# Example 13.1
MKS(deg, N)
q = 30 deg
m0 = 50 kg
w0[2] = -grav() * m0 
f = 400 N * [cos(q), sin(q)]
BEGIN
nc0 = 1 N
nc = nc0 * [ -0.3, 1]
a[1] = 1 m/s^2
sumF = f + w0  + nc - m0 * a
END
solve(sumF[1], sumF[2], nc0, a[1])
a * (3 s)

# Example 13.2
MKS(deg, N)
m0 = 10 kg
v0 = 50 m/s
c = 0.01 N / (1 m^s)^2
w = m0 * grav()
a = w / m0
h = -(v0)^2 / 2 / a
v = 50 
h = 500 * log(9810) - 500 * log(v^2 + 9810)

# Example 13.3
FPS
m1 = 900 lb
m2 = 550 lb
m3 = 325 lb
c = 40 lb / (1 s)
t = 1 s
a = c * t / ((m1 + m2 + m3) / grav())
v = (c/2) * t^2 / ((m1 + m2 + m3) / grav())
t = 2 s
a = c * t / ((m1 + m2 + m3) / grav())
v = (c/2) * t^2 / ((m1 + m2 + m3) / grav())

# Example 13.4
MKS(deg)
m0 = 2 kg
w0 = m0 * grav()
kk = 3 N/m
x = 0.75 m
BEGIN
   q = 45 deg
   y = x * tan(q)
   err = y - 1 m
END
solve(err, q)
fs = kk *(sqrt(y^2 + x^2) - x)
nc = fs * cos(q)
a = (w0 - fs * sin(q)) / 2

# Example 13.5
MKS(deg)
BEGIN
   aa = 1 m/s^2
   ab = -2 * aa
   tt = 1 N
    fx = 981 N - 2 * tt - 100 kg * aa
    fy = 196.2 N - tt - 20 kg * ab
END
solve(fx,fy,aa,tt)
ab * 2 s

# Example 13.7
MKS(deg)
tt = 100 N
m0 = 3 kg
r = 1 m
BEGIN
   v = sqrt(r * tt / m0)
   nd = 1 N
   at = 1 m/s^2
    ft0 = 0.1 * nd - m0 * at
    fb = nd - m0 * grav()
END
solve(ft0,fb,nd,at)
t = v / at

# Example 13.8
FPS
x = 0 m
dydx = x / 100 ft
dy2dx2 = 1 / 100 ft
rho = (1 + dydx^2)^1.5 / dy2dx2
w0 = 150 lb
v = 65 ft/s
na = w0 + w0 * v^2 / rho / grav()
a = v^2 / rho

# Example 13.9
MKS(deg)
BEGIN
  q = 45 deg
  v = sqrt(9.81 * (1 - cos(q)) + 1)
  fn = 19.62 * cos(q) - 2 * v^2 / 0.5
END
solve(fn,q)

# Example 13.10
FPS()
w0 = 2 lb
m0 = w0 / grav()
t = 1 s
cq = 0.5 rad / (1 s)
q = cq * t
qdot = cq
qdotdot = 0 rad / s^2
cr = 10 ft / (1 s)^2
r = cr * t^2
rdot = 2 * cr * t
rdotdot = 2 * cr
ar = rdotdot - r * qdot^2
aq = r * qdotdot + 2 * rdot * qdot
phi = atan(0.25); deg
BEGIN
   f = 1 lb
   n = 1 lb
   fr = f * cos(phi) - n * sin(phi) - m0 * ar
   fq = f * sin(phi) + n * cos(phi) - m0 * aq
END
solve(fr,fq, f, n)

# Example 13.11
MKS(N)
m0 = 2 kg
q = 60 deg
qdot = 0.5 rad/s
qdotdot = 0
cr = 0.4 m
r = cr / sin(q)
rdot = - cr * csc(q) * cot(q) * qdot
rdotdot = -cr * qdot^2 * (-csc(q) * cot(q)^2 - csc(q)^3)
ar = rdotdot - r * qdot^2
aq =  2 * rdot * qdot
f = 19.62 N
BEGIN
   nc = 1 N
   fp = 1 N
   fr = f * sin(q) - nc * sin(q) - m0 * ar
   fq = f * cos(q) + fp - nc * cos(q) - m0 * aq
END
solve(fr,fq,nc,fp)

# Example 13.12
MKS(N)
m0 = 0.5 kg
q = pi()
qdot = 4 rad/s
cr = 0.1 m / (1 rad)
r = cr * q
rdot = cr * qdot
ar =  -r * qdot^2
aq =  2 * rdot * qdot
psi0 = atan(q); deg
phi = pi() rad / 2 - psi0; deg
BEGIN
  nc = 1 N
  fc = 1 N
  fr = nc * cos(phi) - m0 * ar
  fq = fc - nc * sin(phi) - m0 * aq
END
solve(fr,fq,nc,fc)

# Example 13.13
MKS(N)
me = 5.976e24 kg
re = 6378 km
rs = 600 km
rp = re + rs
v0 = 30e6 m/hr
h = rp * v0
c = (1 - GEarth() * me / (rp * v0^2)) / rp
e = c * h^2 / (GEarth() * me)
ra = rp / (2 * GEarth() * me / (rp * v0^2) - 1)
va = rp * v0 / ra; m/s; m / hr

# Homework Problems:

TBD