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    "# Moto lungo un piano inclinato\n",
    "\n",
    "## Esperimento sul moto 1D ed analisi dati\n",
    "\n",
    "Il moto di un corpo lungo un piano inclinato può essere studiato come esempio di **moto in una dimensione**. Obiettivo di questo esempio è quello di studiare la posizione, la velocità e l'accelerazione in funzione del tempo.\n",
    "\n",
    "<div id = \"immagine\">\n",
    "\n",
    "<img src = \"Immagini/Inclinato_01.jpg\" alt = \"Immagine\">\n",
    "\n",
    "</div>\n",
    "\n",
    "### Descrizione\n",
    "\n",
    "L'oggetto che si muove lungo il piano inclinato può essere descritto come un punto materiale che si muove lungo una retta. La posizione del punto materiale può essere individuata tramite la coordinata $ x $, il cui valore corrisponde in questo caso alla distanza tra l'oggetto ed un sensore situato all'inizio della pista.\n",
    "\n",
    "<div id = \"immagine\">\n",
    "\n",
    "<img src = \"Immagini/Inclinato_02.jpg\" alt = \"Immagine\">\n",
    "\n",
    "</div>\n",
    "\n",
    "In particolare, utilizziamo un **sensore ad ultrasuoni HC-SR04** che viene alimentato e controllato tramite una scheda [**Raspberry Pi**](https://www.raspberrypi.org/) (Raspberry Pi 3 Model B).\n",
    "\n",
    "<div id = \"immagine\">\n",
    "\n",
    "<img src = \"Immagini/Inclinato_03.jpg\" alt = \"Immagine\">\n",
    "\n",
    "</div>\n",
    "\n",
    "Semplici codici Python permettono di:\n",
    "\n",
    "* Registrare i valori di distanza tra il sensore fisso ed il veicolo in movimento.\n",
    "\n",
    "* E contemporaneamente misurare il tempo trascorso da un certo istante iniziale.\n",
    "\n",
    "I collegamenti del sensore alla scheda Raspberry Pi ed i codici Python per effettuare le misure sono descritti nel riferimento [1. Physics Education 2020](https://iopscience.iop.org/article/10.1088/1361-6552/ab73d2) (v. anche Supplementary Information)\n",
    "\n",
    "### Outline dell'attività\n",
    "\n",
    "1. **Effettuare un esperimento** registrando i valori della distanza sensore - oggetto durante il moto lungo il piano inclinato. Lo script Python permette di memorizzare i dati in un file di testo **distance-table.csv** strutturato nel modo seguente:\n",
    "\n",
    "| Tempo (s)             | Distanza (m)        |\n",
    "| :-------------------- | :------------------ |\n",
    "| 6.300999302766286e-06 | 0.04921078322613539 |\n",
    "| 0.20044025799870724   | 0.04400026829147464 |\n",
    "\n",
    "2. Ottenere una **rappresentazione grafica** dei dati.\n",
    "\n",
    "3. **Elaborare i dati** per ottenere i valori della velocità in funzione del tempo.\n",
    "\n",
    "4. Rappresentare graficamente l'andamento della velocità in funzione del tempo.\n",
    "\n",
    "5. Calcolare i valori dell'accelerazione in funzione del tempo e mostrare l'andamento in un grafico.\n",
    "\n",
    "6. Analizzare i dati della velocità:\n",
    "\n",
    "    * Scegliendo un intervallo di tempo nel quale l'andamento della velocità in funzione del tempo è lineare.\n",
    "    \n",
    "    * Trovando i parametri della retta che si adatta meglio ai dati sperimentali.\n",
    "\n",
    "        * La pendenza della retta fornisce il valore dell'accelerazione in tale intervallo di tempo.\n",
    "\n",
    "7. Valutare i risultati ottenuti riportando in un'unica figura i grafici di: coordinata $ x $, velocità e accelerazione.\n",
    "\n",
    "8. Confrontare il valore stimato dell'accelerazione con il valore calcolato utilizzando un **modello fisico**.\n",
    "\n",
    "Altri dettagli sui codici Python e sull'analisi dati sono forniti nel notebook Viaggio in ascensore.\n",
    "\n",
    "#### 1. Esperimento\n",
    "\n",
    "Predisponiamo un piano inclinato ed un oggetto che possa essere lasciato muovere lungo il piano inclinato.\n",
    "\n",
    "* Cerchiamo di svolgere l'esperimento in modo che le **condizioni** siano **ripetibili**.\n",
    "\n",
    "Una grandezza che caratterizza le condizioni in cui viene svolto l'esperimento è la misura dell'**angolo** che il piano inclinato forma con la direzione orizzontale. Si può misurare facilmente questo angolo installando sullo smartphone l'applicazione [phyphox](https://phyphox.org/). Tra i menù disponibili, sotto la voce **Strumenti** scegliere **Inclinazione** (misura l'angolo d'inclinazione del telefono). Premere il tasto **play** per iniziare la misura.\n",
