Skip to main content
Engineering LibreTexts

6.2 Problem Set

  • Page ID
    9469
  • Plot \(y=a+b x\), using the specified coefficients and ranges (use increments of 0.1):

    a. \(a=2, b=0.3\) for \(0 \leq x \leq 5\)

    b. \(a=3, b=0\) for \(0 \leq x \leq 10\)

    c. \(a=4, b=-0.3\) for \(0 \leq x \leq 15\)


    Answer:
    a. a=2; b=.3; x=[0:.1:5]; y=a+b*x; plot(x,y),title('Graph of y=a+bx'),xlabel('x'),ylabel('y'),grid b. a=3; b=.0; x=[0:.1:10]; y=a+b*x; plot(x,y),title('Graph of y=a+bx'),xlabel('x'),ylabel('y'),grid c. a=2; b=.3; x=[0:.1:5]; y=a+b*x; plot(x,y),title('Graph of y=a+bx'),xlabel('x'),ylabel('y'),grid

    Plot the following functions, using increments of 0.01 and \(a=6, b=0.8,0 \leq x \leq 5\):

    a. \(y=a+x^{b}\)
    b. \(y=a x^{b}\)
    c. \(y=a \sin (x)\)

    Answer:

    a. a=6; b=.8; x=[0:.01:5]; y=a+x.^b; plot(x,y),title('Graph of y=a+x^b'),xlabel('x'),ylabel('y'),grid

    屏幕快照 2019-05-25 21.25.41.png

    b. a=6; b=.8; x=[0:.01:5]; y=a*x.^b; plot(x,y),title('Graph of y=ax^b'),xlabel('x'),ylabel('y'),grid

    屏幕快照 2019-05-25 21.26.42.png

    c. a=6; x=[0:.01:5]; y=a*sin(x); plot(x,y),title('Graph of y=a*sin(x)'),xlabel('x'),ylabel('y'),grid

    屏幕快照 2019-05-25 21.27.27.png

    Plot function \(y=\frac{\sin (x)}{x}\) for \(\frac{\pi}{100} \leq x \leq 10 \pi\) using increments of \(\frac{\pi}{100}\)

    Answer:

    x = pi/100:pi/100:10*pi; y = sin(x)./x; plot(x,y),title('Graph of y=sin(x)/x'),xlabel('x'),ylabel('y'),grid

    屏幕快照 2019-05-25 21.34.03.png

    Data collected from Boyle's Law experiment are as follows: (Data available for download.)

    Volume [cm^3] Pressure [Pa]
    7.34 100330
    7.24 102200
    7.14 103930
    7.04 105270
    6.89 107400
    6.84 108470
    6.79 109400
    6.69 111140
    6.64 112200

    Plot a graph of Pressure vs Volume, annotate your graph.


    Answer:

    Pressure=[100330,102200,103930,105270,107400,108470,109400,111140,112200]; Volume=[7.34,7.24,7.14,7.04,6.89,6.84,6.79,6.69,6.64]; plot(Volume, Pressure),title('Pressure Volume Graph'),xlabel('Volume'),ylabel('Pressure'),grid

    屏幕快照 2019-05-25 21.38.53.png

    The original data collected from Boyle's 1 experiment are as follows: (Data available for download.)

    Volume [tube-inches] Pressure [inches-Hg]
    12 29.125
    10 35.000
    8 43.688
    6 58.250
    5 70.000
    4 87.375
    3 116.500

    Plot a graph of Pressure vs Volume, annotate your graph.


    Answer:

    >> P=[29.125,35,43.688,58.25,70,87.375,116.5]; >> V=[12,10,8,6,5,4,3]; >> plot(V,P),title('Pressure Volume Graph'),xlabel('Volume'),ylabel('Pressure'),grid

    屏幕快照 2019-05-26 12.13.42.png

    Display the two plots created earlier in one plot.


    Answer:

    屏幕快照 2019-05-26 12.14.46.png

    A tensile test of SAE 1020 steel produced the data below (Data available for download.) 2 experiment are as follows:

    Extension [mm] Load [kN]
    0.00 0.0
    0.09 1.9
    0.31 6.1
    0.47 9.4
    2.13 11.0
    5.05 11.7
    10.50 12.0
    16.50 11.9
    23.70 10.7
    27.70 9.3
    34.50 8.1

    Plot a graph of Load vs Extension, annotate your graph.


    Answer:

    Extension=[0.00,0.09,0.31,0.47,2.13,5.05,10.50,16.50,23.70,27.70,34.50]; Load=[0.0,1.9,6.1,9.4,11.0,11.7,12.0,11.9,10.7,9.3,8.1]; plot(Extension, Load),title('Load versus Extension Curve'),xlabel('Extension'),ylabel('Load'),grid

    屏幕快照 2019-05-26 12.21.36.png

    Given below is Stress-Strain data for a type 304 stainless steel. 3 experiment are as follows: (Data available for download.)

    Stress [MPa] Strain [mm/mm]
    0.0 0.0000
    38.6 0.0002
    77.2 0.0004
    115.8 0.0006
    154.4 0.0008
    193.0 0.0010
    218.0 0.0012
    232.0 0.0014
    258.0 0.0020
    268.0 0.0025
    273.0 0.0030
    278.0 0.0035
    282.0 0.0040
    320.0 0.0200
    382.0 0.0500
    466.0 0.1000
    520.0 0.1500
    548.0 0.2000
    550.0 0.2100
    538.0 0.2500
    480.0 0.3000

    Plot a graph of Stress vs Strain, annotate your graph.


    The data can be entered using Variable Editor:

    屏幕快照 2019-05-26 12.30.06.png

    Then execute the following:
    plot(Strain,Stress),title('Stress versus Strain Curve'),xlabel('Strain [mm/mm]'),ylabel('Stress [mPa]'),grid

    屏幕快照 2019-05-26 12.30.43.png

    Footnotes

    • 1 Introduction to Engineering: Modeling and Problem Solving by J. B. Brockman, John Wiley and Sons, Inc. © 2009, (p.246)
    • 2 Introduction to Materials Science for Engineers | Instructor's Manual by J. F. Shackelford, Macmillan Publishing Company. © 1992, (p.440)
    • 3 Introduction to Materials Science for Engineers by J. F. Shackelford, Macmillan Publishing Company. © 1985, (p.304)