1re Spé - Seconde loi de Newton.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# On détaille ici un programme python affichant les différentes positions de la masse d'un pendule ainsi que les vecteurs vitesse et variations de vitesse de la masse.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Le pendule"
   ]
  },
  {
   "attachments": {
    "pendule-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un pendule est constitué d'une masse m suspendue à un fil. La masse oscille de gauche à droite autour de la verticale, l'axe z dans l'image ci-dessous. \n",
    "La position de la masse m est repérée par son absisse $x_m$ et son ordonnée $z_m$.\n",
    "![pendule-2.png](attachment:pendule-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans cette [animation](https://web-labosims.org/animations/App_pendule_v3/App_pendule.html), on observe le pendule osciller.\n",
    "\n",
    "En cliquant sur \"Afficher les forces\" en bas à gauche, on voit les deux forces s'exerçant sur la masse.\n",
    "\n",
    "* Le poids $\\color {red} {\\vec P}$ de la masse. Il est vertical, vers le bas en rouge.\n",
    "\n",
    "* La tension $\\color {orange} {\\vec T}$ du fil qui retient la masse. Elle est de couleur jaune.\n"
   ]
  },
  {
   "attachments": {
    "chrono_pendule.jpg": {
     "image/jpeg": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On réalise une chronophotographie des oscillations du pendule puis, grâce à un logiciel on repère les différentes positions $x_m$ et $z_m$ de la masse au cours d'une oscillation.![chrono_pendule.jpg](attachment:chrono_pendule.jpg)"
   ]
  },
  {
   "attachments": {
    "DonneesPendule.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Voici le tableau regroupant les différentes positions de la masse au cours du temps. ([Ex 47 p 257 du Hatier 1re Physique Chimie](https://www.hatier-clic.fr/s/pc1257))\n",
    "![DonneesPendule.png](attachment:DonneesPendule.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dans cet exercice il faudra :\n",
    "###     1. Compléter les listes des coordonnées des positions de la masse du pendule au cours du temps\n",
    "###     2. Compléter les formules permettant de calculer les vecteurs vitesse\n",
    "###     3. Compléter les formules permettant de calculer les vecteurs variation de vitesse\n",
    "###     4. Comparer le vecteur variation de vitesse à la sommes des forces s'exerçant sur le pendule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chaque partie de code est précédée d'un titre.\n",
    "### Certaines parties de code sont à modifier par vous, cela est indiqué par la mention \"A VOUS DE JOUER !\" dans le titre de la partie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 0 : Initialisation des bibliothèques python nécessaires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.close() # On ferme les fenêtres graphiques éventuellement ouvertes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 1 : On entre les coordonnées des valeurs expérimentales des pointés."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### 1. dans l'ordre de numérotation et en mètre, compléter les listes x et z ci-dessous avec les 16 valeurs x et z expérimentales, les valeurs sont séparées par une virgule.\n",
    "### 2. Préciser la valeur de l'écart de temps delta_t entre chaque point, la valeur est en seconde."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-1-1a519b963136>, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-1-1a519b963136>\"\u001b[0;36m, line \u001b[0;32m3\u001b[0m\n\u001b[0;31m    delta_t =\u001b[0m\n\u001b[0m             ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "x = []\n",
    "z = []\n",
    "delta_t ="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 2 : On trace le graphique représentant la position des différents points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### Compléter le titre du graphique ainsi que les noms des axes avec leur unité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "min() arg is an empty sequence",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-206-a9d8cce8877a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mabs_debut\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Abscisse de début du graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mabs_fin\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Abscisse de fin du graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Définit la taille de l'affichage du graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# Affiche une grille sur le graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Titre du graphique\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m22\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#Définit le titre du graphique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: min() arg is an empty sequence"
     ]
    }
   ],
   "source": [
    "abs_debut = min(x) #Abscisse de début du graphique\n",
    "abs_fin =max(x) #Abscisse de fin du graphique\n",
    "plt.figure(figsize=(12,8)) #Définit la taille de l'affichage du graphique\n",
    "plt.grid() # Affiche une grille sur le graphique\n",
    "plt.title(\"Titre du graphique\", size=22) #Définit le titre du graphique\n",
    "plt.ylabel(\"Nom de l'axe et unité\", size=18) #Affiche le titre des ordonnées\n",
    "plt.xlabel(\"Nom de l'axe et unité\", size=18) #Affiche le titre des abscisses\n",
    "plt.xlim(abs_debut, abs_fin) #Définit le début et la fin des abscisses.\n",
    "plt.axis('equal') #Les axes sont orthonormés\n",
    "plt.plot(x, z, 'o', color ='blue', label = 'Positions pointées') #Affiche les points expérimentaux\n",
