aircraft for loading. c) After reading the V.P. s comments, your team realizes they need to improve the of their draft solution, to make it more valuable to the BIGBROWN company. (Hint: Think about the 3 attributes of a high quality, generalizable solution)

5 Frequency Problem 6 The following MATLAB statement has been executed, establishing a vector of wait times in minutes, for people getting their order at the local 24-hour burger joint: >> WaitTimes = [10,5,6,3,7,6,5,1,6,1,6,6,5,3,4,12,6,10,2,7] A. The histogram below was created from the vector WaitTimes. The values along the x-axis mark the centers of the intervals. Write one or two line(s) of the MATLAB code to plot the histogram as shown in the figure below Wait Times at the Local Burger Joint Wait Times [min] B. For the vector WaitlTimes, the mean is 5.6 and the standard deviation is For your convenience in answering the following questions, MATLAB's sort command was executed as follows: SortedTimes = sort(waittimes) resulting in SortedTimes being: [1,1,2,3,3,4,5,5,5,6,6,6,6,6,6,7,7,10,10,12] How many data points fall within one standard deviation of the mean? Problem 7 In MATLAB, vector B = [2, 4, 6, 8] and vector C = [8, 7, 5, 9] are assigned. a. Write the proper MATLAB command to Multiply vector B and vector C b. Write the results MATLAB gives you after performing the element-by-element multiplication. c. Write the proper MATLAB command to raise vector B to the third power d. Write the results MATLAB gives you after performing this operation.

6 Problem Average High Temperatures by Month in West Lafayette, IN Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Referring to the chart above, indicate whether each statement is true or false. a. January is, on average, the coldest month in West Lafayette, Indiana. b. There is no need to include units since it can be assumed that the temperatures shown are in Fahrenheit. c. The chart readability could be improved with the addition of vertical gridlines and data markers. d. Line charts are used to show theoretic expressions, functional dependencies, or display evenly spaced or sampled data. e. Axis labels are extraneous. Problem 9 The following command lines were typed in a MATLAB script file. run_distance_data = load('rundistance_noheader'); male_distance = run_distance_data(1:83,1); % Male running distance [km] female_distance = run_distance_data(84:166,1);% Female running distance [km] You want to make a histogram of the female running distance. How many bins are needed according to the rule of thumb?

7 Conflic Effectiveness Problem 10 The graph below is used to describe the five stages of team dynamics. The dark curve shows the process of how conflict increases and then later decreases over time. The light curve shows the process of how effectiveness increases over time. A. B. C. D. E. Time a. State the names of the five stages (A, B, C, D, E) in this graph b. Which stage relates to the use of a Code of Cooperation? c. Justify your answer to #b

8 Problem 11 Circle ALL of the MATLAB commands that WILL or COULD potentially produce an error. a. >> 5 = a b. >> min(3,5,1) c. >> 4/3*sine(pi/2) d. >> velocity_1 = 30 e. >> data-run = [ ] Problem 12 Circle ALL of the MATLAB file names that WILL or COULD potentially produce an error. [circle all that apply] a. Hw8_prob2.m b. Hw8_prob2.m c. 10steptask1.m d. plot.m e. hole_diam_0.5.m f. Time@contact.m Problem 13 Given the MATLAB commands below: >> height = [ 6, 14 ; 3, 5 ] >> weight = [ 114, 188 ; 53, 91 ] >> total = [ height(:,1) weight(:,2) ] a. Create(write out) the matrix with the values that would populate height after the first line of code? b. Create (write out) the matrix with the values that would populate total after the second line of code?

9 Problem 14 A box is being pulled by a rope. The force that is required to move the box is given by: F F mg cos sin m where 0. 55is the friction coefficient and g 9. 81m/s 2. The values of the mass m and θ are given below. Cases m (kg) θ (degrees) Add one line of MATLAB code to complete the computation of the force for all three cases. (NOTE: You will be penalized for any extraneous dot notation in the code) >> friction_coeff = 0.55; >> gravity = 9.81; >> mass = [10, 20, 30]; >> theta = [30, 45, 60]; Problem 15 A mathematical model is reusable if [Circle only one] a) the user can apply the model and replicate results b) the model addressing the complexity of the problem in its context c) the purpose of the model and the assumptions and limitations concerning the use of the model are provided d) the steps in the model are adequately rationalized so that the user can rework the model for new but similar situations

10 Problem 16 Ball bearings are hardened through a process of heating and then rapid cooling by submersion in a water bath. The temperature of the ball as a function of time can be estimated using the following equation: T = (Ti Tw) e -t/α + Tw Where: T = temperature of the ball at time t (in degrees Celsius) Ti = initial temperature of the ball (in degrees Celsius) Tw = temperature of the water bath (in degrees Celsius) t = time (seconds) α = time constant (seconds) The following Excel spreadsheet was created to compute T, the ball temperature as a function of time, for two different initial ball temperatures. Excel was also used to create the plot shown. A B C D E 1 Temperature of water (Tw, C): 25 2 Time constant (α, sec): Initial Ball Temperature (C) 5 Time (t, sec)

11 Temperature (C) Ball bearing temperature as a function of time Initial Temp 250 C Time (s) Write a MATLAB script to verify the analysis above and replicate the plot. Use the MATLAB script below as a guide. Note that two variables have been created for you, but others still need to be created to complete the calculations. Adequately comment your code. You do not need to worry about replicating the location of the legend. More space is provided than may be necessary to complete the task. 1 % --- INPUTS Twater = 25 % water temperature (deg C) 3 ball_initt = [250,600] % 1st and 2nd initial ball temperature (deg C) % --- CALCULATIONS % --- OUTPUT % create a plot suitable for technical presentation of temperature as a function of time 17 % that includes two lines with different line colors, data markers, and line styles 18 % for initial ball temperatures of 250 and 600 C

12 Problem 17 Given the MATLAB commands: >> a = [1 2 3; 7 8 9] >> a(2,3) = 6 What will the resulting matrix a look like? Problem 18 The following matrix is already created in MATLAB: A = a) Write the proper MATLAB code to extract the first ROW from Matrix A. b) Write the proper MATLAB code to extract the third COLUMN from Matrix A.