1.5.E.sagews

from sympy import *
from sympy import N as Num

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

# quantity = symbol:
a, F = var("a, F")

print("\n--- a: -------------------------------")

# unknowns:
A_h, A_v, B_h, B_v, C_h, C_v = var("A_h, A_v, B_h, B_v, C_h, C_v")
unknowns = [A_h, A_v, B_h, B_v, C_h, C_v]

# Equilibrium conditions:
eq1 = Eq(0, A_h - C_h)
eq2 = Eq(0, A_v + C_v - 2*F )
eq3 = Eq(0, a*F + 2*a*F - 2*a*C_v - a*C_h)

eq4 = Eq(0, C_h - B_h)
eq5 = Eq(0, B_v - F - C_v)
eq6 = Eq(0, a*F + 2*a*C_v - a*C_h)

eqns = [eq1,eq2,eq3,eq4,eq5,eq6]

# Solve:
sol = solve(eqns, unknowns)
pprint(sol)

print("\n--- b: -------------------------------")

unknowns = [A_h, A_v, C_h]

# Equilibrium conditions:
eq1 = Eq(0, A_h - C_h)
eq2 = Eq(0, A_v  - 3*F/2 )
eq3 = Eq(0, a*F + 2*a*F/2- a*C_h)

eqns = [eq1,eq2,eq3]

# Solve:
sol = solve(eqns, unknowns)
pprint(sol)

--- User input ----------------------- --- a: ------------------------------- 3*F 3*F F {A_h: 2*F, A_v: ---, B_h: 2*F, B_v: ---, C_h: 2*F, C_v: -} 2 2 2 --- b: ------------------------------- 3*F {A_h: 2*F, A_v: ---, C_h: 2*F} 2