    "\n",
    "<div id = \"immagine\">\n",
    "\n",
    "<img src = \"Immagini/Phyphox.png\" alt = \"Immagine\">\n",
    "\n",
    "</div>\n",
    "\n",
    "Si manda in esecuzione sulla Raspberry Pi il codice **distance_recorder.py** e si lascia che l'oggetto si muova lungo il piano inclinato, mentre i valori di distanza vengono misurati e memorizzati in un array. Lo script Python produce il file **distance_table.csv** in cui sono riportati i dati del tempo e della distanza.\n",
    "\n",
    "#### 2. Rappresentazione grafica dei dati\n",
    "\n",
    "Con il seguente codice leggiamo i dati contenuti nel file **distance-table.csv** e riportiamo in grafico la distanza sensore - oggetto in funzione del tempo trascorso da un certo istante iniziale."
   ]
  },
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   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Utilizzato per importare la libreria adoperata per le strutture e le funzioni matematiche.\n",
    "import numpy as np\n",
    "# Utilizzato per importare la libreria adoperata per i grafici.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# Utilizzato per importare un file di dati.\n",
    "inputDataFile = \"Dati/distance-table.csv\"\n",
    "\n",
    "# Utilizzato per leggere il file di dati.\n",
    "t, x = np.loadtxt(inputDataFile, delimiter = \",\", unpack = True)\n",
    "\n",
    "# Utilizzato per il grafico.\n",
    "plt.figure(1, figsize = (15, 15)) # Utilizzato per creare, numerare e dimensionare il grafico.\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Distanza sensore - oggetto in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Distanza $ (m) $\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t, x, \"o\", color = \"#0075E2\", markersize = 5)\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per mostrare il grafico.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Calcolare la velocità\n",
    "\n",
    "Per calcolare la velocità consideriamo gli spostamenti $ \\Delta x $ e la durata degli intervalli di tempo $ \\Delta t $ tra due misure successive. La velocità media riferita ad ogni intervallo di tempo viene calcolata come:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ v = \\dfrac{\\Delta x}{\\Delta t} $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Questo valore di velocità media viene riferito ad un tempo $ t' $ ottenuto come valore medio del tempo nell'intervallo $ \\Delta t $ considerato. I dati calcolati vengono memorizzati in un file **Incline-Speed.csv**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Utilizzato per importare il file.\n",
    "speedDataFile = \"Dati/Incline-Speed.csv\"\n",
    "\n",
    "# Utilizzato per impostare il numero di cifre decimali nella stampa dei dati su file.\n",
    "np.set_printoptions(precision = 20)\n",
    "# Utilizzato per calcolare delta t.\n",
    "delta_t = np.diff(t)\n",
    "# Utilizzato per calcolare delta x.\n",
    "delta_x = np.diff(x)\n",
    "# Utilizzato per calcolare la velocità in m/s.\n",
    "v = delta_x / delta_t\n",
    "# Utilizzato per calcolare il valore medio del tempo in ogni intervallo di tempo.\n",
    "t_prime = t[:-1] + (delta_t / 2)\n",
    "\n",
    "# Utilizzato per salvare i dati in un file.\n",
    "np.savetxt(speedDataFile, np.column_stack((t_prime, v)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Grafico della velocità in funzione del tempo\n",
    "\n",
    "Abbiamo già importato in una delle celle di codice di questo notebook Jupyter la libreria **Matplotlib**, quindi con le seguenti righe di codice possiamo utilizzare la funzione **plt.plot()** e tutte le altre funzioni della libreria per costruire un grafico della velocità in funzione del tempo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Utilizzato per il grafico.\n",
    "plt.figure(2, figsize = (15, 15)) # Utilizzato per creare, numerare e dimensionare il grafico.\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Velocità in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Velocità $ (m/s) $\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y e.\n",
    "plt.plot(t_prime, v, \"o\", color = \"#0075E2\", markersize = 5)\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per mostrare il grafico.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Calcolo dell'accelerazione\n",
