# 6.2 Problem Set

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 $$0 \leq x \leq 15$$

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. $$y=a \sin (x)$$

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

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 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.

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 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.

>> 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 Display the two plots created earlier in one plot. 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 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: Then execute the following:
plot(Strain,Stress),title('Stress versus Strain Curve'),xlabel('Strain [mm/mm]'),ylabel('Stress [mPa]'),grid ## 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)