Etude mécanique.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etude en mécanique, avec un import de fichier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\"> L'objectif est de mener une analyse complète du mouvement d'un système dans un référentiel galiléen. C'est à dire établir et représenter :<ul> <li> son vecteur vitesse pour chacune des positions <li> la variation du vecteur vitesse pour chacune des positions <li> une étude énergétique (cinétique, potentielle et mécanique) </li> </ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import matplotlib.patches as mpatches\n",
    "from math import *\n",
    "from PIL import Image \n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Importer les données expérimentales. </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consignes </b> \n",
    "<br> Charger vos données, au format csv. Dans l'exemple,le nom du fichier est <i>pointage.csv</i>.\n",
    "<ul>\n",
    "<li>Le fichier de données ne doit contenir <b> QUE</b> les valeurs expérimentales, il faut donc supprimer d'abord toute entête de paramètre, unité, titre etc.... </li>\n",
    "<li>Le fichier doit être chargé (glisser déposer) dans le repertoire github clône créé par mybinder.  </li>\n",
    "<li>Cliquer ensuite sur le bouton Téléverser.  </li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGBA size=1153x137 at 0x17637398148>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Image.open(\"Etude mécanique.PNG\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consignes </b> \n",
    "<br> Modifier le programme \n",
    "<ul>\n",
    "<li> Il faut indiquer le nom de votre fichier en csv que vous avez impoté. L'exemple par défaut est <i> pointage.csv </i>, il convient de changer bien évidement cette chaine de caractères dans le code. </li> \n",
    "<li> Attention à conserver les ' ' déjà présent ci-dessous.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesures=pd.read_csv(r'pointage.csv',sep=';',decimal=',', header=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Extraction des données relatives à chaque position </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>Compléter le programme en indiquant le numéro de colonne correspondant à chacune des grandeurs à indiquées.</li><li>Relever la valeur de Tau.</li></ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <details>\n",
    "        <summary> <b> Aides </b> </summary>\n",
    "        <ul>\n",
    "            <li> la numérotation commence par 0! </li>\n",
    "        </ul>\n",
    "    </details>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesures=pd.DataFrame(mesures).to_numpy()\n",
    "\n",
    "# extraction du nombre totale de positions successives mesurées appelé nbr\n",
    "nbr=len(mesures)\n",
    "\n",
    "# extraction du temps et des positions au cours du mouvement\n",
    "t=list(mesures.T[XXX])  #Indiquer le numéro de la colonne correspondant aux valeurs de la durée t \n",
    "x=list(mesures.T[XXX])  #Indiquer le numéro de la colonne correspondant aux valeurs des abscisses x\n",
    "y=list(mesures.T[XXX])  #Indiquer le numéro de la colonne correspondant aux valeurs des ordonnées y\n",
    "\n",
    "# Calcul de l'intervalle Tau de temps entre deux positions successives\n",
    "Tau=t[1]-t[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t=t[1:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Cinématique du mouvement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Représentation de la trajectoire et du vecteur vitesse du système </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "    <ul><li>Etablir la formule du vecteur vitesse pour la position Mi.</li>\n",
    "   <li> Compléter le programme en décomposant cette formule selon les coordonnées.</li></ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <details>\n",
    "        <summary> <b> Aides </b> </summary>\n",
    "        <ul>\n",
    "            <li> Pour chaque position Mi il faut regarder le point d'avant (Mi-1) et le point d'après (Mi+1) pour définir la vitesse au passage en Mi </li>\n",
    "            <li> le temps du trajet se défini d'après la constante Tau qui représente la durée entre deux positions successives </li>\n",
    "        </ul>\n",
    "    </details>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "v_x=[]\n",
    "v_y=[]\n",
    "for i in range(1,len(x)-1):\n",
    "    v_x.append(XXX)     #écrire la formule de la vitesse pour les abscisses de position. On note x[i] l'abscisse du point Mi\n",
    "    v_y.append(XXX)     #écrire la formule de la vitesse pour les ordonnées de position. On note y[i] l'abscisse du point Mi\n",
    "\n",
    "def representation_graphique1(x,y,v_x,v_y):\n",
    "    plt.figure(figsize=(10,10))\n",
    "    plt.scatter(x,y,marker='+')\n",
    "    plt.title('Vecteur vitesse')\n",
    "    plt.xlabel('x en (m)')\n",
    "    plt.ylabel('Altitude y en (m)')\n",
    "    plt.xlim(0.8*min(x),1.2*max(x))\n",
    "    plt.ylim(0.8*min(y),1.2*max(y))\n",
    "    for i in range(0,len(v_x),1):\n",
