Mouvement parabolique et accélération (version avec fonctions)

Télécharger le pdf

Télécharger le notebook, le csv et la vidéo

Lancer le notebook sur binder (lent)

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
import csv

def charge_fichier_csv(fichier, delimiter=";",N=0):
    with open(fichier, 'r', encoding='utf-8') as f :
        rfichier = csv.reader(f, delimiter=delimiter)
        tableau=[]
        index_row=0
        for row in rfichier:
            if index_row < N:
                index_row = index_row+1
            else :
                for i in range (len(row)):
                    if len(tableau) <= i:
                        X = []
                        tableau.append(X)
                    try:
                        tableau[i].append(float(row[i].replace(",",'.')))
                    except ValueError:
                        print('erreur:contenu de cellule non numérique')
                        continue

        return (tableau)

def derivee(t,z):
    dz=[]
    for i in range (len(z)-1) :
        dzi=(z[i+1]-z[i])/(t[i+1]-t[i])
        dz.append(dzi)
    return (dz)

def graphacceleration (x,y,ax,ay):
    fig = plt.figure()
    plt.plot(x,y,'bo-')
    for i in range (0, len (ay)):
        plt.arrow(x[i],y[i],0.03*ax[i],0.03*ay[i],head_width=0.1,
                  length_includes_head=True)
        plt.arrow(x[i],y[i],0,0.1*(-9.8),fc='r',ec='r',
                  head_width=0.1,length_includes_head=True)
    plt.xlim(min(x)-1,max(x)+1)
    plt.ylim(min(y)-1,max(y)+1)
    plt.grid()
    plt.xlabel("x(m)")
    plt.ylabel("y(m)")
    plt.title("Comparaison entre accélération et champ de "
              "pesanteur")
    plt.show()

def comparaison (t,ax,ay):
    t2=np.array(t[:-2])
    axth=0*t2
    ayth=0*t2-9.8
    coeffax=np.polyfit(t2,ax,0)
    axmod=0*t2+coeffax[0]
    coeffay=np.polyfit(t2,ay,0)
    aymod=0*t2+coeffay[0]
    fig = plt.figure()
    plt.plot(t2,ay,'bo-',label="ay")
    plt.legend()
    plt.grid()
    plt.ylim(min(ay)-1,max(ay)+1)
    plt.plot(t2,ayth,'r-',label="g")
    plt.legend()
    plt.plot(t2,aymod,'g-',label="moyenne")
    plt.legend()
    plt.xlabel("temps")
    plt.ylabel("accélération verticale")
    plt.title("Comparaison entre accélération verticale et "
              "champ de pesanteur vertical")
    plt.show()
    print("la valeur moyenne de l'accélération verticale est"
          ,round(coeffay[0],1),"m/s²")
    plt.plot(t2,ax,'bo-',label="ax")
    plt.legend()
    plt.grid()
    plt.ylim(min(ax)-1,max(ax)+1)
    plt.plot(t2,axth,'r-',label="0")
    plt.legend()
    plt.plot(t2,axmod,'g-',label="moyenne")
    plt.legend()
    plt.xlabel("temps")
    plt.ylabel("accélération horizontale")
    plt.title("Comparaison entre accélération horizontale "
              "et champ de pesanteur horizontal")
    plt.show()
    print("la valeur moyenne de l'accélération horizontale est"
          ,round(coeffax[0],1),"m/s²")

tableau = charge_fichier_csv("parabole2.csv",N=1)
print(tableau)
t=tableau[0]
x=tableau[1]
y=tableau[2]
vx=derivee(t,x)
vy=derivee(t,y)
ax=derivee(t,vx)
ay=derivee(t,vy)
graphacceleration (x,y,ax,ay)
comparaison (t,ax,ay)

[[0.24, 0.28, 0.32, 0.36, 0.4, 0.44, 0.48, 0.52, 0.56, 0.6, 0.64, 0.68, 0.72, 0.76, 0.8, 0.84, 0.88, 0.92, 0.96, 1.0, 1.04, 1.08, 1.12, 1.16], [-0.223951998822, -0.343580601208, -0.51009038223, -0.707225408616, -0.904090917691, -1.06952262947, -1.26584910392, -1.46177130241, -1.61175563285, -1.78383296605, -1.97894661261, -2.17352122454, -2.35318748976, -2.53150616842, -2.71835708968, -2.8809588697, -3.06740551499, -3.24478088307, -3.42283004442, -3.60792910316, -3.78490019527, -3.97731866872, -4.13111868882, -4.2990185037], [1.76458242983, 1.97872907661, 2.22294809106, 2.45118719902, 2.66398567058, 2.84644213942, 3.02835933818, 3.18711558233, 3.36984168622, 3.49040079194, 3.60283512689, 3.68438818904, 3.79709215904, 3.83259294703, 3.91428082671, 3.93461061335, 3.99313753842, 3.97459609901, 3.9946562506, 3.97597999367, 3.93427759966, 3.8923055706, 3.85100762916, 3.73223687067], [-3.35881386319, -3.83926907511, -4.39437831948, -4.6984222285, -4.61537628747, -4.59800458895, -4.6734998329, -4.39648990626, -4.26517089855, -4.53285206253, -4.72307275216, -4.66513122103, -4.53973738179, -4.51201266471, -4.41596392065, -4.41034897667, -4.48905549951, -4.47657956306, -4.52581793104, -4.52774853362, -4.51639558597, -4.33379221852, -4.15861517319, -4.15321687131], [5.54030774149, 5.7088992284, 5.72816977458, 5.44184327251, 4.98744077131, 4.60697343994, 4.32141849032, 4.12782399047, 3.67426409878, 3.02603583823, 2.55077455354, 2.30508951049, 1.88360398803, 1.52476923155, 1.24757155895, 0.925891633931, 0.51693242311, 0.109564808036, -0.143354032685, -0.647506495101, -0.990538125172, -1.24691830515, -1.81555270826, -2.43219952115]]

la valeur moyenne de l'accélération verticale est -9.5 m/s²

la valeur moyenne de l'accélération horizontale est -1.4 m/s²