    "\n",
    "L'accelerazione dell'oggetto che si muove lungo il piano inclinato viene calcolata in questo esempio come accelerazione media riferita a ciascun intervallo di tempo $ \\Delta t' $.\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ a = \\dfrac{\\Delta v}{\\Delta t'} $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Ciascun valore di accelerazione viene associato ad un tempo uguale al valore medio del corrispondente intervallo $ \\Delta t' $. I dati vengono memorizzati in un file **Incline-Acceleration.csv**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Utilizzato per importare il file.\n",
    "accelerationDataFile = \"Dati/Incline-Acceleration.csv\"\n",
    "\n",
    "# Utilizzato per impostare il numero di cifre decimali nella stampa dei dati su file.\n",
    "np.set_printoptions(precision = 20)\n",
    "# Utilizzato per calcolare delta t'.\n",
    "delta_t_prime = np.diff(t_prime)\n",
    "# Utilizzato per calcolare delta v.\n",
    "delta_v = np.diff(v)\n",
    "# Utilizzato per calcolare l'accelerazione in m/s^2.\n",
    "a = delta_v / delta_t_prime\n",
    "# Utilizzato per calcolare il valore medio del tempo' in ogni intervallo di tempo.\n",
    "t_double_prime = t_prime[:-1] + (delta_t_prime / 2)\n",
    "\n",
    "# Utilizzato per salvare i dati in un file.\n",
    "np.savetxt(accelerationDataFile, np.column_stack((t_double_prime, a)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I valori ottenuti vengono riportati in un grafico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Utilizzato per il grafico.\n",
    "plt.figure(3, figsize = (15, 15)) # Utilizzato per creare, numerare e dimensionare il grafico.\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Accelerazione in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Accelerazione $ (m/s^{2} $)\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_double_prime, a, \"o\", color = \"#0075E2\", markersize = 5, label = \"Calculated\")\n",
    "# Utilizzato per la legenda.\n",
    "plt.legend(loc = \"lower left\", shadow = True, fontsize = \"large\")\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "#plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per mostrare il grafico.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Possiamo osservare che l'accelerazione assume anche valori negativi. Questi valori corrispondono all'intervallo di tempo in cui l'oggetto, dopo essersi mosso lungo tutto il piano inclinato, viene rallentato bruscamente di proposito contro un ostacolo morbido.\n",
    "\n",
    "#### 6. Analisi dei dati della velocità\n",
    "\n",
    "##### 6.1. Selezione di un sottoinsieme di dati\n",
    "\n",
    "Il numero di coppie (tempo $ t' $, velocità $ v $) è dato dalla dimensione dell'array che può essere calcolata tramite la funzione **np.size()** della libreria **NumPy**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizzato per calcolare la dimensione dell'array.\n",
    "np.size(t_prime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per poter restringere l'analisi ad un determinato intervallo di tempo utilizzamo due **marker**, ciascuno dei quali corrisponde al numero progressivo del dato considerato."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valori consigliati: 9, 17\n",
      "Primo marker = 9 - Secondo marker = 17\n",
      "Primo tempo = 1.9042753854992043 s - Secondo tempo = 3.5076683864990628 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.funzione(MarkerOne, MarkerTwo)>"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizzato per importare la libreria adoperata per i widget.\n",
    "import ipywidgets as widgets\n",
    "\n",
    "\n",
    "# Utilizzato per creare un widget (IntSlider) adoperato per cambiare interattivamente il valore del primo marker.\n",
    "sliderMarkerOne = widgets.IntSlider(min = 0, max = (np.size(t_prime) - 1), step = 1, value = 9, continuous_update = False)\n",
    "# Utilizzato per creare un widget (IntSlider) adoperato per cambiare interattivamente il valore del secondo marker.\n",
    "sliderMarkerTwo = widgets.IntSlider(min = 0, max = (np.size(t_prime) - 1), step = 1, value = 17, continuous_update = False)\n",
    "\n",
    "# Funzione.\n",
    "def funzione(MarkerOne, MarkerTwo):\n",
    "    print(\"Valori consigliati: 9, 17\") # Utilizzato per stampare.\n",
