{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lectii www.quarq.ro"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mișcarea rectilinie uniformă - MRU"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Este cel mai simplu exemplu de mișcare mecanică. Este mișcarea unui mobil pe o traiectorie rectilinie cu\n",
"viteză constantă. De exemplu vitezomentrul unui automobil care se mișcă pe o traiectorie rectilinie indică vitezele din tabelul de mai jos. Acesta este un exemplu de mobil care are o viteză constantă de $2m/s$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Alt Text](c1.PNG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Viteza medie coincide cu viteza momentană. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$v= \\frac{\\Delta x}{\\Delta t}=\\frac{x-x_0}{t-t_0 }=const. $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Rezultă:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x = x_0 + v (t-t_0)$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Relația de mai sus se numește lege de mișcare. O lege de mișcare este o funcție care exprimă modul în care variază \n",
"coordonata/poziția unui mobil în funcție de timp în raport cu originea axei de coordonate (vezi figura de mai jos)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Alt Text](c2.PNG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dacă momentul inițial se alege astfel încât $t_0=0s$ atunci legea de mișcare se scrie mai simplu astfel:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x = x_0 + v t$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Exemplu **"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Să considerăm 3 automobile care se deplasează rectiliniu uniform și care la momentul inițial $t_0=0s$ se găsesc în pozițiile de mai jos."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Alt Text](c3.PNG)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Legile de mișcare ale celor 3 mobile sunt:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x_1(t)= 10+2t $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x_2(t)= 40-t $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x_3(t)= -10+5t $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Reprezentarea grafică a acestora este redată mai jos."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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HGhoasH//fhw8eBAuLi4ICAjAs88+i2+++QZPPPEEAMDLywuLFi0CADz66KP46KOP8MMP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\nERHphYGEiIj0wkBCRER6+f/yledGVpyKGwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"%matplotlib inline\n",
"plt.style.use('ggplot')\n",
"\n",
"x = np.linspace(0, 50, 100) \n",
"y1 = 10+2*x\n",
"y2 = 40-x\n",
"y3 = -10+5*x\n",
"\n",
"plt.xlabel('t(s)')\n",
"plt.ylabel('x(m)')\n",
"\n",
"plt.title('Graficul pozitie-timp')\n",
"\n",
"plt.plot(x, y1,'-b', label='Mobilul 1')\n",
"plt.plot(x, y2,'-r', label='Mobilul 2')\n",
"plt.plot(x, y3,'-g', label='Mobilul 3')\n",
"\n",
"\n",
"plt.legend(loc='upper right')\n",
"#plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Punctele de intersecție a graficelor reprezintă locul și momentul întâlnirii mobilelor."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Punctele de întâlnire se pot calcula analitic dacă se pune condiția ca la momentul întâlnirii mobilele să se afle în \n",
"acelasi punct. De exemplu condiția ca mobilul 1 să întâlnească mobilul 2 este:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$x_1(t)=x_2(t)$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$10+2t =40-t $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$3t =30$ $\\quad$ $t =10 s$, momentul intalnirii $\\quad$ $ x=30m$, locul întâlnirii"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [Root]",
"language": "python",
"name": "Python [Root]"
},
"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
}