1.2.D.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)

# Derived units:
N = kg*m/s/s

print("------ User input ---------------------")

symbolic = True
# symbolic = False

if symbolic:
    # quantity = symbol:
    F, a = var("F, a")
else:
    # factors:
    F_val = 5
    a_val = 3
    # quantity =  factor times unit:
    F = F_val * N
    a = a_val * m

print("\n--- b: Section forces ----------------")
alpha, beta = var("alpha beta")
S1, S2 = var("S1, S2")

ca, sa = cos(alpha), sin(alpha)
cb, sb = cos(beta), sin(beta)

# equilibrium conditions:
# symbolic:
eq1 = Eq(0, -S1*sa + S2*sb)
eq2 = Eq(0, F + S1*ca + S2*cb)
pprint(eq1)
pprint(eq2)

# using values:
cav = 2*sqrt(5)/5
sav = sqrt(5)/5
cbv = sqrt(2)/2
sbv = cbv
subs_lst=[(ca,cav),(sa,sav),(cb,cbv),(sb,sbv)]
eq1 = eq1.subs(subs_lst)
eq2 = eq2.subs(subs_lst)

pprint(eq1)
pprint(eq2)

# solve linear system:
eqs = [eq1, eq2]
sol = solve(eqs, [S1, S2])

# print:
pprint(sol)


print("\n--- c: Reaction forces ---------------")
# symbolic:
A_h, A_v, B_h, B_v = var("A_h, A_v, B_h, B_v")
eq1 = Eq(A_h, -S1*sa)
eq2 = Eq(A_v, -S1*ca)
eq3 = Eq(B_h, -S2*sb)
eq4 = Eq(B_v, -S2*cb)

# print:
for eq in [eq1, eq2, eq3, eq4]:
    pprint(eq)

# substitute angles and S1, S2:
[eq1,eq2,eq3,eq4] = [eq.subs(subs_lst) for eq in [eq1,eq2,eq3,eq4]]
subs_lst=[(S1, sol[S1]), (S2, sol[S2])]
[eq1,eq2,eq3,eq4] = [eq.subs(subs_lst) for eq in [eq1,eq2,eq3,eq4]]

# print:
for eq in [eq1, eq2, eq3, eq4]:
    pprint(eq)

------ User input --------------------- --- b: Section forces ---------------- 0 = -S1*sin(alpha) + S2*sin(beta) 0 = F + S1*cos(alpha) + S2*cos(beta) ___ ___ \/ 5 *S1 \/ 2 *S2 0 = - -------- + -------- 5 2 ___ ___ 2*\/ 5 *S1 \/ 2 *S2 0 = F + ---------- + -------- 5 2 ___ ___ -\/ 5 *F -\/ 2 *F {S1: ---------, S2: ---------} 3 3 --- c: Reaction forces --------------- A_h = -S1*sin(alpha) A_v = -S1*cos(alpha) B_h = -S2*sin(beta) B_v = -S2*cos(beta) F A_h = - 3 2*F A_v = --- 3 F B_h = - 3 F B_v = - 3