# Example 15.1
MKS(deg, N)
m0 = 100 kg
f = 200 N
q = 45 deg
delt = 10 s
v2 = f * delt * cos(q) / m0
nc = (m0 * grav() * delt - f * delt * sin(q)) / delt

# Example 15.2
FPS(deg)
q = 30 deg
cp0 = 20 lb / (1 s)
delt = 2 s
v1 = 3 ft/s
mu = 0.3
w0 = 50 lb
m0 = w0 / grav()
BEGIN
  v2 = 1 m/s
  nc = 1 N
  e1 = m0 * v1 + cp0 * delt^2 / 2 - mu * nc * delt + w0 * delt * sin(q) - m0 * v2
  e2 = nc - w0 * cos(q)
END
solve(e1,e2,v2,nc)

# Example 15.3
MKS(deg, N)
ma = 3 kg
mb = 5 kg
delt = 6 s
BEGIN
   va = 1 m/s
   vb = -2 * va
   tb = 1 N
   ta = 2 * tb
   e1 = -2 * tb * delt + ma * grav() * delt - ma * va
   e2 = mb * grav() * delt - tb * delt - mb * vb
END
solve(e1,e2,va,tb)

# Example 15.4
MKS(deg, kN)
ma = 15e3 kg
mb = 12e3 kg
va = 1.5 m/s
vb = 0.75 m/s
v2 = (ma * va - mb * vb) / (ma + mb)
delt = 0.8 s
fav = ma * (v2 - va) / delt

# Example 15.5
FPS(kip)
wc = 1200 lb
mc = wc / grav()
wp = 8 lb
mp = wp / grav()
v = 1500 ft/s
delt = 0.03 s
v2 = v * mp / mc
fave = mp * v / delt

# Example 15.6
MKS()
mt = 350e3 kg
mb = 50e3 kg
vt1 = 3 m/s
vt2 = mt * vt1 / (mt + mb)

# Example 15.7
MKS()
mp = 800 kg
mh = 300 kg
y0 = 0.5 m
v = sqrt(mh * grav() * y0 / (0.5 * mh))
v2 = mh * v / (mh + mp)
ii = mh * v - mh * v2

# Example 15.8
MKS()
mb = 40 kg
mt = 15 kg
x = 2 m
ss = 2 * mb / (mb + mt)

# Example 15.9
FPS()
w1 = 6 lb
m1 = w1 / grav()
w2 = 18 lb
m2 = w2 / grav()
e = 0.5
r = 3 ft
va1 = sqrt(w1 * r/ (0.5 * m1))
BEGIN
   va2 = 1 m/s
   vb2 = 1 m/s
   e1 = m1 * va1 - m2 * vb2 - m1 * va2
   e2 = (vb2 - va2) / (va1) - e
END
solve(e1,e2,va2,vb2)

# Example 15.10
m0 = 1.5 kg
x0 = 1 m
delx = 0.25 m
k = 800 N/m
e = 0.8
y0 = x0 + delx
BEGIN
   vb1 = 1 m/s
   u1 = -y0 * grav() * m0 + 0.5 * k * delx^2 - 0.5 * m0 * vb1^2
END
solve(u1,vb1)
BEGIN
  vb2 = 1 m/s
  u2 = vb2 / (-vb1) - e
END
solve(u2,vb2)
BEGIN
  s3 = 0.2 m
  u3 = 0.5 * m0 * vb2^2 - (-m0 * grav() * (x0 + s3) + 0.5 * k * s3^2)
END
solve(u3,s3)

# Example 15.11
MKS(deg)
ma = 1 kg
va = 3 m/s
qa = 30 deg
mb = 2 kg
vb = 1 m/s
qb = 45 deg
e = 0.75
va1 = PolarVec(va, qa)
vb1 = -PolarVec(vb, qb)
BEGIN
   vax2 = 1 m/s
   vbx2 = 1 m/s 
    e1 = ma * va1[1] + mb * vb1[1] - (ma * vax2 + mb * vbx2)
    e2 = (vbx2 - vax2) / (va1[1] - vb1[1]) - 1
END
solve(e1,e2,vax2,vbx2)

# Example 15.13
p = 10 N
r = 0.4 m
m0 = 5 kg
cm0 = 3 N m / (1 s)
delt = 4 s
va = (r * p * delt + cm0 * delt^2 / 2) / (m0 * r)

# Example 15.14
FPS
w0 = 0.8 lb
m0 = w0 / grav()
r1 = 1.75 ft
v1 = 4 ft/s
vc = 6 ft/s
r2 = 6 ft
v2 = v1 * r1 / r2
v20 = sqrt(v2^2 + vc^2)
uf = 0.5 * m0 * v20^2 - 0.5 * m0 * v1^2

# Example 15.15
MKS
m0 = 2 kg
k = 20 N/m
vd1 = 1.5 m/s
x = 0.2 m
x0 = 0.5 m
vd2 = vd1 * x0 / (x0 + x)
BEGIN
   vd3 = 1 m/s
   e = 0.5 * m0 * vd1^2 - (0.5 * m0 * vd3^2 + 0.5 * k * x^2)
END
solve(e,vd3)
sqrt(vd3^2 - vd2^2)

# Example 15.16
MKS(kN)
rho = 1000 kg/m^3
pa = 100 kPa
q = 0.2 m^3 / s
me = 20 kg
ab = pi() * (5 cm)^2
aa = pi() * (10 cm)^2
dmdt = rho * q
vb = q / ab
va = q / aa
fa = pa * aa
fx = fa - dmdt * (-va)
fy = -me * grav()  - dmdt * (-vb)
M0 = dmdt * (0.3 m * vb) - me * grav() * 0.125 m

# Example 15.17
FPS
d = 2 in
vw = 25 ft/s
vblade = 5 ft/s
gw = 62.4 lb/ft^3
dmdt = gw / grav() * (vw - vblade) * pi() * d^2 / 4
f = dmdt *  (vw - vblade) 
p = f * vblade; hp

# Homework Problems:

TBD