    "    print(\"Primo marker =\", MarkerOne, \"-\", \"Secondo marker =\", MarkerTwo) # Utilizzato per stampare.\n",
    "    MarkerOneTime = t_prime[MarkerOne] # Utilizzato per il primo marker.\n",
    "    MarkerTwoTime = t_prime[MarkerTwo] # Utilizzato per il secondo marker.\n",
    "    # Utilizzato per stampare.\n",
    "    print(\"Primo tempo =\", MarkerOneTime, \"s\", \"-\", \"Secondo tempo =\", MarkerTwoTime, \"s\")\n",
    "    makeplots(MarkerOne, MarkerTwo) # Utilizzato per adoperare la funzione grafico.\n",
    "    # Utilizzato per avere il sottoinsieme dei valori del tempo compresi tra i due marker.\n",
    "    t_subset = t_prime[MarkerOne:MarkerTwo]\n",
    "    # Utilizzato per avere il sottoinsieme dei valori della velocità compresi tra i due marker.\n",
    "    v_subset = v[MarkerOne:MarkerTwo]\n",
    "\n",
    "# Funzione grafico.\n",
    "def makeplots(MarkerOne, MarkerTwo):\n",
    "    # Utilizzato per creare e dimensionare il grafico.\n",
    "    fig = plt.figure(figsize = (15, 15))\n",
    "\n",
    "    # Grafico 1.\n",
    "    plt.subplot(2, 1, 1)\n",
    "    # Utilizzato per il titolo.\n",
    "    plt.title(\"Velocità in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "    # Utilizzato per la x.\n",
    "    plt.xlabel(\"Tempo  $ (s) $\", fontsize = 12.5)\n",
    "    # Utilizzato per la y.\n",
    "    plt.ylabel(\"Velocità $ (m/s) $\", fontsize = 12.5)\n",
    "    # Utilizzato per rappresentare x e y.\n",
    "    plt.plot(t_prime, v, \"o\", color = \"#0075E2\", markersize = 5)\n",
    "    # Utilizzato per rappresentare il primo marker.\n",
    "    plt.plot(t_prime[MarkerOne], v[MarkerOne], \"o\", color = \"black\", markersize = 7.5, zorder = -1)\n",
    "    # Utilizzato per rappresentare il secondo marker.\n",
    "    plt.plot(t_prime[MarkerTwo], v[MarkerTwo], \"o\", color = \"black\", markersize = 7.5, zorder = -1)\n",
    "    # Utilizzato per disegnare il primo marker.\n",
    "    plt.axvline(color = \"black\", x = t_prime[MarkerOne], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "    # Utilizzato per disegnare il secondo marker.\n",
    "    plt.axvline(color = \"black\", x = t_prime[MarkerTwo], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "    # Utilizzato per avere gli assi con la stessa scala.\n",
    "    #plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "    # Utilizzato per la griglia.\n",
    "    plt.grid(True)\n",
    "\n",
    "    # Grafico 2.\n",
    "    plt.subplot(2, 1, 2)\n",
    "    # Utilizzato per il titolo.\n",
    "    plt.title(\"Accelerazione in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "    # Utilizzato per rappresentare x e y.\n",
    "    plt.plot(t_double_prime, a, \"o\", color = \"#0075E2\", markersize = 5)\n",
    "    # Utilizzato per disegnare il primo marker.\n",
    "    plt.axvline(color = \"black\", x = t_prime[MarkerOne], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "    # Utilizzato per disegnare il secondo marker.\n",
    "    plt.axvline(color = \"black\", x = t_prime[MarkerTwo], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "    # Utilizzato per la x.\n",
    "    plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "    # Utilizzato per la y.\n",
    "    plt.ylabel(\"Accelerazione $ (m/s^{2} $)\", fontsize = 12.5)\n",
    "    # Utilizzato per avere gli assi con la stessa scala.\n",
    "    #plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "    # Utilizzato per la griglia.\n",
    "    plt.grid(True)\n",
    "\n",
    "# Utilizzato per collegare i widget alla funzione e per interagire con gli slider.\n",
    "widgets.interact(funzione, MarkerOne = sliderMarkerOne, MarkerTwo = sliderMarkerTwo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 6.2 Fit lineare dei dati della velocità\n",
    "\n",
