# Example 15.1
MKS(N)
c1 = 700 N
c2 = -150 N / (1 m)
mu = 0.26
m0 = 180 kg
i1 = 1 m
i2 = 0.5 m^2
n = m0 * grav()
ii = c1 * i1 + c2 * i2 - mu * n * i1
v2 = sqrt(2 * ii / m0)



# Example 15.2
MKS(N, deg)
ma = 40 kg
mb = 30 kg
mu = 0.15
h = 400 mm
q = 20 deg
ii = (ma * sin(q) - mu * ma * cos(q) + mb) * grav() * h
v2 = sqrt(2 * ii / (ma + mb))

# Example 15.4
MKS(deg)
v0 = 15 m/s
h = 20 m
v2 = sqrt(2 * grav() * h + v0^2)
vy = 3 m/s
v3 = mag([v2, vy])
y = 0.5 * (v3^2 - v2^2) / grav()



# Example 15.5
mh = 40 kg
k = 1500 N/m
ten = 150 N
delt = 0.02 s
r0 = 0.3 m - ten / k
Us = -k * ((0.1 m)^2 - (0.3 m)^2)
Uw = mh * grav() * 0.4 m
v2 = sqrt((Us + Uw)/ (0.5 * mh))
pave = 0.5 * mh * v2^2 / delt; kW


# Example 15.6
k = 1800 N/m
BEGIN
 m0 = 22 kg
 b = 1700 N
 ax = 1330 N
 x = 0.05 m
 s1 = sqrt((0.1 m)^2 + (0.3  m)^2) - 0.2 m
 s2 = sqrt((0.1 m)^2 + (0.3 m + x)^2) - 0.2 m
 U12 = (b - ax) * x  - 0.5 * k * (s2^2 - s1^2)
  v2 = sqrt(2 * U12 / m0)
END
func(x, 0.1 m)
p = b * v2

# Example 15.8
k = 1500 N/ m
s1 = 0.3 m
m0 = 40 kg
y1 = 0.4 m
s2 = 0.1 m
ii = k * s1^2 + m0 * grav() * y1 - k * s2^2
v2 = sqrt(2 * ii / m0)



# Example 15.9
k = 300 N/m
ma = 90 kg
mb = 135 kg
h = 1 m
BEGIN
  xb = h
  xa = 1 m
  e = sqrt((3 m)^2 + (2 m)^2) - sqrt((3 m - xa)^2 + (2 m)^2) - xb
END
solve(e,xa)
BEGIN
   va = 1 m / s
   vb = va * (3 m - xa) / sqrt((3 m - xa)^2 + (2 m)^2)
   U1 = 0.5 * k * (-ma * grav() / k)^2
   t2 = 0.5 * ma * va^2 + 0.5 * mb * vb^2
   U2 = ma * grav() * xa - mb * grav() * xb + 0.5 * k * (xa - ma * grav() / k)^2
   e = t2 + U2 - U1
END
solve(e, va)


# Example 15.13
MKS(deg)
m0 = 1 kg
k = 40 N/m
r0 = 50 mm
R = 200 mm
h = 100 mm
BEGIN
   q = 33 deg
   s1 = sqrt(4 * R^2 + h^2) - r0
   ss = sqrt((R + R * cos(q))^2 + (h + R * sin(q))^2) - r0
   v = sqrt((k/m0) * s1^2 - (k / m0) * ss^2 + 2 * grav() * R * sin(q))
END
max(v,q)


# Homework Problems:

TBD