    "        V=plt.quiver(x[i+1], y[i+1] ,2*v_x[i] ,2*v_y[i],\n",
    "         scale_units='xy',angles='xy', scale=12)\n",
    "representation_graphique1(x,y,v_x,v_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Calcul de la norme des différents vecteur vitesse nommés vit </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>Retenir pour la suite que vit correspond à la norme donc la valeur de la vitesse pour chaque position.</li>\n",
    "    <li>Justifier la formule écrite.</li>\n",
    "    </ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vit=[]\n",
    "for i in range(0,len(v_x)):\n",
    "    vit.append(sqrt(v_x[i]**2+v_y[i]**2)) #calcul de la valeur de la vitesse. En python la fonction racine carrée s'écrit sqrt et la puissance de 2 s'écrit **2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Représentation de la trajectoire et de la variation du vecteur vitesse du système </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>Etablir la formule de la variation du vecteur vitesse pour chaque position Mi.</li>\n",
    "    <li>Décomposer cette formule selon ses composantes.</li>\n",
    "    </ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Dv_x=[]\n",
    "Dv_y=[]\n",
    "for i in range(1,len(v_x)-1):\n",
    "    Dv_x.append(XXX) #écrire la formule de la variation de l'abscisse du vecteur vitesse. On note v_x[i] l'abscisse du vecteur vitesse au point Mi\n",
    "    Dv_y.append(XXX) #écrire la formule de la variation de l'ordonnée du vecteur vitesse. On note v_y[i] l'ordonnée du vecteur vitesse au point Mi\n",
    "    \n",
    "def representation_graphique2(x,y,Dv_x,Dv_y):\n",
    "    plt.figure(figsize=(10,10))\n",
    "    plt.scatter(x,y,marker='+')\n",
    "    plt.title('Variation du vecteur vitesse')\n",
    "    plt.xlabel('x en (m)')\n",
    "    plt.ylabel('Altitude y en (m)')\n",
    "    plt.xlim(0.8*min(x),1.2*max(x))\n",
    "    plt.ylim(0.8*min(y),1.2*max(y))\n",
    "    for i in range(0,len(Dv_x)):\n",
    "        V=plt.quiver(x[i+2], y[i+2] ,2*Dv_x[i] , 2*Dv_y[i],\n",
    "         scale_units='xy',angles='xy', scale=12)\n",
    "representation_graphique2(x,y,Dv_x,Dv_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Calcul et affichage de la valeur moyenne de la variation du vecteur vitesse </b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Dv=[]\n",
    "for i in range(0,len(Dv_y)):\n",
    "    Dv.append(sqrt(Dv_x[i]**2+Dv_y[i]**2)) #calcul de la valeur de la vitesse. En python la fonction racine carrée s'écrit sqrt et la puissance de 2 s'écrit **2\n",
    "Dvm=np.mean(Dv)\n",
    "print(Dvm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Etude énergétique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>estimer la masse du système en faisant une recherche sur internet.</li>\n",
    "\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m=XXX   #masse du système en kg\n",
    "g=9.81   #intensité de la pesanteur en N/kg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>Etablir la formule de l'énergie cinétique.</li>\n",
    "<li>Etablir la formule de l'énergie potentielle de pesanteur.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <details>\n",
    "        <summary> <b> Aides </b> </summary>\n",
    "        <ul>\n",
    "            <li> La variable vitesse, telle qu'écrite dans le programme, est vit.</li>\n",
    "            <li> La variable altitude, tel qu'écrite dans le programme, est y.  </li>\n",
    "        </ul>\n",
    "    </details>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ec=[]\n",
    "for i in range(0,len(vit)):\n",
    "    Ec.append(XXX)  #Ecrire la formule de l'énergie cinétique pour créer la liste Ec\n",
    "\n",
    "Ep=[]\n",
    "for i in range(0,len(y)):\n",
    "    Ep.append(XXX)  #Ecrire la formule de l'énergie potentiel de pesanteur pour créer la liste Ep \n",
    "Ep=Ep[1:-1]\n",
    "print(len(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "        <b> Consigne </b> \n",
    "<ul><li>Etablir la formule de l'énergie mécanique que possède le système à la position Mi.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Em=[]\n",
    "for i in range(0,len(Ec)):\n",
    "    Em.append(XXX) #calcul de l'énergie mécanique pour chaque position Mi. On notera Ec[i] et Ep[i] les énergies cinétique et potentiel correspondantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.grid(True)\n",
    "plt.plot(t,Ec,marker='o',c='red') \n",
    "plt.plot(t,Ep,marker='o',c='blue')\n",
    "plt.plot(t,Em,marker='o',c='green') \n",
    "plt.xlabel(\"t en s\")\n",
    "plt.ylabel(\"Energie en J\")\n",
    "plt.title(\"Bilan énergétique\")\n",
    "red_patch = mpatches.Patch(color='red', label='Ec')\n",
    "blue_patch = mpatches.Patch(color='blue', label='Ep')\n",
    "green_patch = mpatches.Patch(color='green', label='Em')\n",
    "plt.legend(handles=[red_patch,blue_patch,green_patch ])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=\"1\"> contact : sophie.gronlier@ac-lille.fr </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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