    "In una certa regione del grafico l'andamento della velocità in funzione del tempo è lineare. I valori della velocità soddisfano un'equazione del tipo:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ v - v_0 = a \\cdot (t - t_0) $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Considerando che la velocità iniziale è nulla, si ha:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ v = a \\cdot (t - t_0) $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Ovvero:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ v = (a \\cdot t) - (a \\cdot t_0) $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Il grafico di $ v $ in funzione di $ t $ può essere quindi descritto con l'equazione di una retta che, in un piano cartesiano $ O xy $, è:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ y = A x + B $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Nel codice Python che segue definiamo una funzione che permette di calcolare i parametri $ A $ e $ B $ che forniscono il miglior accordo tra un insieme di dati e una retta. Applichiamo l'algoritmo all'insieme dei dati della velocità nell'intervallo di tempo che abbiamo selezionato ed otteniamo:\n",
    "\n",
    "* Il valore del parametro A\n",
    "\n",
    "    * Che fornisce una stima dell'**accelerazione** $ a $ nell'intervallo di tempo considerato.\n",
    "\n",
    "* Il valore del parametro B\n",
    "\n",
    "    * Dal quale possiamo ricavare il valore di $ t_0 $, essendo:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ t_0 = - \\dfrac{B}{A} $$\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valore stimato dell'accelerazione (dal fit lineare): \n",
      "a = 1.295 m/s^2\n",
      "Tempo iniziale: \n",
      "t0 = 1.829 s\n"
     ]
    }
   ],
   "source": [
    "# Utilizzato per avere il sottoinsieme dei valori del tempo' compresi tra i due marker.\n",
    "t_prime_subset = t_prime[sliderMarkerOne.value:sliderMarkerTwo.value]\n",
    "# Utilizzato per avere il sottoinsieme dei valori della velocità compresi tra i due marker.\n",
    "v_subset = v[sliderMarkerOne.value:sliderMarkerTwo.value]\n",
    "\n",
    "# Funzione fit lineare.\n",
    "def LineFit(x, y):\n",
    "    x_avg = x.mean()\n",
    "    slope = (y * (x - x_avg)).sum() / (x * (x - x_avg)).sum()\n",
    "    y_intercept = y.mean() - slope * x_avg\n",
    "    return slope, y_intercept\n",
    "\n",
    "# Utilizzato per calcolare i valori dell'accelerazione e della velocità con la funzione LineFit e per inserirli in due variabili.\n",
    "a_est, v_intercept = LineFit(t_prime_subset, v_subset)\n",
    "\n",
    "print(\"Valore stimato dell'accelerazione (dal fit lineare): \\na = {0:0.4} m/s^2\".format(a_est)) # Utilizzato per stampare.\n",
    "t0 = - v_intercept / a_est # Tempo iniziale in s.\n",
    "print(\"Tempo iniziale: \\nt0 = {0:0.4} s\".format(t0)) # Utilizzato per stampare."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7. Figura riassuntiva: coordinata x, velocità, accelerazione\n",
    "\n",
    "Vogliamo riassumere i risultati ottenuti in un'unica figura. I grafici sono organizzati in una tabella costituita da tre righe ed una colonna."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x1620 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_fit = a_est * t_prime_subset + v_intercept # Velocità fit lineare in m/s.\n",
    "a_fit = v_fit / v_fit * a_est # Accelerazione fit lineare in m/s^2.\n",
    "x_fit = 0.5 * a_est * (t_prime_subset - t0) ** 2 + 0.029 # Distanza fit lineare in m.\n",
    "\n",
    "# Utilizzato per il grafico.\n",
    "fig = plt.figure(figsize = (15, 22.5)) # Utilizzato per creare e dimensionare il grafico.\n",
    "\n",
    "# Grafico 1.\n",
    "plt.subplot(3, 1, 1)\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Distanza in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Distanza $ (m) $\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t, x, \"o\", color = \"#0075E2\", markersize = 5, label = \"Dati\")\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_prime_subset, x_fit, \"-\", color = \"black\", linewidth = 1, zorder = -1, label = \"Fit\")\n",
    "# Utilizzato per disegnare il primo marker.\n",
    "plt.axvline(color = \"black\", x = t_prime_subset[0], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "# Utilizzato per disegnare il secondo marker.\n",
    "plt.axvline(color = \"black\", x = t_prime_subset[-1], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "# Utilizzato per la legenda.\n",
    "plt.legend(loc = \"upper left\", shadow = True, fontsize = \"large\")\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "#plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "\n",
    "# Grafico 2.\n",
    "plt.subplot(3, 1, 2)\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Velocità in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Velocità $ (m/s) $\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_prime, v, \"o\", color = \"#0075E2\", markersize = 5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_prime_subset, v_fit, \"-\", color = \"black\", linewidth = 1)\n",
