# Example 3.1
MKS(N, deg)
m0 = 1440 kg
fg[2] = -m0 * grav()
q = 20 deg
BEGIN
   n = 1 N # initial guess
   t = 1 N # initial guess
   sumf = fg + PolarVec(n, -90 deg + q) + PolarVec(t, 0 deg)
END
solve(sumf[1], sumf[2], n, t)


# Example 3.2
MKS(N, deg)
m0 = 200 kg
q1 = 45 deg
q2 = 60 deg
fg[2] = -m0 * grav()
BEGIN
   tac = 1 N
   tab = 1 N
   sumf = fg + PolarVec(tac, q1) + PolarVec(tab, 180 deg - q2)
END
solve(sumf[1], sumf[2], tac, tab)



# Example 3.4
MKS(kN, deg)
m0 = 72000 kg
gam = 6 deg
d[1] = 125 kN
LL[2] = 680 kN
BEGIN
   t = 100 kN
   a = 6 deg
   sumf = PolarVec(t, a) - PolarVec(m0 * grav() , 90 deg - gam) - d + LL
END
solve(sumf[1], sumf[2], t, a)


# Example 3.5
MKS(N, deg)
m0 = 100 kg
w[2] = -m0 * grav()
ra = [0, -4, 0] m
rb = [4, 0, 2] m
rc = [-2, 0, -2] m
rd = [-3, 0, 3] m
ub = (rb - ra) / mag(rb - ra)
uc = (rc - ra) / mag(rc - ra)
ud = (rd - ra) / mag(rd - ra)
BEGIN
   tb = 100 N
   tc = 100 N
   td = 100 N
   sumf = w + tb * ub + tc * uc + td * ud
END
solve(sumf[1], sumf[2], sumf[3], tb, tc, td)



# Example 3.6
FPS(deg)
w[2] = -100 lb
rb = [0, 0, 0] ft
ra = [0, 0, 4] ft
rd = [4, -7, 4] ft
ud = (rd - rb) / mag(rd - rb)
rc = 6 ft * ud
rac = ra - rc
uac = rac / mag(rac)
BEGIN
   t = 1 lb
   sumf = w - t * uac 
   n = -(w - t * uac)
   n_axis = dot(n , ud)
   mag(n)
END
solve(n_axis, t)




# Example 3.7
FPS(deg)
w[2] = -12 lb
k = 300 lb/ft
l0 = 1ft
b = 1 ft
BEGIN
   h = 1 ft
   r = [b, h]
   fs = k * (mag(r) - l0)
   ur = r / mag(r)
   fy = component(fs * ur + w, 2)

END
solve(fy,h)

# Homework Problems:

TBD