1.9.A.sagews

from sympy import *
from sympy import N as Num

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

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

symbolic = True
# symbolic = False

if symbolic:
    # quantity = symbol:
    g = var("g")
    m1 = var("m1")
    mu0 = var("mu0")
    r1, r2 = var("r1, r2")
    F = var("F")
else:
    # Derived units:
    N = kg*m/s/s

    # factors:
    g_val = 10
    m1_val = 1
    mu0_val = S(3)/10
    r1_val, r2_val = 1, 2
    F_val = 1
    #
    # quantity =  factor times unit:
    g = g_val * m/s/s
    m1 = m1_val*kg
    mu0 = mu0_val
    r1, r2= r1_val*m, r2_val*m
    F = F_val * N

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

S1, S2, S3, S4, S5, S5 = var("S1, S2, S3, S4, S5, S5")
H1, H2 = var("H1, H2")

# Equilibrium conditions:
eq1 = Eq(S5, F)
eq2 = Eq(r1*S5, r2*S1)
eq3 = Eq(S1, S2 + S3)
eq4 = Eq(S2, S3)
eq5 = Eq(S3, H1 + H2)
eq6 = Eq(S4, H1)
eq7 = Eq(S2, S4)

eqns = [eq1,eq2,eq3,eq4,eq5,eq6,eq7]

# Solve:
unknowns = [S1, S2, S3, S4, S5, S5, H1, H2]
sol = solve(eqns, unknowns)
pprint(sol)

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

H1_max = mu0*m1*g
eq = Eq(F*r1/2/r2, mu0*m1*g)
sol = solve(eq,F)

if symbolic:
    pprint(sol)

--- User input ----------------------- --- a: ------------------------------- F*r1 F*r1 F*r1 F*r1 F*r1 {H1: ----, H2: 0, S1: ----, S2: ----, S3: ----, S4: ----, S5: F} 2*r2 r2 2*r2 2*r2 2*r2 --- b: ------------------------------- 2*g*m1*mu0*r2 [-------------] r1