    "# Utilizzato per disegnare il primo marker.\n",
    "plt.axvline(color = \"black\", x = t_prime_subset[0], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "# Utilizzato per disegnare il secondo marker.\n",
    "plt.axvline(color = \"black\", x = t_prime_subset[-1], linewidth = 1.5, linestyle = \"--\", zorder = -1)\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "#plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "\n",
    "# Grafico 3.\n",
    "plt.subplot(3, 1, 3)\n",
    "# Utilizzato per il titolo.\n",
    "plt.title(\"Accelerazione in funzione del tempo\", fontdict = {\"fontsize\": 17.5}, pad = 10)\n",
    "# Utilizzato per la x.\n",
    "plt.xlabel(\"Tempo $ (s) $\", fontsize = 12.5)\n",
    "# Utilizzato per la y.\n",
    "plt.ylabel(\"Accelerazione $ (m/s^{2} $)\", fontsize = 12.5)\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_double_prime, a, \"o\", color = \"#0075E2\", markersize = 5, label = \"Calculated\")\n",
    "# Utilizzato per rappresentare x e y.\n",
    "plt.plot(t_prime_subset, a_fit, \"-\", color = \"black\", markersize = 1, label = \"Fit\")\n",
    "# Utilizzato per la legenda.\n",
    "plt.legend(loc = \"lower left\", shadow = True, fontsize = \"large\")\n",
    "# Utilizzato per avere gli assi con la stessa scala.\n",
    "#plt.gca().set_aspect(\"equal\", adjustable = \"box\")\n",
    "# Utilizzato per la griglia.\n",
    "plt.grid(True)\n",
    "\n",
    "# Utilizzato per salvare i dati in un file.\n",
    "plt.savefig(\"Dati/Incline-Results.pdf\")\n",
    "\n",
    "# Utilizzato per mostrare il grafico.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* I valori della velocità sono riportati insieme al grafico della retta che meglio approssima i dati sperimentali nell'intervallo considerato. (**Grafico 2/3**)\n",
    "\n",
    "* La pendenza di tale retta fornisce una stima dell'accelerazione. Questo valore costante di accelerazione è rappresentato come una linea orizzontale nel grafico che riporta i valori di accelerazione in funzione del tempo. (**Grafico 3/3**)\n",
    "\n",
    "* I valori sperimentali di $ x $ in funzione del tempo sono mostrati in grafico (**Grafico 1/3**) insieme ai dati calcolati utilizzando l'equazione:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ x = x_0 + \\dfrac{a \\cdot (t - t_0)^2}{2} $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Con i valori di $ a $ e $ t_0 $ ottenuti dal fit lineare dei dati di velocità e con il valore di $ x_0 $ che fornisce il miglior adattamento della curva (parabola) ai valori sperimentali di $ x $ vs. $ t $.\n",
    "\n",
    "#### 8. Confronto con le previsioni di un modello fisico\n",
    "\n",
    "Se si considera come modello fisico il sistema costituito da un punto materiale che si muove **senza attrito** lungo il piano inclinato sotto l'azione della forza peso, conoscendo l'angolo di inclinazione $ \\theta $, si può prevedere che il moto sarà un **moto con accelerazione costante** pari a:\n",
    "\n",
    "<div id = \"colorbox\">\n",
    "\n",
    "$$ g \\cdot \\sin(\\theta) $$\n",
    "\n",
    "</div>\n",
    "\n",
    "Dove $ g $ è l'accelerazione di gravità.\n",
    "\n",
    "Nel nostro esempio:\n",
    "\n",
    "* Consideriamo la misura dell'angolo $ \\theta $ ottenuta usando l'App **phyphox**.\n",
    "\n",
    "* Convertiamo la misura in **radianti**.\n",
    "\n",
    "* Calcoliamo il **valore atteso** dell'accelerazione in base alla previsione del modello."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inclinazione theta = 0.191986 rad\n"
     ]
    }
   ],
   "source": [
    "ang_grad = 11 # Inclinazione in gradi.\n",
    "ang_rad = ang_grad / 180 * np.pi # Inclinazione in radianti.\n",
    "\n",
    "print(\"Inclinazione theta = {0:0.6} rad\".format(ang_rad))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1908089953765448"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizzato per calcolare il seno dell'angolo in radianti.\n",
    "np.sin(ang_rad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valore stimato dell'accelerazione in assenza di attrito: \n",
      "a = 1.870 m/s^2\n",
      "Valore dell'accelerazione stimato tramite fit lineare dei dati sperimentali: \n",
      "a = 1.295 m/s^2\n",
