{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## O problemă de fizică" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cele doua ecuații de mișcare:\n", " " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "$x_1(t)=20t+1.25t^2 $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$x_2(t)=1000-30t+1.6t^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Legile vitezelor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v_1(t)=20+1.25t$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v_2(t)=-30+1.6t$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dacă se reprezintă grafic legile de mișcare pentru t între -20s și 130s rezultă graficul de mai jos. Se vede că parabolele se întâlnesc în cele două puncte $t=24 $ și $t=118s$ aproximativ și coordonatele corespunzătoare NU sunt între 0 și 1000." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VPiKKjIzk6NGjZGdnM3bsWMLDw0lMTOTXX39F0zT8/f0Z/dvRy0FBQXTu3Jmp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\naanSTEKI2qHWFlFCQgJr165FKUWPHj3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "plt.style.use('ggplot')\n", "\n", "x = np.linspace(-20, 130, 150) \n", "\n", "\n", "y1 =20*x +1.25*x*x\n", "y2 = 1000-30*x +1.6*(x**2)\n", "\n", "plt.xlabel('t')\n", "plt.ylabel('x(t)')\n", "\n", "plt.title('Legi de miscare x1 si x2')\n", "\n", "plt.plot(x, y1,'-b', label='x1')\n", "plt.plot(x, y2,'-r', label='x2')\n", "\n", "\n", "\n", "#plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dacă se face reprezentare în interval de timp în jurul valorii $t=24s$ se obține mai exact locul corespunzător al întâlnirii. Si se vede că până în 1000m cele două mobile nu se întâlnesc." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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lPT0di6VgMpu8vDyOHDlCcHAw4eHhfPvttwAcOHCAiIgIACIiIjhw4AAABw8e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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "plt.style.use('ggplot')\n", "\n", "x = np.linspace(-0, 50, 50) \n", "\n", "\n", "y1 =20*x +1.25*x*x\n", "y2 = 1000-30*x +1.6*(x**2)\n", "\n", "plt.xlabel('t')\n", "plt.ylabel('x(t)')\n", "plt.title('Legi de miscare x1 si x2')\n", "\n", "plt.plot(x, y1,'-b', label='x1')\n", "plt.plot(x, y2,'-r', label='x2')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fel în jurul valorii $t=118s$ al doilea loc al întâlnirii:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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o16yhce/emN3cyEpOvmz4ZGWpmTjRg0cf9aFPnzISE2/cAUPrk5wBCSHERWgy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\nWrQIq1evhhAChYWF+Oijj2A0GvHBBx8gLS0NcXF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "plt.style.use('ggplot')\n", "\n", "x = np.linspace(110, 130, 20) \n", "\n", "\n", "y1 =20*x +1.25*x*x\n", "y2 = 1000-30*x +1.6*(x**2)\n", "plt.xlabel('t')\n", "plt.ylabel('x(t)')\n", "plt.title('Legi de miscare x1 si x2')\n", "\n", "plt.plot(x, y1,'-b', label='x1')\n", "plt.plot(x, y2,'-r', label='x2')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vitezele în funcție de timp sunt reprezentate mai jos. Reprezentarea este între $t=0s$ și $t=200s$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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N3Q8/m9LSaDSIiYlp8vYOWbpNFMUaRyEFBQWWr7/77ju0bdsWABAeHo5vvvkG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\n/PQTjP/8J0y9ekHt6KLchEK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AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "plt.style.use('ggplot')\n", "\n", "x = np.linspace(0, 200, 200) \n", "\n", "\n", "v1 =20+1.25*x\n", "v2 =-30 +1.6*x\n", "\n", "plt.xlabel('t')\n", "plt.ylabel('v(t)')\n", "plt.title('Viteze v1 si v2')\n", "\n", "plt.plot(x, v1,'-b', label='v1')\n", "plt.plot(x, v2,'-r', label='v2')\n", "\n", "#plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "În graficul de mai sus se vede că al doilea mobil(roșu) are la un moment dat viteza zero, intersecteaza axa $v(t)=0$ într-un punct.\n", "Ala e momentul opririi. Din acest punct accelerează și se întoarce în sensul pozitiv al axei." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v_2=-30+1.6t=0$ rezultă $t=30/1.6=18,75s$ momentul opririi." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Locul opririi este $x_2=814m$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mai trebuie aflat când trece pe la 814m mobilul 1. Din primul grafic se vede \n", "că trece în jurul lui 20s.Dar se poate calcula si exact." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cam asta ar fi ideea, dacă nu am greșit pe undeva." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }