{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PFD et analyse d'une force de frottement.\n", "## (Enseignement de spécialité première S)\n", "\n", "- Capacité numérique : Utiliser un langage de programmation pour étudier la relation approchée entre la variation du vecteur vitesse d’un système modélisé par un point matériel entre deux instants voisins et la somme des forces appliquées sur celui-ci.\n", "\n", "- activité support: Etude de la chute verticale d'un système avec ou sans frottement (acquisition vidéo). Enregistrement à l'aide d'une table à coussin d'air du mouvement rectiligne d'un système.\n", "\n", "- Dans ces conditions les élèves déterminent les vitesses en différents points de la trajectoire. (remarque: il est possible de modifier le programme pour calculer les vitesses en fonction des positions.)\n", "\n", "- Le programme permet de représenter la courbe donnant l'évolution de la vitesse en fonction du temps. Il permet de modéliser les forces de frottement. Ici seul le cas des frottements f=k*v est modélisé. \n", "- Il est possible de faire les autres modèles de frottements en modifiant la puissance sur la vitesse.\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ":download:`Télécharger le pdf <./PFD_modelisation_frottement.pdf>`\n", "\n", ":download:`Télécharger le notebook <./PFD_modelisation_frottement.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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" ] }, "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.\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", "\n", " \n", "# programme principal\n", "#Initialisation des données vitesse.\n", "vitesse=np.array([0,14,23,29,34,37,39,40,41,42,43,43,43,43,43,43,43,43]) \n", "\n", "#initialisation des listes qui recevront les instants et l'accélération.\n", "acceleration=[]\n", "temps=[]\n", "\n", "# repérage temporel des instants dans la liste temps[], à partir de la fréquence d'aquisition et du nombre total de points.\n", "for i in range(len(vitesse)): \n", " t=20*i\n", " temps.append(t)\n", "\n", "#calcul des accélération en utilisant la fonction dérivation utilisation de la boucle for.\n", "for i in range(len(vitesse)-1):\n", " derivation(vitesse[i],vitesse[i+1],temps[i],temps[i+1])\n", " acceleration.append(derivee)\n", " \n", " \n", "#modélisation de la force de frottement à partir de l'interprétation du PFD.\n", "v0=vitesse[:-1]\n", "# regression lineaire à partir de la fonction prédéfinie polyfit. Les arguments sont la vitesse, l'accélération,\n", "# et la puissance envisagée pour le modèle ici par défaut elle est prise égale à 1.\n", "mod=np.polyfit(v0,acceleration,1)\n", "model=mod[0]*v0+mod[1]\n", "#(mod[0] coefficient directeur et mod[1] ordonnée à l'origine.\n", "#représentation graphique pour interprétation avec le PFD.\n", "plt.figure()\n", "plt.plot(temps,vitesse,'bo', label='vitesse')\n", "plt.legend()\n", "plt.grid()\n", "plt.xlabel(\"temps\")\n", "plt.ylabel(\"vitesse\")\n", "plt.title(\"Vitesse de la bille en fonction du temps\")\n", "plt.show()\n", "#représentation de la modélisation de la force de frottement\n", "plt.figure()\n", "plt.plot(v0,acceleration,'ro',label='points expérimentaux')\n", "plt.plot(v0,model,'b-',label='modèle affine')\n", "plt.legend()\n", "plt.grid()\n", "plt.xlabel(\"vitesse\")\n", "plt.ylabel(\"accélération\")\n", "plt.title(\"Modèle de la force subie par la bille\")\n", "plt.show()" ] } ], "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 }