      "Errore relativo = 30.7 %\n"
     ]
    }
   ],
   "source": [
    "a_model = 9.8 * np.sin(ang_rad) # Accelerazione in assenza di attrito in m/s^2.\n",
    "\n",
    "# Utilizzato per stampare.\n",
    "print(\"Valore stimato dell'accelerazione in assenza di attrito: \\na = {0:0.3f} m/s^2\".format(a_model))\n",
    "# Utilizzato per stampare.\n",
    "print(\"Valore dell'accelerazione stimato tramite fit lineare dei dati sperimentali: \\na = {0:0.3f} m/s^2\".format(a_est))\n",
    "\n",
    "relative_error = (a_model - a_est) / a_model # Errore relativo in percentuale.\n",
    "\n",
    "# Utilizzato per stampare.\n",
    "print(\"Errore relativo = {0:0.1f} %\".format(relative_error * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Per eseguire il codice Python contenuto in questo **notebook** Jupyter, anche se Python e Notebook Jupyter non sono installati sulla macchina che stai adoperando, puoi utilizzare l'ambiente [**binder**](https://mybinder.org) online.\n",
    "\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/Darkaquon/Physics-with-Open-Source-Software/master?filepath=%2FNotebook%2FPiano_inclinato.ipynb)\n",
    "\n",
    "## Osservazione\n",
    "\n",
    "Possiamo osservare che l'accelerazione ottenuta dai dati sperimentali è minore di quella stimata sulla base del modello.\n",
    "\n",
    "> La presenza di una forza di attrito costante ha come conseguenza che la forza totale costante che agisce sul corpo in movimento è costante ed è minore rispetto al caso ideale. Si otterrebbe quindi un'accelerazione costante minore rispetto a quella attesa in assenza di attrito, in accordo con i risultati di questa indagine sperimentale.\n",
    "\n",
    "## What we have learned\n",
    "\n",
    "*Python*\n",
    "\n",
    "* Acquisizione di dati con un apparato sperimentale controllato tramite software.\n",
    "\n",
    "* Elaborazione dei dati, analisi dei dati.\n",
    "\n",
    "* Rappresentazione grafica dei risultati.\n",
    "\n",
    "*Fisica*\n",
    "\n",
    "* Misure di distanza in funzione del tempo.\n",
    "\n",
    "* Analisi dei dati.\n",
    "\n",
    "* Andamento grafico della velocità nell'esempio di moto con accelerazione costante.\n",
    "\n",
    "* Fit lineare dei dati della velocità e determinazione dell'accelerazione.\n",
    "\n",
    "* Equazioni del moto uniformemente accelerato.\n",
    "\n",
    "## References and notes\n",
    "\n",
    "#### Experimental setup: hardware and software\n",
    "\n",
    "1. [Experiments and data analysis on one-dimensional motion with **Raspberry Pi** and **Python**](https://iopscience.iop.org/article/10.1088/1361-6552/ab73d2) (See also Supplementary Information)\n",
    "\n",
    "## Grafica notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "/* File CSS */\n",
       "\n",
       "/* File utilizzato per modificare la visualizzazione del notebook. */\n",
       "\n",
       "<style>\n",
       "\n",
       "@font-face {\n",
       "    font-family: \"Computer Modern\";\n",
       "    src: url(\"http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf\");\n",
       "}\n",
       "\n",
       "/* Utilizzato per creare un box colorato. */\n",
       "#colorbox {\n",
       "    background-color: #0075E2;\n",
       "    padding: 10px;\n",
       "    border: 1px solid black;\n",
       "    margin-top: 10px;\n",
       "}\n",
       "\n",
       "#immagine {\n",
       "    margin-top: 10px;\n",
       "}\n",
       "\n",
       "/* Main background. */\n",
       "#notebook_panel {\n",
       "    background: rgb(245, 245, 245);\n",
       "}\n",
       "\n",
       "/* Utilizzato per impostare la larghezza delle celle. */\n",
       "div.cell {\n",
       "    width: 800px;\n",
       "}\n",
       "\n",
       "/* Utilizzato per centrare il materiale del notebook. */\n",
       "div #notebook {\n",
       "    background: #fff;\n",
       "    width: 1000px;\n",
       "    margin: auto;\n",
       "    padding-left: 0em;\n",
       "}\n",
       "\n",
       "/* Utilizzato per modificare lo spazio tra gli elementi di una lista. */\n",
       "#notebook li {\n",
       "    margin-top: 0.5em;\n",
       "}\n",
       "\n",
       "/* Utilizzato per disegnare un bordo attorno alle celle in esecuzione. */\n",
       "div.cell.border-box-sizing.code_cell.running {\n",
       "    border: 1px solid #111;\n",
