ENGR 132. Fall Exam 1 SOLUTIONS

Transcription

1 ENGR 3 Fall 03 Exam SOLUTIONS INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work! Keep your work covered at all times!. Each studet is resposible for followig directios. Read carefully.. MATLAB ad Excel commads are provided o the ext page. 3. This exam cosists of 7 questios o 7 pages (4 sheets frot AND back). Check to be sure that you have all of the pages. 4. Write your ame, PUID, Sectio #, ad Team # o both sides of the aswer sheet. 5. Closed book ad otes. 6. No calculators. 7. Please make sure you retur the aswer sheet (you may keep this booklet). 8. Elemet-by-elemet computatios are to use appropriate otatio ONLY where ecessary. Academic Itegrity Statemet I have ot used material obtaied from ay other uauthorized source, either modified or umodified. Neither have I provided access to my work to aother. The solutios I am submittig are my ow origial work.

2 Exam Formula Sheet ENGR 3 Fall 03 Statistics Equatios Liear Regressio Liear y = mx + b = ( x i x) a xi + b = yi Expoetial y = b e a xi + b xi = xi y mx i xi x y = b 0 i mx s = ( ) SSE = [ yi f ( x i )] Logarithmic x = b e my x = b 0 my SST = [ y i y] Power SSE y = b x r = m SST x = b y m s + - * / ^ =.*./.^ % & ~ && = = < > <= >= ' (traspose), : ; [ ] (ull vector) ( )... (ellipsis) abs acos all ay asi ata as char clc clear cos csc disp doc cumsum else elseif ed error exit exp factorial figure fid for format fpritf fuctio MATLAB Fuctios / Operators grid NaN help umstr hist oes hold pi i, j plot if polyfit If polyval iput prod leged quit legth roud lispace sec load semilogx log semilogy log0 si loglog size logspace sort lookfor sqrt max std mea strum media subplot mi sum ta title while who whos xlabel xor ylabel zeros GUI: hadles (variable) get guidata guide set Selectio of MATLAB plot Special Characters Lie Type Idicator Poit Type Idicator Color Idicator solid - circle o blue b dotted : x-mark x gree g dash-dot -. plus + red r dashed -- square s black k Excel Fuctios + - * / ^ = COS LOG0 MODE SQRT ABS EXP MAX OR STDEV AND IF MEDIAN PI SUM AVERAGE LN MIN SIN TAN

3 ENGR 3 Exam September 4, 03 Problem # (5 poits) The followig variables have bee assiged i the MATLAB Commad Widow: >> A = 3; >> B = 9; >> C = [, 4, 7, ]; >> D = [7, 0,, 5]; >> E = [4, 8; 0, 6]; >> F = [, 5, 7; 4, 0, ]; >> G = [6, ; 0, 4]; What is displayed i the MATLAB Commad Widow after each of the followig operatios is performed? If ay error message will result, explai the reaso for the error message. A. >> V = B / A >= C - B. >> W = ay(f > 4) all(d) C. >> X = all(~ay(g > )) D. >> Y = sum(fid((e > A) & (A + G < B))) E. >> Z = fid(e & G) Solutio: A. >> V = 0 B. >> W = 0 C. >> X = 0 D. >> Y = 7 E. >> Z = 3 4 Problem # (0 poits) For each of the scearios below, idetify the stage of team developmet, ad explai how a Code of Cooperatio is used durig that stage of team developmet. A. Tim ad Mary are ot gettig alog withi their team at all. They are costatly arguig with each other ad their teammates. B. Sasha, Jamal, Liz, ad Patrick are still learig how to work with each other ad are workig o their MEA Draft. C. Eve though they are oly a team of three, Mario, Luigi, ad Yoshi are workig well together will little coflicts or issues. 3

4 ENGR 3 Exam September 4, 03 Solutio: (Role of COC is a example respose, there are other possible resposes) A. Stormig A COC is a set of rules used to help teams get past persoal ad team coflicts ad mediate issues durig stormig B. Formig A COC is a documet that is writte whe a team first gets together to help the team work well i the future C. Performig A COC is used ad revised to maitai a team with peaked performace Problem #3 (5 poits) While you were tryig to ru a MATLAB user defied fuctio, the followig error message is displayed i the MATLAB Commad Widow: >> result = exam_prob3(x) Udefied fuctio or variable 'exam_prob3'. Which of the followig cause(s) explai the error message: [Circle ALL that apply.] a. The file exam_prob3.m does ot start with the word fuctio b. The ame of the file / fuctio is ot typed correctly c. Too may or too few iput argumets d. Too may or too few output argumets e. The file exam_prob3.m is ot i the curret path / active directory Solutio: b. The ame of the file is ot typed correctly e. The file exam_prob3.m is ot i the curret path / active directory 4

5 ENGR 3 Exam September 4, 03 Problem #4 (0 poits) Match each statemet from a MEA Team Memo (o the left) to ONE correspodig MEA Assessmet Dimesio (o the right). Note that ot all optios may be used ad some might be re-used. [Circle ONE respose for each.] A. Our model predicts that the roughess of gold sample A is 7.657%. B. Break the dataset ito four pieces, the take the mea of a radom sample of each piece. C. This procedure is limited to ao-scale surfaces. D. This step uses the distace from the highest peak to the lowest valley as described i ASME Stadard Y4.36M 996 Surface Texture Symbols. a. Usability b. Mathematical Model c. Reusability d. Modifiability e. Shareability E. The Materials Research Team eeds a way to determie the roughess of a surface give ay AFM image. Solutio: A. e. Shareability B. b. Mathematical Model C. c. Reusability D. d. Modifiability E. c. Reusability 5

