HW3 Palm Chapter 2 (17, 18, 21, 22, 23, 35, 40).

Dr. Tim Placek - placetd@auburn.edu

Contents

Prob 17

clear, clc, format compact, format short g
%  part (a)
d1 = [-60,-25,30];
d2 = [-30,-55,20];
magD1 = norm(d1)
%  part (b)
D = d2 - d1
%  part (c)
magD = norm(D)
%  So diver 1 is 71.5891 ft from the starting point.
%  To get to diver 2, diver 1 must swim 30 ft west, 30 ft south,
%  and 10 ft up. To reach diver 2 in a straight line, diver 1 must swim
%  43.589 ft.

magD1 =
       71.589
D =
    30   -30   -10
magD =
       43.589

Prob 18

clear, clc, format compact, format short g
force = [11,7,8,10,9];
k = [1000,600,900,1300,700];
x = force./k           % distance (compression) unit meters
energy = 0.5*k.*x.^2   % energy unit joule

x =
        0.011     0.011667    0.0088889    0.0076923     0.012857
energy =
       0.0605     0.040833     0.035556     0.038462     0.057857

Prob 21

clear, clc, format compact, format short g
r = [2:0.01:10];
V = 500;
h = @(r) (V-2*pi*r.^3/3)./(pi*r.^2);
cost = 600*pi*r.*h(r)+800*pi*r.^2;
plot(r,cost)
xlabel('Radius (meters)')
ylabel('Cost ($)')
[radius,mincost] = ginput(1)
hmin = (V-2*pi*radius.^3/3)./(pi*radius.^2)
% min cost found using fminbnd
hcost = @(r) 600*pi*r.*h(r)+800*pi*r.^2;
mincost_using_fminbnd = fminbnd(hcost,4,6)

radius =
       4.9032
mincost =
        91126
hmin =
       3.3512
mincost_using_fminbnd =
       4.9237

Prob 22

clear, clc, format compact, format short g
% f = 1./sqrt(2*pi*c./x);
% E = (x + w./(y + z))./(x + w./(y - z));
% A = exp(-c./(2*x))./(log(y).*sqrt(d*z));
% S = x.*(2.15 + 0.35*y).^1.8./(z.*(1-x).^y);

Prob 23(a)

%C(t) = 0.5C(0) implies that 0.5 = e?kt. Solve for t: t = ?(ln 0.5)/k.
clear, clc, format compact, format short g
k = [0.047:0.001:0.107];
thalf = @(k) -log(0.5)./k;
plot(k,thalf(k))
xlabel('Elimination Rate Constant (h^1)')
ylabel('Half-Life (h)')

Prob 23(b)

clear, clc, format compact, format short g
a = 1;
k = [0.047:0.001:0.107];
C = a*(1 - exp(-k))./k;
plot(k,C)
xlabel('Elimination Rate Constant (1/h)')
ylabel('Concentration (dimensionless)')

Prob 35

clear, clc, format compact, format short g
p1 = [3,-6,8,4,90];
p2 = [3, 5, -8, 70];
x=[-3:0.01:3];
y = polyval(p1,x);
z = polyval(p2,x);
plot(x,y,x,z,'--')
xlabel('x')
ylabel('y and z')
gtext('y')
gtext('z')

Prob 40

arrange as PV^2(V ? b) = RT V^2 ? a(V ? b) put in function form: PV^3 - (Pb + RT) V^2 + aV - ab = 0

clear, clc, format compact, format short g
P = 0.95;
T = 300;
R = 0.08206;
a = 6.49;
b = 0.0562;
idealV = R*T/P
waalsV = roots([P,-(P*b + R*T),a,-a*b])

idealV =
       25.914
waalsV =
       25.705
      0.18403
     0.081164

Published with MATLAB® 7.10