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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Determination of unknown mass by proinciple of moments\n", "## Theory:\n", "\n", "Apply the principle of moments to a metre rule to first determine its mass and then determine the mass of an unknown object.\n", "\n", "## Apparatus:\n", "*\n", "![image.png](attachment:image.png)\n", "\n", "Loop a 200 g (1.96N) mass over the metre rule and adjust it until the ruler is horizontal. \n", "\n", "Note down the distance, Ɩ, of the mass from the pivot. The mass (or weight) of the metre rule can now be calculated using the principle of moments:\n", "\n", "0.20 × metre rule weight = Ɩ × 1.96\n", "\n", "Now remove the 200 g mass and replace it with the unknown weight, W, and again adjust the position of the weight until the ruler balances. Measure the distance, d, of the unknown weight from the pivot. The unknown weight can again be calculated by applying the principle of moments:\n", "\n", "0.20 × metre rule weight = d × unknown weight\n", "\n", "The unknown weight can be converted into a mass (in kilograms) by dividing by 9.81. This can then be checked using a top pan balance.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The parameters of the line: [[0.01971429]\n", " [0.68571429]]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "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", "# Preparing the data to be computed and plotted\n", "dt = np.array([\n", " \n", " [100, 2.7],\n", " [250, 5.5],\n", " [400, 8.7],\n", " [550, 11.4],\n", " [700, 14.6],\n", " [850, 17.4]\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('Distance $ d$/mm')\n", "plt.ylabel('Force $F$ /N')\n", "\n", "fig, ax = plt.subplots()\n", "table = ax.table(cellText=dt, loc='center', colLabels=('$ Distance $ d$/mm$','Force $F$ /N'))\n", "table.set_fontsize(14)\n", "table.scale(1,4)\n", "ax.axis('off')\n", "\n", "\n", "plt.show()\n" ] }, { "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 }