3.1.G.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 -----------------------")

half=S(1)/2

# symbols:
M, v0, mu, g = var("M, v0, mu, g")

# quantities:
quants = [
    (M, 100 *kg),
    (v0, 40 *m/s),
    (mu, S(4)/5),
    (g, 10 *m/s/s),
    ]

N = kg*m/s/s
k = 1000
kN = k*N

print("\n--- a: -------------------------------")
pprint("E_0 / (kNm):")
E_0 = half*M*v0*v0
E_0 = E_0.subs(quants)
pprint(E_0/(kN*m))

print("\n--- b: -------------------------------")
pprint("W_01:")
x, L = var("x, L")
F = mu*M*g
W_01 = integrate(F,(x,0,L))
pprint(W_01)

print("\n--- c: -------------------------------")
pprint("L:")
eq = Eq(W_01, E_0)

sol = solve([eq], [L])
L = sol[L]

pprint(L.subs(quants))

--- User input ----------------------- --- a: ------------------------------- E_0 / (kNm): 80 --- b: ------------------------------- W_01: L*M*g*mu --- c: ------------------------------- L: 100*m