    "plt.legend(fontsize=18)# Affiche la légende\n",
    "plt.show() #Affiche le graphique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 3 : Ajout des vecteurs vitesse sur le graphique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 1. Calcul des coordonnées des vecteurs vitesse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les coordonnées v_x et v_z des vecteurs vitesse du point \"i\" se calculent par les formules suivantes :\n",
    "\n",
    "$v_{x}[i] = \\dfrac{x_{[i+1]} - x_{[i]}} {\\Delta t}$\n",
    "\n",
    "$v_{z}[i] = \\dfrac{z_{[i+1]} - z_{[i]}} {\\Delta t}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 2. Définition de la fonction de calcul des coordonnées des vecteurs vitesse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### A l'aide de l'expression de vz donnée ci-dessus dans le 1. et du calcul de vx donné dans la fonction \"vitesse\" ci-dessous , compléter la formule pour calculer vz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vitesse(x, z, delta_t): #la fonction se nomme vitesse\n",
    "    \n",
    "    vx = []\n",
    "    for i in range(0, len(x)-1): #création de la liste vx\n",
    "        vx.append((x[i+1]-x[i])/delta_t)\n",
    "        \n",
    "    vz = []\n",
    "    for j in range(0, len(z)-1): #création de la liste vz\n",
    "        vz.append(\"A modifier : Ecrire l'expression du calcul de vz\") \n",
    "  \n",
    "    return vx, vz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Tracé des vecteurs vitesse sur le graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [],
   "source": [
    "vx, vz = vitesse(x, z, delta_t) #La fonction vitesse() retourne deux listes stockées dans vx et vz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### Compléter le titre du graphique ainsi que les noms des axes avec leur unité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8)) #Définit la taille de l'affichage du graphique\n",
    "plt.grid() # Affiche une grille sur le graphique\n",
    "plt.title(\"Titre du graphique\", size=22) #Définit le titre du graphique\n",
    "plt.ylabel(\"Nom de l'axe avec son unité\", size=18) #Affiche le titre des ordonnées\n",
    "plt.xlabel(\"Nom de l'axe avec son unité\", size=18) #Affiche le titre des abscisses\n",
    "plt.xlim(abs_debut, abs_fin) #Définit le début et la fin des abscisses.\n",
    "plt.axis('equal') #Les axes sont orthonormés\n",
    "plt.plot(x, z, 'o', color ='blue', label = 'Positions pointées') #Affiche les points expérimentaux\n",
    "plt.legend(fontsize=18)# Affiche la légende\n",
    "\n",
    "for k in range (len(vx)):# ajout des vecteurs vitesse en rouge\n",
    "    plt.quiver(x[k], z[k], vx[k], vz[k], scale=19, scale_units='xy', color='red', angles='xy')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ETAPE 4 : Représentation des vecteurs variations de vitesse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 1. Calcul des coordonnées des vecteurs variations de vitesse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Delta v_x[i] = v_x[i+1] - v_x[i]$\n",
    "\n",
    "$\\Delta v_z[i] = v_z[i+1] - v_z[i]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 2. Définition de la fonction de calcul des corrdonnées des vecteurs variations de vitesse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### A l'aide des expressions de delta_vx et delta_vz données ci-dessus dans le 1. , compléter les formules ci-dessous pour calculer delta_vx et delta_vz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_v(vx, vz): #la fonction se nomme delta_v\n",
    "    \n",
    "    delta_vx = []\n",
    "    for i in range(0, len(vx)-1): #création de la liste delta_vx\n",
    "        delta_vx.append(\"A modifier : Ecrire l'expression du calcul de delta_vx\")\n",
    "        \n",
    "    delta_vz = []\n",
    "    for i in range(0, len(vz)-1): #création de la liste delta_vz\n",
    "        delta_vz.append(\"A modifier : Ecrire l'expression du calcul de delta_vz\")\n",
    "    \n",
    "    return delta_vx, delta_vz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Tracé des vecteurs vitesse sur le graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_vx, delta_vz = delta_v(vx, vz) #la fonction delta_v() retourne deux listes stockées dans delta_vx et delta_vz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A VOUS DE JOUER !\n",
    "### Compléter le titre du graphique ainsi que les noms des axes avec leur unité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8)) #Définit la taille de l'affichage du graphique\n",
    "plt.grid() # Affiche une grille sur le graphique\n",
    "plt.title(\"Titre du graphique\", size=22) #Définit le titre du graphique\n",
    "plt.ylabel(\"Nom de l'axe avec son unité\", size=18) #Affiche le titre des ordonnées\n",
    "plt.xlabel(\"Nom de l'axe avec son unité\", size=18) #Affiche le titre des abscisses\n",
    "plt.xlim(abs_debut, abs_fin) #Définit le début et la fin des abscisses.\n",
    "plt.axis('equal') #Les axes sont orthonormés\n",
    "plt.plot(x, z, 'o', color ='blue', label = 'Positions pointées') #Affiche les points expérimentaux\n",
    "plt.legend(fontsize=18)# Affiche la légende\n",
    "\n",
    "for i in range (len(vx)): # ajout des vecteurs vitesse en rouge\n",
    "    plt.quiver(x[i], z[i], vx[i], vz[i], scale=20, scale_units='xy', color='red', angles='xy')\n",
    "\n",
    "for j in range(len(delta_vx)): # ajout des vecteurs variations de vitesse en vert\n",
    "    plt.quiver(x[j+1], z[j+1], delta_vx[j], delta_vz[j], scale=5, scale_units='xy', color='green', angles='xy')"
   ]
  }
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