# Example 9.1
FPS(deg)
w = 180 lb
mus = 0.4
frope = 90 lb
q = 20 deg
f = w * sin(q) - frope * cos(q)
BEGIN
  t = 1 lb
  n = 1 lb
  fx = t - n * sin(q) - mus * n * cos(q)
  fy = n * cos(q) - mus * n * sin(q) - w
END
solve(fx,fy,t,n)


# Example 9.4
m0 = 80 kg
tab = 130 N
tac = 220 N
e = [-0.182, 0.818, 0.545]
w[2] = -m0 * grav()
ra = [3, 0, 4] m
rb = [2, 2, 0] m
rc = [5, 2, -1] m
eab = (rb - ra) / mag(rb - ra)
eac = (rc - ra) / mag(rc - ra)
R = -(tab * eab + tac * eac + w)
n = dot(e, R) * e
f = mag(R - n)
mu = f / mag(n)

# Example 9.5
MKS(N, deg)
a = 10 deg
mus = 0.22
muk = 0.20
f = 1 N
n = 0.5 * f / (sin(a/2) + muk * cos(a /2 ))
mus = tan(a/2)



# Example 9.6
IPS(deg)
r = 1.6 in
p = 0.2 in
mus = 0.25
muk = 0.22
w = 400 lb
f = w * (20 in) / (40 in)
a = atan(p / (2 * pi() * r))
q = atan(muk)
M = r * f * tan(q + a)
qs = atan(mus)


# Example 9.7
FPS(deg)
w = 1000 lb
rp = 6 in
rs = 0.5 in
mu = 0.2
q = 45 deg
qk = atan(mu)
BEGIN
   t = 1 lb
   f = sqrt((w + t * sin(q))^2 + (t * cos(q))^2)
   M1 = 6 in * (t - w)
   M2 = rs * f * sin(qk)
   err = M1 - M2
END
solve(err, t)


# Example 9.8
IPS
r = 4 in
f = 15 lb
mu = 0.6
M = (2/3) * mu * r * f


# Example 9.9
FPS
w = 100 lb
mul = 0.2
mur = 0.4
beta = pi() / 2
tl = w * exp(-mul * beta)
f = tl * exp(-mur * beta)


# Example 9.10
MKS(N, N m, deg)
f = 200 N
mu = 0.8
b = 500 mm
ra = 200 mm
rb = 100 mm
a = asin((ra - rb) / b)
BEGIN
   t1 = 1 N
   t2 = 1 N
   e1 = (t1 + t2) * cos(a) - f
   e2 = t2 - t1 * exp(mu * (pi() - 2 * a))
END
solve(e1,e2,t1,t2)
Ma = ra * (t2 - t1)
Mb = rb * (t2 - t1)



# Example 9.11
ma = 20 kg
mu = 0.3
k = 1 kN / m
x0 = 1 m
BEGIN
  x = 1 m
  h = k * (1 + mu) * (sqrt(x0^2 + x^2) - x0) - mu * ma * grav() * sqrt(x0^2 + x^2) / x0
END
solve(h,x)

# Homework Problems:

TBD