1.3.B.sagews

from sympy.physics.units import *
from sympy import *
from sympy import N as Num

# 3/5, 4/5:
f35 = S(3)/5
f43 = S(4)/3
f45 = S(4)/5

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

symbolic = True
symbolic = False

if symbolic:
    # quantity = symbol:
    a = var("a")
    F = var("F", positive=True)
    Bv = var("B_v")
    Ah, Av = var("A_h, A_v")
else:
    # quantity = number and unit:
    a = 1 * meter
    F = 15 * newton

M = a * F

print("\n--- a: -------------------------")
Fh, Fv = var("F_h, F_v", positive=True)

eq1 = Eq(Fv/Fh, f43)
eq2 = Eq(Fv*Fv + Fh*Fh, F*F)
eqns = [eq1, eq2]
sol = solve(eqns, [Fh,Fv], dict=True)

pprint(sol)
Fh=sol[0][Fh]
Fv=sol[0][Fv]

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

Ah, Av, Bv= var("A_h, A_v, B_v")

eq1 = Eq(0, Ah + Fh)
eq2 = Eq(0, Av + Bv + Fv)
eq3 = Eq(0,- M + 9*a*Fv - a*Fh + 12*a*Bv)

sol = solve([eq1,eq2,eq3],[Ah,Av,Bv])

Ah=sol[Ah]
Av=sol[Av]
Bv=sol[Bv]

for s in [Ah, Av, Bv]:
    pprint(s)

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

rF = Matrix([  9*a, a, 0 ])
rB = Matrix([ 12*a, 0, 0 ])

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

# B_v is unknown:
Bv = var("B_v")
F = Matrix([ Fh, Fv, 0])
B = Matrix([ 0, Bv, 0 ])

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

M = Matrix([ 0, 0, -M ])

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

MF = rF.cross(F)
MB = rB.cross(B)

sum_M = MF + MB + M

Zero = Matrix([ 0, 0, 0 ])

eq_M = Eq(Zero, sum_M)

pprint(eq_M)
sol=solve([eq_M], [Bv])

pprint(sol)

--- User input ----------------- --- a: ------------------------- 9*kg*m 12*kg*m [{F_h: ------, F_v: -------}] 2 2 s s --- b: ------------------------- -9*kg*m -------- 2 s -5*kg*m -------- 2 s -7*kg*m -------- 2 s --- c: ------------------------- --- d: ------------------------- --- e: ------------------------- --- f: ------------------------- [0] = [ 0 ] [ ] [ ] [0] [ 0 ] [ ] [ ] [0] [ 2] [ 84*kg*m ] [12*B_v*m + --------] [ 2 ] [ s ] -7*kg*m {B_v: --------} 2 s