# Example 9.9
MKS(mm)
l1 = 188.5 mm
x1 = 60 mm
y1 = -38.2 mm
z1 = 0 mm
l2 = 40 mm
x2 = 0 mm
y2 = 20 mm
z2 = 0 mm
l3 = 20 mm
x3 = 0 mm
y3 = 40 mm
z3 = -10 mm
suml = l1 + l2 + l3
xbar = (x1 * l1 + x2 * l2 + x3 * l3) / suml
ybar = (y1 * l1 + y2 * l2 + y3 * l3) / suml
zbar = (z1 * l1 + z2 * l2 + z3 * l3) / suml

# Example 9.10
FPS()
a1 = 4.5 ft^2
x1 = 1 ft
y1 = 1 ft
a2 = 9 ft^2
x2 = -1.5 ft
y2 = 1.5 ft
a3 = -2 ft^2
x3 = -2.5  ft
y3 = 2  ft
suma = a1 + a2 + a3
xbar = (x1 * a1 + x2 * a2 + x3 * a3) / suma
ybar = (y1 * a1 + y2 * a2 + y3 * a3) / suma

# Example 9.11
MKS(mm)
m1 = 4.189 kg
m2 = 1.047 kg
m3 = -0.524 kg
m4 = -1.571 kg
z1 = 50 mm
z2 = -18.75 mm
z3 = 125 mm
z4 = 50 mm
zbar = (m1 * z1 + m2 * z2 + m3 * z3 + m4 * z4) / (m1 + m2 + m3 + m4)

# Example 9.13
MKS(kPa, kN, kN /m)
rw = 1000 kg /m^3
za = 2 m
zb = 5 m
pa = rw * grav() * za
pb = rw * grav() * zb
b = 1.5 m
wa = b * pa
wb = b * pb
fr = 0.5 * 3 * (29.4 + 73.6) kN
h0 = 3 m
h = (1/3) * (2 * wa + wb) / (wa + wb) * h0
fre = wa * h0
fte = 0.5 * (44.15 kN /m) * h0

fr = fre + fte
h1 = (fre * h0 / 2 + fte * 1 m) / fr

# Example 9.14
MKS(kPa, kN, kN /m)
rw = 1020 kg /m^3
za = 3 m
pa = rw * grav() * za
b = 5 m
wa = b * pa
fx = 0.5 * za * wa
area = (1/3) * (1 m) * (3 m)
fy = rw * grav() * 5 m * area
mag([fx,fy])

# Homework Problems:

TBD