Leiter mit Reibung
Author: Matthias Kittel

0

B

A

0

M_A

M_B

M_G

M_G

G

Kräftegleichgewicht

Momentegleichgewicht

Leiterlänge = 6.9 (slider from 1 to 8, step 0.1)
A = Point(xAxis)
c = Circle(A, Leiterlänge)
B_1, B = Intersect(c, yAxis)
a = Segment(A, B)
D = Intersect(xAxis, yAxis)
α = Angle(B, A, D)
E = Point(a)
b = OrthogonalLine(E, yAxis)
d = OrthogonalLine(E, xAxis)
F = Intersect(yAxis, b)
G_1 = Intersect(d, xAxis)
H = Point(xAxis)
e = Line(H, a)
f = OrthogonalLine(E, e)
I = Intersect(e, f)
g = Circle(A, Leiterlänge / 5)
h_1 = Circle(A, 2 * Leiterlänge / 5)
k = Circle(A, 3 * Leiterlänge / 5)
p = Circle(A, 4 * Leiterlänge / 5)
J = Intersect(g, a)
K = Intersect(h_1, a)
L = Intersect(k, a)
M = Intersect(p, a)
N = Point(xAxis)
i = Line(N, a)
j = Line(K, xAxis)
S = Point(b)
Masse = 74 (slider from 20 to 100, step 1)
μ_A = 0.27 (slider from 0 to 1, step 0.01)
μ_B = 0.7 (slider from 0 to 1, step 0.01)
hoehe: (cos(α) * sin(α) * Leiterlänge * μ_A * μ_B + sin(α) * sin(α) * Leiterlänge * μ_B) / (cos(α) * μ_A * μ_B + cos(α))
h = Segment(G_1, E)
C = Point(Circle[A, 1])
m = Segment(A, C)
Z: (x(C), 0.1)
O = Point(yAxis)
P = Intersect(xAxis, yAxis)
n = Segment(P, O)
Q = Point(xAxis)
q = Segment(P, Q)
r = Segment(G_1, E)
G_2 = Vector((0, -Masse * 9.81))
F_1 = Vector(((-Masse * 9.81) / (μ_A + 1 / μ_B), (Masse * 9.81) / (μ_A + 1 / μ_B) / μ_B))
F_A: ((Masse * 9.81) / (μ_A + 1 / μ_B), (Masse * 9.81) / (μ_A + 1 / μ_B) * μ_A)
R: ((Masse * 9.81) / (μ_A / (1 / μ_B)), (Masse * 9.81) / (μ_A / (1 / μ_B)) * μ_A)
T = Point(P, F_A)
U = Point(T, F_1)
F_B = Vector(T, U)
G = Vector(U, P)
V = (3569.2840192803824, -11.305940135172243)
u = Vector(((-Masse * 9.81) / (μ_A + 1 / μ_B) * Leiterlänge * sin(α), 0))
W = Point(V, u)
v = Vector(V, W)
w = Vector(((Masse * 9.81) / (μ_A + 1 / μ_B) / μ_B * Leiterlänge * cos(α), 0))
A_1 = Point(W, w)
Y = (1002.642898562289, 43.540471468192266)
W_1: (x(W), 50)
A_2: (x(A_1), 50)
z = Vector(W_1, A_2)
s = Vector((-Masse * 9.81 * (Leiterlänge * cos(α) - hoehe / tan(α)), 0))
C_1 = Point(A_2, s)
A_3: (x(A_2), 100)
D_1 = Point(A_3, s)
t = Vector(A_3, D_1)
a_1 = OrthogonalLine(V, xAxis)
b_1 = OrthogonalLine(V, xAxis)