1.2.A.sagews

from sympy import *
from sympy import N as Num

from mpmath import degrees, radians

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

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

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

# quantity =  factor times unit:
alpha = radians(40)
F1 = 6 * N
F2 = 8 * N

beta = var("beta")

n_sig = 3

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

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

F1_v = F1 * ca
F1_h = F1 * sa

F2_v = F2 * cb
F2_h = F2 * sb

for F in [F1_v, F1_h, F2_v, F2_h]:
    pprint(F / N)

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

# overwrite beta:
beta = acos(ca*F1/F2)

beta_deg= degrees(beta)
pprint(Num(beta_deg,3))

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

# now with known beta:
cb = cos(beta)
sb = sin(beta)
F2_v = F2 * cb
F2_h = F2 * sb

R_h = F1_h + F2_h

# must be zero:
R_v = F1_v - F2_v

R = Matrix([R_h, R_v])
pprint(R/N)
pprint(Num(R.norm()/N,3))

--- User input ----------------------- --- a: ------------------------------- 4.59626665871387 3.85672565811924 8*cos(beta) 8*sin(beta) --- b: ------------------------------- 54.9 --- c: ------------------------------- [10.404575137299] [ ] [ 0 ] 10.4