# Example 7.4
MKS(mm)
R = 100 mm
x = 200 mm
y = 280 mm
xbar_rect = 0.5 * x
xbar_circ = 4 * R / (3 * pi())
a_rect = x * y
a_circ = 0.5 * pi() * R^2

xbar = (xbar_rect * a_rect - xbar_circ * a_circ) / (a_rect - a_circ)



# Example 7.5
x = 12 m
xbar = (2/3) * x
f = 0.5 * x * (100 N/m)
BEGIN
  ax = 1 N
  ay = 1 N
  b = 1 N
  fx = ax
  fy = ay + b - f
  M0 = x * b - xbar * f
END
solve(fx,fy,M0, ax,ay,b)



# Example 7.6
MKS(N)
w = 400 N/m
f1 = 6 m * w
f2 = 6 m * w
f3 = 0.5 * 6 m * w
BEGIN
   ax = 1 N
   ay = 1 N
   b = 1 N
   fx = ax + f2 + f3
   fy = ay + b + f1
   M0 = (6 m) * b - 3 m * f3 - (2 m) * f2 - 3 m * f1
END
solve(fx,fy,M0, ax, ay, b)


# Example 7.7
FPS
f1 = 4330 lb
m1 = 25000 ft lb
BEGIN
   ay = 1 lb
   ma = 1 ft lb
   fy = ay - f1 + 2000 lb
   MM = ma - m1 + 10000 ft lb
END
solve(fy,MM,ay,ma)



# Example 7.12
MKS(mm)
x1 = 4 * 25 mm / (3 * pi())
v1 = pi() * (25 mm)^2 * 20 mm / 2

x2 = 100 mm
v2 = 200 mm * 50 mm * 20 mm

x3 = 200 mm + 4 * (25 mm) / (3 * pi())
v3 = pi() * (25 mm)^2 * (20 mm) / 2

x4 = 0 mm
v4 = pi() * (25 mm)^2 * (40 mm)

x5 = 200 mm
v5 = -pi() * (10 mm)^2 * (20 mm)

sumV = v1 + v2 + v3 + v4 + v5
xbar = (x1 * v1 + x2 * v2 + x3 * v3 + x4 * v4 + x5 * v5) / sumV

zbar = (30 mm) * v4 / sumV





# Example 7.13

x1 = 0 m
y1 = 2 * 2 m / pi()
z1 = 2 * 2 m / pi()
l1 = pi() * 2 m / 2

x2 = 2 m
y2 = 0 m
z2 = 2 m
l2 = 4 m

x3 = 2 m
y3 = 1 m
z3 = 1 m
l3 = 4.9 m

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 7.16
m0 = 80 kg
w1 = (m0 / 2) * grav()
BEGIN
   ax = 1 N
   ay = 1 N
   bx = 1 N
   fx = ax - bx
  fy = ay -  w1 - w1
   Ma = (1 m) * bx - (1 m) * w1 - 0.5 m * w1
END
solve(fx,fy,Ma,ax,ay,bx)



# Example 7.18
MKS(mm)
m1 = 10.75 kg
x1 = 40 mm
y1 = 120 mm

m2 = 5.99 kg
x2 = 200 mm
y2 = 40 mm

xbar = (x1 * m1 + x2 * m2) / (m1 + m2)
ybar = (y1 * m1 + y2 * m2) / (m1 + m2)



# Example 7.19
FPS
rho_al = 168 lb/ft^3
rho_br = 530 lb / ft^3

v_cyl = 12 in * (pi() * (4 in)^2 - pi() * (2 in)^2)
w_cyl = rho_br * v_cyl
x_cyl = 10 in

v_bar = 10 in * 8 in * 2 in  + 0.5 * pi() * (4 in)^2 * (2 in) - 0.5 * pi() * (4 in)^2 * (2 in)
w_bar = rho_al * v_bar

x_bar = ((-4 * (4) / (3 * pi()) * (0.5 * pi() * 4^2 * 2)  + 5 * 10 * 8 * 2 \
        - (10 - 4 * 4 / (3 * pi()) * (0.5 * pi() * 4^2 * 2))) \
        / (0.5 * pi() * 4^2 * 2 + 10 * 8 * 2  - 0.5 * pi() * 4^2 * 2)) in


x = (x_bar  * w_bar + x_cyl * w_cyl) / (w_bar + w_cyl); in



# Example 7.20
MKS(N, deg)

a0 = 0 deg
f1 = 5104 N
f2 = 5027 N
f3 = 3613 N
f4 = 3559 N

a = 15 deg
g1 = 4463 N
g2 = 4396 N
g3 = 3956 N
g4 = 3898 N

w1 = f1 + f2 + f3 + f4
w2 = g1 + g2 + g3 + g4

wheel_base = 2.82 m
xbar = wheel_base * (f1 + f2) / w1

track = 1.55 m
zbar = track * (f2 + f4) / w1

ybar = (xbar * w1 * cos(a) - wheel_base * (g1 + g2)) / (w1 * sin(a))


# Homework Problems:

TBD