# Example 3.1
FPS
f1 = PolarVec(800 lbf, 45 deg)
f2 = PolarVec(350 lbf, 110 deg)
f3 = PolarVec(150 lbf, 180 deg)
R = f1 + f2 + f3
mag(R); lbf
PolarAngle(R); deg
atan2(R[2], R[1]); deg
atan2(component(R, 2), component(R, 1)); deg

# Example 3.2
FPS(deg)
f1 = PolarVec(25 lbf, 180 deg)
f2 = PolarVec(10 lbf, 140 deg)
R = f1 + f2
mag(R); lbf

# three equivalent methods
PolarAngle(R); deg
atan2(R[2], R[1]); deg
atan2(component(R, 2), component(R, 1)); deg


# Example 3.3
f = 35 lbf
d1 = 6 in
M1 = f * d1; lbf ft
d2 = 5.375 in
M2 = f * d2; lbf ft

# Example 3.4
f = PolarVec(250 N, -125 deg)
x = [200, -75] mm
M = Cross(x, f); N m

# Example 3.5
f1 = PolarVec(300 lbf, 60 deg)
f2 = PolarVec(300 lbf,  0 deg)
f = -(f1 + f2)
mag(f); lbf
PolarAngle(f); deg

# Example 3.6
MKS(N, N m)
BEGIN
   r_handle = [90, 0] mm
   r_jaw = [-20, 0] mm
   r_hinge = [0, 0] mm

   f1 = 100 N # initial guess
   f_jaw = PolarVec(f1, 90 deg)
   M_jaw = cross(r_jaw, f_jaw)

   f2 = 200 N # initial guess
   f_hinge = PolarVec(f2, -90 deg)
   M_hinge = cross(r_hinge, f_hinge)

   f_handle = PolarVec(70 N, 90 deg)
   M_handle = cross(r_handle, f_handle)

   sum_forces = f_handle + f_jaw + f_hinge
   sum_moments = M_handle + M_jaw + M_hinge

   err1 = component(sum_forces, 2)
   err2 = component(sum_moments, 3)
END
solve(err1,err2,f1,f2)

# Example 3.7
FPS
r_load = [-96, 0] in
r_front = [-72, 0] in
r_cart = [-30, 0] in
r_back = [0, 0] in

f_load = [0, -800] lbf
f_cart = [0, -3500] lbf

M_load = cross(r_load, f_load)
M_cart = cross(r_cart, f_cart)

BEGIN

   f1 = 1 # initial guess
   f_front = [0, 2 * f1] lbf

   f2 = 2 # initial guess
   f_back = [0, 2 * f2] lbf

   sumf = f_load + f_front + f_cart + f_back

   M_front = cross(r_front, f_front)
   M_back = cross(r_back, f_back)

   summ = M_load + M_front + M_cart + M_back

   e1 = component(sumf, 2)
   e2 = component(summ, 3)
END

solve(e1,e2,f1,f2)

# Example 3.7b
FPS
r_load = [-24, 0] in
r_front = [0, 0] in
r_cart = [42, 0] in

f_cart = [0, -3500] lbf
M_cart = cross(r_cart, f_cart)

BEGIN
   f1 = 1 # initial guess
   f_load = [0, -f1] lbf
   M_load = cross(r_load, f_load)
   summ = component(M_load + M_cart, 3)
END
solve(summ, f1)

# Example 3.8
IPS
ra = [0, 0] in
r1 = [4, 0] in
r2 = [19, 0] in
rb = [36, 0] in

f1 = [0, 110] lbf
f2 = [0, -70] lbf


M1 = cross(r1, f1)
M2 = cross(r2, f2)

BEGIN

   a = 1; # initial guess
   fa = [0, a] lbf

   b = 1; # initial guess
   fb = [0, b] lbf

   sumF = f1 + f2 + fa + fb
   
   Ma = cross(ra, fa)
   Mb = cross(rb, fb)

   sumM = Ma + Mb + M1 + M2

   e1 = component(sumF, 2)
   e2 = component(sumM, 3)
END

solve(e1,e2,a, b)


# Example 3.9
MKS(N, N m)
wgt = (13.5 kN) / 4
mass = wgt / grav()
v = 50 kph
r = 60 m
at = v^2 / r
fr = mass * at
f = sqrt(wgt^2 + fr^2)

# Homework Problems:

TBD