{
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  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Determination of the young modulus of a metal in the form of a wire\n",
    "\n",
    "## Theory:\n",
    "\n",
    "Young modulus 𝐸= Stress/Strain \n",
    "\n",
    "If a graph of applied load, F (y-axis) is drawn against extension, x (x-axis) the gradient is 𝐹/𝑥 and so: \n",
    "\n",
    "$$ 𝐸 =gradient \\times \\frac{𝑙}{𝐴}$$\n",
    "\n",
    "The original length $l$ and the cross sectional area of the wire $A$ can be measured, hence E can be determined.\n",
    "\n",
    "## Apparatus:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "## Method:\n",
    "\n",
    "Hang two identical wires from a beam and attach a scale to the first wire and a small weight to keep it straight. Also put a small weight on the second wire to straighten it and a Vernier scale linking with the scale on the comparison wire. Measure the original length, l, of the test wire and its diameter at various points along its length. Use this to calculate the mean cross-sectional area A.\n",
    "Then place a load of 5N on the test wire and find the extension, x. Repeat this in 5N steps up to at least 50N. Plot a graph of load (y-axis) against extension (x-axis) and calculate the gradient. Use this to find a value for the Young modulus.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The parameters of the line: [[0.0896793]\n",
      " [0.0147619]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importing the necessary libraries\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "#from prettytable import PrettyTable\n",
    "\n",
    "# Wire original length = 2.43 m\n",
    "# Wire mean diameter = 0.38 mm \n",
    "\n",
    "\n",
    "# Preparing the data to be computed and plotted\n",
    "dt = np.array([\n",
    "          \n",
    "    [0.0, 0.0],\n",
    "    [4.9, 0.52],\n",
    "    [9.8, 0.80],\n",
    "    [14.7, 1.35],\n",
    "    [19.6, 1.83],\n",
    "    [24.5, 2.18]\n",
    "])\n",
    "\n",
    "\n",
    "# Preparing X and y data from the given data\n",
    "x = dt[:, 0].reshape(dt.shape[0], 1)\n",
    "X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)\n",
    "y = dt[:, 1].reshape(dt.shape[0], 1)\n",
    "\n",
    "# Calculating the parameters using the least square method\n",
    "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "\n",
    "print(f'The parameters of the line: {theta}')\n",
    "\n",
    "# Now, calculating the y-axis values against x-values according to\n",
    "# the parameters theta0 and theta1\n",
    "y_line = X.dot(theta)\n",
    "\n",
    "# Plotting the data points and the best fit line\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_line, 'r')\n",
    "plt.title('Best fit line using regression method')\n",
    "plt.xlabel('Load /N')\n",
    "plt.ylabel('Extention /mm')\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "table = ax.table(cellText=dt, loc='center', colLabels=('Load /N','Extention /mm'))\n",
    "table.set_fontsize(14)\n",
    "table.scale(1,4)\n",
    "ax.axis('off')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "In comparison, our calculated resistivity is 0.13 Ohm/m vs a databook value of 0.105 Ohm/m  This is well within the expected variance of an A-level practical.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}