{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analyse énergétique d'un mouvement \n", "## (spécialité physique première S)\n", "\n", "- Capacité numérique : Utiliser un langage de programmation pour effectuer le bilan énergétique d’un système en mouvement.\n", "\n", "activité support:\n", "\n", "- Les positions d'un système sont obtenues à partir d'une table à coussin d'air ou d'un enregistrement vidéo. Après avoir pour chaque point de la trajectoire précisé les coordonnées (X,Y), les élèves doivent les rentrer dans les deux listes dédiées.\n", "- Les élèves doivent ensuite indiquer l'intervalle de temps qui sépare deux positions consécutives en modifiant la valeur par défaut 0.1 dans la ligne:t=0.1*i\n", "- Le programme permet à partir de ces positions de calculer puis représenter les différentes énergies associées aux mouvements.Les élèves doivent pour cela modifier la valeur de la masse pour les fonctions energie_cinetique et energie_potentielle.\n", " " ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ":download:`Télécharger le pdf <./mouvement_etude_energetique.pdf>`\n", "\n", ":download:`Télécharger le notebook <./mouvement_etude_energetique.ipynb>`\n", "\n", ":download:`Lancer le notebook sur binder (lent) `" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#!/usr/bin/env python3\n", "# -*- coding: utf-8 -*-\n", "#\n", "#On importe les bibliothèques et les modules nécessaires.\n", "\n", "from math import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "\n", "#définition d'une fonction permettant de calculer la dérivée à un instant donné\n", "# les conditions initiales sont imposées par défaut par précaution.\n", "def derivation(position1=0,position2=1,instant1=0,instant2=1):\n", " #initialisation d'une variable globale v \n", " global derivee\n", " derivee=0\n", " derivee=(position2-position1)/(instant2-instant1)\n", " \n", "#définition d'une fonction premettant de calculer la norme d'un vecteur ou une distance\n", "def module (valeurx=0,valeury=0):\n", " global norme\n", " norme=0\n", " norme= sqrt(valeurx*valeurx+valeury*valeury) \n", "\n", "#définition d'une fonction pour calculer l'énergie cinétique d'un système\n", "# la vitesse et la masse sont définies par défaut. On peut être amener à changer la masse. \n", "def energie_cinetique( v=1, masse=1):\n", " global energiecinetique\n", " energiecinétique=0\n", " energiecinetique=0.5*masse*v*v\n", " #Si nécessaire pour vérifier le bon fonctionnement de la fonction retirer # devant print.\n", " #print (energiecinetique)\n", "\n", "#définition d'une fonction pour calculer l'énergie potentielle d'un système\n", "# la position et la masse sont définies par défaut. On peut être amener à changer la masse.\n", "def energie_potentielle(position,masse=1):\n", " global energiepotentielle\n", " energiepotentielle=0\n", " energiepotentielle=masse*9.8*position\n", " #Si nécessaire pour vérifier le bon fonctionnement de la fonction retirer # devant print.\n", " #print(energiepotentielle)\n", "\n", "#définition d'une fonction pour calculer l'énergie potentielle d'un système\n", "def energie_mecanique():\n", " global energiemecanique\n", " energiemecanique=0\n", " energiemecanique= energiepotentielle+energiecinetique\n", " #Si nécessaire pour vérifier le bon fonctionnement de la fonction retirer # devant print.\n", " #print(energiemecanique)\n", " \n", "def representation_graphique (abscisse=[1],ordonnee=[1],etiquette=\"légende\",titre=\"Energie en fonction du temps\",abs=\"temps(s)\",ordo=\"Energie(J)\"):\n", " plt.plot(abscisse,ordonnee,'o-',label=etiquette)\n", " plt.grid()\n", " plt.legend()\n", " plt.xlabel(abs)\n", " plt.ylabel(ordo)\n", " plt.title(titre)\n", " plt.show() \n", " \n", "\n", "#programme prinipal\n", "\n", "#entrer les positions du système suivant les deux axes du repère.\n", "X=np.array([0.01,0.41,0.91,1.39,1.86,2.33,2.81,3.33,3.79,4.31,4.83,5.36,5.86,6.34,6.77])\n", "#liste contenant les abscisses.\n", "Y=np.array([0.01,0.52,1.01,1.42,1.77,2.02,2.16,2.19,2.13,1.96,1.71,1.38,0.97,0.50,0])\n", "#liste contenant les ordonnées.\n", "# repérage temporel des positions à partir de la fréquence d'aquisition et du nombre total de points.\n", "temps=[]\n", "for i in range(len(X)): \n", " t=0.1*i\n", " temps.append(t)\n", "#initialisation des deux listes qui recevront les valeurs des. vitesses instantanées suivant les deux axes.\n", "vity=[]\n", "vitx=[]\n", "#initialisation de la liste recevant la valeur de la vitesse.\n", "vinstantanee=[]\n", "#initialisation des listes recevant les valeurs des differentes energies.\n", "ecinetique=[]\n", "epotentielle=[]\n", "emecanique=[]\n", "#calcul des énergies pour les différentes positions utilisation d'une boucle for.\n", "for i in range(len(X)-1):\n", " derivation(Y[i],Y[i+1],temps[i],temps[i+1])\n", " vity.append(derivee)\n", " derivation (X[i], X[i+1],temps[i],temps[i+1])\n", " vitx.append(derivee)\n", " module(vitx[i],vity[i])\n", " vinstantanee.append(norme)\n", " energie_cinetique(norme,2)\n", " ecinetique.append(energiecinetique)\n", " energie_potentielle(Y[i],2)\n", " epotentielle.append(energiepotentielle)\n", " energie_mecanique()\n", " emecanique.append(energiemecanique)\n", "# On ajuste le nombre d'éléments des deux listes en enlevant le dernier élément de la liste des instants.\n", "tps=temps[:-1]\n", "#modifier les arguments des différents paramètres de ces fonctions pour obtenir l'affichage désiré.Selon l'exemple ci-dessous.\n", "representation_graphique(tps,emecanique,\"energie mécanique\",)\n", "representation_graphique(tps,ecinetique,\"Energie cinétique\")\n", "representation_graphique(tps,epotentielle,\"Energie potentielle\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }