# Example 5.1
MKS(N, N m)
w = 100 kg * grav()
m1 = 1200 N * 2 m
ma = m1 + w * 3 m

# Example 5.2
IPS(lb in)
k = 20 lb/in
ss = 1.5 in
fs = k * ss

# Example 5.3
MKS(N, N m)
w = 300 kg * grav()

# Example 5.4
MKS(N, N m)
w = 200 kg * grav()

# Example 5.6
MKS(N, N m)
f = 600 N
q = 45 deg
bx = f* cos(q)
ay = (100 N * 2 m + f * sin(q) * 5 m  - f * cos(q) * 0.2 m) / 7 m
by = -(319 N - 600 N * sin(q) - 100 N - 200 N)
Ma = -f * sin(q) * 2 m - f * cos(q) * 0.2 m - 100 N * 5 m - 200 N * 7 m + by * 7 m

# Example 5.7
FPS()
tt = 100 lb * 0.5 ft / 0.5 ft
ax = 100 lb * sin(30 deg)
ay = 100 lb + 100 lb * cos(30 deg)

# Example 5.8
MKS(N, N m)
nb = (90 N m + 60 N * 1 m) / 0.75 m
ax = 200 N * sin(30 deg)
ay = 200 N * cos(30 deg) + 60 N

# Example 5.9
MKS(N, N m, deg)
q = 60 deg
f1 = 52 N
f2 = 30 N
ax = f1 * (5/13) - f2 * cos(q)
ay = f1 * (12 / 13) + f2 * sin(q)
ma = f1 * (12/13) * 0.3 m + f1 * sin(q) * 0.7 m
fa = [ax, ay]
mag(fa)
PolarAngle(fa)
Mc = f1 * (12/13) * 0.4 m + ma - ay * 0.7 m

# Example 5.10
FPS()
q = 30 deg
fbc = (560 lb * cos(q) * 8 ft + 560 lb * sin(q) * 0.25 ft) / 2ft
ax = fbc
ay = 560 lb
Mb = -1975 lb * 2 ft + 560 lb * 4 ft * cos(q) + 560 lb * 4 ft * cos(q) + 560 lb * 0.25 ft * sin(q)

# Example 5.11
MKS(kN, N m deg)
q = 30 deg
BEGIN
  ax = 1 N
  by = 1 N
  cy = 1 N
  fx = cy * sin(q) + by * sin(q) - ax
  fy = -300 N + cy * cos(q) + by * cos(q)
  ma = -by * 2 m + 4000 N m - cy * 6 m + 300 N * cos(q) * 8 m
END
solve(fx,fy,ma,ax,by,cy)

# Example 5.12
FPS(deg)
q1 = 20 deg
q2 = 30 deg
TT = (400 lb * 4 ft * cos(q2)) / (-sin(q1) * 7 ft * cos(q2) + cos(q1) * sin(q2) * 7 ft)
d = 7ft * sin(10 deg) / sin(20 deg)

# Example 5.13
MKS(kN, deg)
q = atan(0.7  / 0.4)
q2 = 45 deg
BEGIN
   fa = 1 N
   f = 1 N
   fx = fa * cos(q) - f * cos(q2) + 400 N
   fy = fa * sin(q) - f * sin(q2)
END
solve(fx,fy,fa,f)

# Example 5.15
MKS(N, N m, deg)
BEGIN
   az = 1 N
   bz = 1 N
   tc = 1 N
   fz = az + bz + tc - 300 N - 981 N
   mx = tc * 2 m - 981 N * 1 m + bz * 2 m
   my = 300 N * 1.5 m + 981 N * 1.5 m - bz * 3 m - az * 3 m - 200 N m
END
solve(fz,mx,my,az,bz,tc)

# Example 5.16
MKS(N, N m, deg)
p = 981 N * 0.1 m / (0.3 m * cos(30 deg))
az = (981 N * 0.5 m - p * 0.4 m) / 0.8 m
bz = 981 N - az + p

# Example 5.17
MKS(N, N m, deg)
f = [0, -1000, 0] N
q = 45 deg
rb = [0, 0, 6 ] m
BEGIN
  tc = 1 N
  ax = 1 N
  ay = 1 N
  az = 1 N
  td = 1 N
  fa = [ax, ay, az]
  ftc = tc * [cos(q) , -sin(q)]
  ftd = td * [-3/9, 6/9, -6/9]
  sumf = f + fa + ftc + ftd
  ma = cross(rb, f + ftc + ftd)
  e1 = sumf[1]
  e2 = sumf[2]
  e3 = sumf[3]
  e4 = ma[1]
  e5 = ma[2]
END
solve(e1,e2,e3,e4,e5,tc,td,ax,ay,az)

# Example 5.18
MKS(N, N m, deg)
f = [0, 0, -200] N
rb = [1, 2, -2] m
rc = 0.5 * rb
BEGIN
  ax = 1 N
  ay = 1 N
  az = 1 N
  fa = [ax, ay, az]
  te = 1 N
  fte = [te,0,0]
  td = 1 N
  ftd = [0, td]
  sumf = fa + fte + ftd + f
  ma = cross(rc,f) + cross(rb, fte + ftd)
  e1 = sumf[1]
  e2 = sumf[2]
  e3 = sumf[3]
  e4 = ma[1]
  e5 = ma[2]
END
solve(e1,e2,e3,e4,e5,te,td,ax,ay,az)

# Example 5.19
MKS(N, N m, deg)
rda = [-1, -1] m
u = rda / mag(rda)
rb = [0, -1] m
re = [0, -0.5] m
w = [0, 0, -981] N
BEGIN
  tb = 1 N
  ftb = tb * [0.2/0.7, -0.3/ 0.7, 0.6 / 0.7]
  M = dot(u, cross(rb, ftb) + cross(re, w))
END
solve(M, tb)

# Homework Problems:

TBD