# Example 10.1
f = 1 N
len = 1 m
BEGIN
   pc = 1 N
   vc = 1 N
  Mc = 1 N m
   fx = pc
   fy = 0.25 * f - vc
   M = Mc - 0.25 * len * (0.25 * f)
END
solve(fx,fy,M,pc,vc,Mc)


# Example 10.2
f = 180 N
BEGIN
   ax = 1 N
   ay = 120 N
   c = 60 N
   fx = ax
   fy = ay + c - f
   M = 12 m * c - 4 m * f
END
solve(fx,fy,M,ax,ay,c)
BEGIN
   f2 = 45 N
   pb = 1 N
   vb = 1 N
   mb = 1 N m
   fx = pb
   fy = f - f2 - vb
   M = mb + (1 m) * f2- 3 m * f
END
solve(fx,fy,M,pb,vb,mb)



# Example 10.3
MKS(kN, kN m)
BEGIN
   a = 1 kN
   b = 1 kN
   fy = a + b - 80 kN + 60 kN
   M = 2 m * b - 1 m * 80 kN + 4 m * 60 kN
END
solve(fy,M,a,b)
   

# Example 10.7
FPS
BEGIN
  xl = 1 ft
  xr = xl + 40 ft
  e1 = xl^2 / xr^2 - 2
END
solve(e1,xl)
   
yl = 40 ft
a = yl / (0.5 * xl^2)
t0 = (100 lb/ft) / a
tmax = t0 * sqrt(1 + a^2 * xl^2)


# Example 10.8
MKS(N)
t0 = 50 N
a = (1 kg/m) * grav() / t0
x = 10 m
h = (1/a) * (cosh(a * x) - 1)
tmax = t0 * sqrt(1 + sinh(a * x)^2)

# Example 10.9
MKS(N, deg)

m1 = 10 kg
m2 = 20 kg
BEGIN
  th = 1 N
  tv = 1 N
  h2 = 1 m

   ma1 = 1 m * th - 1 m * tv
   ma2 = h2 * th - 2 m * tv + 1 m * m1 * grav()
   ma3 = -3 m * tv + 2 m * m1 * grav() + 1 m * m2 * grav()
END
solve(ma1,ma2,ma3,th,tv,h2)
x = 1 m
a = atan((h2 - x) / x)
t2 = th / cos(a)


# Example 10.10
FPS
BEGIN
  a = 0.1 / ft
  ss = sinh(20 ft * a) / a
  e = ss - 21 ft
END
solve(e, a)
t0 = 5 lb / ft / a
tmax = t0 * cosh(a * 20 ft)
ymax = (cosh(a * 20 ft) - 1) / a


# Example 10.11
MKS(N)
patm = 1e5 Pa
gam = 9.81 kN / m^3
x1 = 6 m
x2 = 18 m
x = 8 m
i1 = x2 - x1
i2 = (x2^2 / 2 - x1^2 / 2)
i3 = (x2^3 / 3 - x1^3 / 3)
f = x * patm * i1 + x * gam * i2
M = x * patm * i2 + x * gam * i3
xp = M / f


# Example 10.12
FPS
gam = 62.4 lb/ft^3
x = 3 ft
x1 = 0 ft
x2 = 2 ft
i1 = x2 - x1
i2 = (x2^2 / 2 - x1^2 / 2)
i3 = (x2^3 / 3 - x1^3 / 3)
f = gam * x * i2
M = gam * x * i3
xp = M / f
BEGIN
   ax = 1 lb
   az = 1 lb
  b = 1 lb
  fx = ax + 100 lb
  fz = az + b - f
  MM = 1 ft * b - 2 ft * az + 1.33 ft * f
END
solve(fx,fz,MM,ax,az,b)


# Homework Problems:

TBD