6 ENGR 3 Exam September 4, 03 Problem #5 (5 poits) Cosider the followig three user defied fuctios myfu, myfu, myfu3 below: fuctio out = myfu(i, i) x = i + i; y = i - i; fpritf('i = %i, i = %i, out = Noe \', y, x) out3 = myfu(y,x); fpritf('i = %i, i = %i, out = %i \', i, i, out3) m = out3 + x; = out3 - y; fpritf('i = %i, i = %i, out = %i \', m,, x) [x, y] = myfu(m, ); out = m + + x + y; fpritf('i = %i, i = %i, out = %i \', i, i, out) fuctio [out, out3] = myfu(i3, i4) a = i3 * 5; b = i4 * ; c = (i3 * i4) + a - (a - b); out = a + b - c; out3 = a - b + c; fpritf('i = %i, i = %i, out = %i \', a, b, out3) fuctio myfu3 var = ; var = 3; [result] = myfu(var, var); fpritf('i = %i, i = %i, out = %i \', var, var, result) What will appear i the MATLAB Commad Widow whe the followig lies of code are executed at the MATLAB prompt: >> clear all >> var = 4; >> var = ; >> myfu3 6

7 ENGR 3 Exam September 4, 03 Solutio: i = -, i = 4, out = Noe i = -0, i = 8, out = -8 i =, i = 3, out = - i =, i = 0, out = 4 i = 0, i = 0, out = 0 i =, i = 3, out = i =, i = 3, out = Problem #6 (5 poits) To characterize productio efficiecy o the plat floor, a idustrial egieer ivestigated the percet of time that parts for a project were available whe they were eeded. Usig the data collected, the followig histogram was created i MATLAB. A. The collected data used to geerate the histogram is stored i the variable part_data as a vector. Usig the data variable part_data, write the MATLAB code ecessary to calculate the two vectors eeded to create a cumulative distributio plot. Do ot write the code to make the plot. B. Create a cumulative distributio plot suitable for techical presetatio from the give histogram o the axes provided o the aswer sheet. C. Usig the cumulative distributio plot from Part B, what is the likelihood that a part will be available whe eeded at least 8% of the time? 7

8 ENGR 3 Exam September 4, 03 Solutio: A. ceters = 79::90; bi_width = ceters() ceters(); freq = hist(part_data, ceters); Data = legth(part_data); rel_freq = freq / Data; cum_prob = cumsum(rel_freq); cum_prob_corrected = [0, cum_prob]; right_edges = [ceters() /*bi_width, ceters + /*bi_width]; B. C. % of Time 8 ( 0.30) = or 70% 8

9 ENGR 3 Exam RECORD ALL ANSWERS ON THE ANSWER SHEET September 4, 03 Problem #7 (0 poits) Lucy has created a user-defied fuctio to calculate the surface area, the volume, ad the mass of a thick-walled hollow cylider made out of alumium. Lucy iteds this user-defied fuctio to accept vector iputs. The relevat equatios are listed below: Iputs: Outputs: h = Height [cm] A = Surface Area [cm ] R = Outer Radius [cm] V = Volume [cm 3 ] r = Ier Radius [cm] M = Mass [g] Equatios: V = π h (R r ) OS = π R h IS = π r h BS = π (R r ) A = OS + IS + BS ρ =.7 M = ρ V [Volume cm 3 ] [Outerr Wall Surface Area cm ] [Ier Wall Surface Area cm ] [Basess Surface Area cm ] [Surface Area cm ] [Desity of Alumium g/cm 3 ] [Mass g] Lucy s fuctio is saved to hollowtube.m ad is show below. Ufortuately, Lucy could ever stay awake i ENGR 3 lectures, so the MATLAB code cotais various errors i sytax ad calculatios. (A, V, M) Fuctio = Lucy_tube[H, R, r] volume = pie.* h.* (R^ - r^); % Volume of Hollow Tube outer =.* pie * R * h; ier =.* pie * r * h; bases =.* pie * (R^ + r^); area = OS.+ IS.+ BS; % Surface Area of Outer Wall % Surface Area of Ier Wall % Surface Area of Two Bases % Total Surface Area of Tube rho =.7; mass = V + rho; % Desity of Alumium % Mass of Hollow T [g/cm^3] 9

10 ENGR 3 Exam September 4, 03 A. Re-write Lucy s MATLAB fuctio to elimiate all errors. Variable ames i the code should be cosistet with the equatios give above, ad commets are ot eeded. B. Lucy has defied the followig variables i her MATLAB Workspace: Solutio: A. >> H = [60, 70, 55, 00]; >> R_out = [, 8,, 5]; >> R_i = [, 7,, 3]; Lucy oly requires the mass of the cyliders defied by the variables above ad wats to store it i the variable Mass_Tubes. Write the oe lie of code that Lucy will eed to execute at the MATLAB Commad Widow to use her fuctio to get the mass. fuctio [A, V, M] = hollowtube(h, R, r) V = pi * h.* (R.^ - r.^); OS = * pi * R.* h; IS = * pi * r.* h; BS = * pi * (R.^ - r.^); A = OS + IS + BS; rho =.7; M = V * rho; % Volume of Hollow Tube % Surface Area of Outer Wall % Surface Area of Ier Wall % Surface Area of Two Bases % Total Surface Area of Tube % Desity of Alumium [g/cm^3] % Mass of Hollow Tube B. >> [A, V, Mass_Tubes] = hollowtube(h, R_out, R_i) Note: The ame for the first two output argumets was ot specified ad ca take ay ame. 0