       "}\n",
       "\n",
       "/* Utilizzato per creare un box intorno alle celle e agli outputs per collegarli visivamente. */\n",
       "div.cell.code_cell {\n",
       "    background-color: rgb(256, 256, 256);\n",
       "    border-radius: 0px;\n",
       "    padding: 0.5em;\n",
       "    margin-left: 1em;\n",
       "    margin-top: 1em;\n",
       "}\n",
       "\n",
       "/* Utilizzato per modificare la visualizzazione delle celle di testo */\n",
       "div.text_cell_render {\n",
       "    font-family: \"Source Sans Pro\", sans-serif;\n",
       "    line-height: 140%;\n",
       "    font-size: 110%;\n",
       "    width: 680px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       "\n",
       "/* Utilizzato per modificare le intestazioni. */\n",
       "\n",
       ".text_cell_render h1 {\n",
       "    font-family: \"Merriweather\", serif;\n",
       "    font-style: regular;\n",
       "    font-weight: bold;\n",
       "    font-size: 250%;\n",
       "    line-height: 100%;\n",
       "    color: #000000;\n",
       "    margin-bottom: 1em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h2 {\n",
       "    font-family: \"Merriweather\", serif;\n",
       "    font-weight: bold;\n",
       "    font-size: 180%;\n",
       "    line-height: 100%;\n",
       "    color: #000000;\n",
       "    margin-bottom: 0.5em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h3 {\n",
       "    font-family: \"Merriweather\", serif;\n",
       "\tfont-size: 150%;\n",
       "    margin-top: 12px;\n",
       "    margin-bottom: 3px;\n",
       "    font-style: regular;\n",
       "    color: #000000;\n",
       "}\n",
       "\n",
       "/* Da utilizzare per le didascalie. */\n",
       ".text_cell_render h4 {\n",
       "    font-family: \"Merriweather\", serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 100%;\n",
       "    line-height: 120%;\n",
       "    text-align: left;\n",
       "    width: 500px;\n",
       "    margin-top: 1em;\n",
       "    margin-bottom: 2em;\n",
       "    margin-left: 80pt;\n",
       "    font-style: regular;\n",
       "    color: #0075E2;\n",
       "}\n",
       "\n",
       "/* Da utilizzare per i titoli più piccoli. */\n",
       ".text_cell_render h5 {\n",
       "    font-family: \"Source Sans Pro\", sans-serif;\n",
       "    font-weight: regular;\n",
       "    font-size: 130%;\n",
       "    color: #000000;\n",
       "    font-style: italic;\n",
       "    margin-bottom: .5em;\n",
       "    margin-top: 1em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       "/* Da utilizzare per le note, ad esempio i copyright. */\n",
       ".text_cell_render h6 {\n",
       "    font-family: \"Source Code Pro\", sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 9pt;\n",
       "    line-height: 100%;\n",
       "    color: #000000;\n",
       "    margin-bottom: 1px;\n",
       "    margin-top: 1px;\n",
       "}\n",
       "\n",
       ".CodeMirror {\n",
       "    font-family: \"Source Code Pro\";\n",
       "\tfont-size: 90%;\n",
       "}\n",
       "\n",
       "/*\n",
       "\n",
       ".prompt {\n",
       "    display: None;\n",
       "}\n",
       "\n",
       "*/\n",
       "\n",
       ".warning {\n",
       "    color: rgb(240, 20, 20)\n",
       "}\n",
       "\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizzato per importare la libreria adoperata per visualizzare l'HTML con il Python.\n",
    "from IPython.core.display import HTML\n",
    "\n",
    "\n",
    "css_file = \"Notebook.css\" # File CSS.\n",
    "\n",
    "# Utilizzato per aprire e leggere il file CSS adoperato per modificare la visualizzazione del notebook.\n",
    "HTML(open(css_file, \"r\").read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Copyright and License\n",
    "-------------------------\n",
    "(c) 2020 Andrea Mandanici, Marco Guarnera, Giuseppe Mandaglio, Giovanni Pirrotta. All content is under Creative Common Attribution <a rel = \"license\" href = \"https://creativecommons.org/licenses/by/4.0\"> CC BY 4.0 </a> and all code is under [BSD 3 - Clause License.](https://opensource.org/licenses/BSD-3-Clause)"
   ]
  }
 ],
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   "display_name": "Python 3",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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