# Example 14.1
MKS(N, deg, J)
p = 400 N
q = 30 deg
ss = 2 m
up = p * ss * cos(q)
s1 = 0.5 m
s2 = ss + s1
k = 30 N / m
us = 0.5 * k * s2^2 - 0.5 * k * s1^2
m0 = 10 kg
w0 = m0 * grav()
uw = -w0 * ss * sin(q)
ut = up - us + uw

# Example 14.2
FPS()
w0 = 3500 lb
m0 = w0 / grav()
q = 10 deg
v = 20 ft/s
mu = 0.5
na = w0 * cos(q)
fa = mu * na
BEGIN
  ss = 1 m
  u = 0.5 * m0  * v^2 + w0 * ss * sin(q) - fa * ss
END
solve(u,ss)

# Example 14.3
MKS(kN)
m0 = 2.5e3 kg
h = 3 m
ug = m0 * grav() * h
c1 = 28 kN
c2 = 3 kN / (1 m)^2
ss = 3 m
u1 = c1 * ss + c2 * ss^3 / 3
ss = 0 m
u2 = c1 * ss + c2 * ss^3 / 3
u12 = u1 - u2
v = sqrt((u12 - ug) / (0.5 * m0))

# Example 14.4
MKS(N)
m0 = 2 kg
k = 200 N/m
s2 = 0.6 m
s1 = 0.7 m
h0 = 0.3 m
BEGIN
  h = 1 m
  e = -0.5 * k * s2^2 + 0.5 * k * s1^2 - m0 * grav() * (h - h0)
END
solve(e,h)

# Example 14.5
MKS(N, deg)
m0 = 2 kg
v = 1 m/s
r = 0.5 m
BEGIN
  q = 45 deg
  vmax = 1 m/s

   e1 = 0.5 * m0 * v^2 + m0 * grav() * r * (1 - cos(q)) - 0.5 * m0 * vmax^2
   e2 = m0 * grav() * cos(q) - m0 * vmax^2 / r
END
solve(e1,e2, q,vmax)

# Example 14.6
MKS(N, deg)
mb = 100 kg
ma = 10 kg
BEGIN
  sa = 1 m
  sb = -4 * sa
  vb = 2 m/s
  va = -4 * vb
  u = ma * grav() * sa + mb * grav() * sb - (0.5 * ma * va^2 + 0.5 * mb * vb^2)
END
solve(u,sa)

# Example 14.7
FPS(hp)
e = 0.85
w0 = 75 lb
m0 = w0 /grav()
a = 4 ft/s^2
v = 2 ft/s
ap = a
ac = -ap / 2
tt = (m0 * ac - w0) / (-2)
p = tt * v
p_in = p / e

# Example 14.8
MKS(kN, kW)
m0 = 2e3 kg
v = 25 m/s
mu = 0.35
s0 = 10 m
nc = m0 * grav()
fc = mu * nc
v0 = sqrt((0.5 * m0 * v^2 - fc * s0) / (0.5 * m0))
p = fc * v

# Example 14.9
MKS(deg, kN, kW)
m0 = 8e3 kg
q1 = 60 deg
q2 = 15 deg
x = 20 m
BEGIN
  vb = 1 m/s
  u = -m0 * grav() * x * cos(q1) - 0.5 * m0 * vb^2 + m0 * grav() * x * cos(q2)
END
solve(u,vb)
tt = m0 * grav() * cos(q2) + m0 * vb^2 / x

# Example 14.10
MKS()
m0 = 100 kg
s1 = 0.1 m
ka = 12 kN /m 
kb = 15 kN / m
BEGIN
   sa = 1 m
   sb = sa - s1
   h = 0.75 m + sa
   u = 0.5 * ka * sa^2 + 0.5 * kb * sb^2 - m0 * grav() * h
END
solve(u, sa)

# Example 14.11
MKS()
m0 = 2 kg
y0 = 1 m
va = 2 m/s
k = 3 N/m
BEGIN
   vc = 1 m/s
   scb = 0.5 m
   u = 0.5 * m0 * vc^2 + 0.5 * k * scb^2 - m0 * grav() * y0
END
solve(u,vc)
BEGIN
   vc = 1 m/s
   u = 0.5 * m0 * va^2 - (0.5 * m0 * vc^2 + 0.5 * k * scb^2 - m0 * grav() * y0)
END
solve(u,vc)

# Homework Problems:

TBD