1.2.C.sagews

from sympy.physics.units import *
from sympy import *

pie = 2*pi

print("\n--- User input -----------------------")

symbolic = True
# symbolic = False

if symbolic:
    # quantity = symbol:
    F1= var("F1")
    alpha = var("alpha")
else:
    # pie/12 = 30 deg
    # pie = 2 pi
    alpha = pie/12

    F1_val = 10
    F1 = F1_val *newton

print("\n--- a: -------------------------------")
S1, S2, S3, F2 = var("S1, S2, S3, F2")

# shortcuts:
ca = cos(alpha)
sa = sin(alpha)

# equilibrium conditions:
eq1 = Eq(0, S1 - F1)
eq2 = Eq(0, F2 - S2)
eq3 = Eq(0, S2 - S3*ca)
eq4 = Eq(0, S3*sa - S1)

# solve linear system:
eqs = [eq1, eq2, eq3, eq4]
unknowns = [S1, S2, S3, F2]
sol = solve(eqs, unknowns)
pprint(sol)

print("\n--- b: -------------------------------")
eq1 = Eq(0, F2 - S3*ca)
eq2 = Eq(0, S3*sa - F1)

eqs = [eq1, eq2]
unknowns = [S3, F2]
sol = solve(eqs, unknowns)

pprint(sol)

--- User input ----------------------- --- a: ------------------------------- F1 F1 F1 {F2: ----------, S1: F1, S2: ----------, S3: ----------} tan(alpha) tan(alpha) sin(alpha) --- b: ------------------------------- F1 F1 {F2: ----------, S3: ----------} tan(alpha) sin(alpha)