# Example 8-1
MKS(N,J)
m0 = 1000 kg
y1 = 0
y2 = 10 m
y3 = -15 m
u1 = m0 * grav() * y1
u2 = m0 * grav() * y2
u3 = m0 * grav() * y3
u3 - u2

# Example 8-3
y1 = 3 m
y2 = 1 m
v2 = sqrt(2 * grav() * (y1 - y2))

# Example 8-4
y1 = 40 m
v2 = sqrt(2 * grav() * y1)
v3 = 0.5 * v2
y2 = y1 - v3^2 / (2 * grav())

# Example 8-6
MKS(N,J)
m1 = 70 kg
y1 = 4.1 m
u1 = m1 * grav() * y1
v1 = sqrt(2 * u1 / m1)

# Example 8-7
k = 250 N/m
x1 = 6 cm
m1 = 0.1 kg
v1 = sqrt(k * x1^2 / m1)

# Example 8-8
MKS(N, J, N/m)
m1 = 2.6 kg
h = 55 cm
y = 15 cm
v1 = sqrt(2 * grav() * h)
u1 = 0.5 * m1 * v1^2
k = m1 * (v1^2 + 2 * grav() * y) / y^2

# Example 8-10
y1 = 40 m
y2 = 25 m
x = 400 m
m1 = 1000 kg
del_u = m1 * grav() * (y1 - y2)
fd = del_u / x

# Example 8-12
Me = 5.98e24 kg
Re = 6.38e6 m 
v1 = 1800 m/s
h1 = 1600 km
r2 = Re + h1
v2 = sqrt(v1^2 - 2 * GEarth()  * Me * (1 / r2 - 1 / Re))

# Example 8-13
Mm = 7.35e22 kg
Me = 5.98e24 kg
Rm = 1.74e6 m
Re = 6.38e6 m
ans = sqrt(Me * Rm / (Mm * Re))

# Example 8-14
MKS(N, J, W)
m1 = 60 kg
y1 = 4.5 m
u1 = m1 * grav() * y1
tt = 4 s
p = u1 / tt

# Example 8-15
MKS(N, J, W)
m1 = 1400 kg
q = 10 deg
fg = -m1 * grav()
v1 = 90 kph
v2 = 110 kph
tt = 6 s
v_ave = 0.5 * (v1 + v2)
fr = 700 N
f = fr + fg * sin(q)
p = f * v_ave; W; hp
a = (v2 - v1) / tt
f2 = m1 * a + fr
p_var = f2 * v2; W; hp

# Homework Problems:

TBD