# coding: utf-8
from __future__ import division
from lab import *
import numpy as np

# helpers
length = lambda x: x/100
mass   = lambda x: x/1000

# constants
m = mass(260.04) # cart mass (kg)
g = 9.80665      # acceleration due to gravity

##
## Collisions
##

# 3xmagnet, 2xrubber bumper, 2xputty

I = [0.23, 0.28, 0.36, 0.21, 0.27, 0.11, 0.15]  # force impulse

# cart velocity before-after colliding
v = [ (0.46,-0.44), (0.55,-0.54), (0.70,-0.71)  # elastic 
    , (0.52,-0.29), (0.68,-0.35)                # partially anelastic
    , (0.41, 0.00), (0.59, 0.00)                # anelastic
    ]

for i,_ in enumerate(I):
  K0, K1 = 1/2*m*v[i][0]**2, 1/2*m*v[i][1] # kinetic energy
  p0, p1 = m*v[i][0], m*v[i][1]            # momentuum
  dp = round(p1-p0, 3)
  dk = round(K1-K0, 3)
  print '''
urto {}:
  Δp={:.3f}, I={}, ΔK={:.2f} {:.2f}%
'''.format(i+1, dp, I[i], dk, abs((dp+I[i])/dp*100))


##
## Springs
##

x0 = 0.8675 # spring at rest offset

# force impulse
I = [ 0.32, 0.26, 0.35, 0.21, 0.34 # spring A
    , 0.42, 0.47, 0.50, 0.45, 0.68 # spring B
    ]  

# cart velocity before-after colliding
v = [ (0.61,-0.58), (0.51,-0.48), (0.66,-0.66), (0.41,-0.38), (0.67,-0.63) # spring A
    , (0.81,-0.77), (0.89,-0.87), (0.94,-0.93), (0.85,-0.83), (1.32,-1.26) # spring B
    ]

# maximum position reached (spring compressed)
x = [ 0.888, 0.885, 0.890, 0.882, 0.887 # spring A
    , 0.881, 0.884, 0.885, 0.885, 0.888 # spring B
    ]

# maximum force
F = [  5.55,  4.58,  6.29,  3.66,  6.10 # spring A
    , 18.61, 20.97, 22.25, 19.17, 31.25 # spring B
    ]

ka = []
kb = []

for i,_ in enumerate(I):
  k = F[i]/(x[i]-x0)       # spring elastic constant
  Ep = 1/2*k*(x[i] -x0)**2 # theoretical value (assuming ΔEm=0)

  K0, K1 = 1/2*m*v[i][0]**2, 1/2*m*v[i][1] # kinetic energy
  p0, p1 = m*v[i][0], m*v[i][1]            # momentuum
  dp  = round(p1-p0, 3)
  dk  = round(K1-K0, 3)
  dEm = round(K0-Ep, 3)
  if i<5:
    ka.append(k)
  else:
    kb.append(k)

  print '''
urto {}:
  Δp={:.3f}, I={:.2f}, ΔK={:.2f} {:.2f}%
  k_{}={:.3f}, ΔΕm={:.3f}
'''.format(i+1, dp, I[i], dk, abs((dp+I[i])/dp*100),('a' if i<5 else 'b'), k, dEm)


##
## Attrito
##

## cart

# a=0 => μ=tanθ=h/l
mu_s = length(11.5)/length(128.7)

# a=g(sinθ-μcosθ)
a = sample(1.54,1.54,1.50,1.48,1.54,1.53)
h, l = length(52.0), length(117.1)
mu_d = (h/l) - (a.mean/g)*np.sqrt(1+(h/l)**2)

print 'μs={:.2f} μd={:.2f}'.format(mu_s, mu_d)

## teflon block

# a=0 => μ=tanθ=h/l
mu_s = length(19.8)/length(127.0)

# a=g(sinθ-μcosθ)
a = sample(0.67,0.79,0.76,0.75,0.78,0.73)
h, l = length(34.1), length(125.5)
mu_d = (h/l) - (a.mean/g)*np.sqrt(1+(h/l)**2)

print 'μs={:.2f} μd={:.2f}'.format(mu_s, mu_d)