# Example 5.1
MKS(kN, kN m, deg)
r1 = [3, 0] m
f1 = [0, -2 ] kN
q = 30 deg
r2 = [5 , 0] m
BEGIN
   ax = 1 kN
   ay = 1 kN
   a = [ax, ay]
   b = 1 kN
   bv = PolarVec(b, 90 deg + q)
   sumf = f1 + a + bv
   sumM = cross(r1, f1) + cross(r2, bv)
END
solve(sumf[1], sumf[2], sumM[3], ax, ay, b)


# Example 5.2
FPS
r1 = [2, 0] ft
f1 = [0, -200 ] lb
r2 = [4, 2] ft
f2 = PolarVec(100 lb, 30 deg)
r3 = [6, 0] ft
M0[3] = 300 ft lb
BEGIN
   ax = 1 lb
   ay = 1 lb
   a = [ax, ay]
   M[3] = 1 ft lb
   sumf = a + f1 + f2
   sumM = M + M0 + cross(r1, f1) + cross(r2, f2)
END
solve(sumf[1], sumf[2], sumM[3], ax, ay, M[3])

# Example 5.3
FPS
w = 2800 lb
rw = 6 ft
rb = 9 ft
BEGIN
   a = 1 lb
   b = 1 lb
   sumf = a + b - w
   sumM = -rw * w + rb * b
END
solve(sumf, sumM, a, b)


# Example 5.4
MKS(kN, kN m)
m0 = 2000 kg
w[2] = -m0 * grav()
rw = [2, 1.5] m
rb = [4, 3] m
BEGIN
   a[1] = 1 N
   bx = 1 N
   by = 1 N
   b = [bx, by]
   sumf = w + a + b
   sumM = cross(rw, w) + cross(rb, b)
END
solve(sumf[1], sumf[2], sumM[3], a[1], bx, by)


# Example 5.5
FPS
w = 50 lb
alp = 30 deg
a = 8 in
b = 16 in
d = 48 in
r = 3 in
h = 36 in
f = sin(alp) * (b - a * tan(alp)) * w / (h - r)


# Example 5.8
MKS(N)
rb = [1000, 600, 400] mm
rw = 0.5 * rb
w[2] = -200 N
BEGIN
   tc[3] = 1 N
   td[1] = 1 N
   ax = 1 N
   ay = 1 N
   az = 1 N
   a = [ax, ay, az]

   sumF = a + td + tc + w
   sumM = cross(rw, w) + cross(rb, tc) + cross(rb, td)
END
solve(sumF[1], sumF[2], sumF[3], sumM[1], sumM[2], tc[3], td[1], ax, ay, az)
 

# Example 5.9
FPS
rc = Polarvec(4 ft, -30 deg)
rb = 0.5 * rc
rd = [2, 2, -1] ft
ud = (rd - rb) / mag(rd - rb)
fc = [0, -100] lb
BEGIN
   td = 1 N
   Mx = 1 N m
   My = 1 N m
   M = [Mx, My]
   ax = 1 N
   ay = 1 N
   az = 1 N
   a = [ax, ay, az]

   sumF = fc + a + td * ud
   sumM = M + cross(rb, td * ud) + cross(rc, fc)
END
solve(sumF[1], sumF[2], sumF[3], sumM[1], sumM[2], sumM[3], td, Mx, My, ax, ay, az)
 

# Example 5.10
ra = [0, 0, 200] mm
rb = [0, 0, 0] mm
rc = [200, 0, 0] mm
rd = [200, 0, 200] mm
re = [0, 80, 100] mm
ue = (re - rc) / mag(re - rc)
fd = [-, -400 ] N
BEGIN
   t = 1 N
   ax = 1 N
   ay = 1 N
   bx = 1 N
   by = 1 N
   bz = 1 N

   a = [ax, ay, 0]
   b = [bx, by, bz]

   sumF = fd + a + b + t * ue
   sumM = cross(rd, fd) + cross(ra, a) + cross(rc, t * ue)
END
solve(sumF[1], sumF[2], sumF[3], sumM[1], sumM[2], sumM[3], t, bx, by, bz, ax, ay)
 


# Example 5.11
MKS(kN, N m, deg)
rb = [700, 400] mm
BEGIN
   alp = 30 deg
   fb = PolarVec(6 kN, alp)
   ax = 1 N
   ay = 1 N
   a = [ax, ay]
   sumF = a + fb
   sumM = cross(rb, fb)
END
solve(sumF[1], sumF[2], sumM[3], alp, ax, ay)


# Example 5.12
FPS
w[2] = -100 lb
rw = [2, 0] ft
q = 45 deg
rc = [4, 0] ft
BEGIN
   b = 1 lb
   c = 1 lb
   bv = PolarVec(b, q)
   cv = PolarVec(c, 90 deg + q)
   sumF = w + bv + cv
   sumM = cross(rw, w) + cross(rc, cv)
END
solve(sumF[2], sumM[3], b, c)



# Example 5.13
FPS(deg)
rc = [8, 2] ft
h0 = 2 ft
w[2] = 200 lb
k = 60 lb/ft
BEGIN

   a = 10 deg
   rb = PolarVec(8 ft, - a)
   rw = 0.5 * rb
   del_h = mag(rb - rc) - h0
   ul = (rc - rb) / mag(rc - rb)
   fl = k * del_h * ul
   sumF = w + fl
   sumM = cross(rw, w) + cross(rb, fl)
END

solve(sumM[3], a)



# Homework Problems:

TBD