{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Workshop \"Teaching Sciences and Engineering with Jupyter Notebooks\" 2021\n", "C. Hardebolle, CC BY-NC-SA 4.0 Int.\n", "\n", "
shift + enter
. Figure 1: The suspended jeans situation
\n", "\n", "\n", "The activities below allow you to find out the answer to this question by exploring how the counterweight affects the position of the jeans suspended on the cable. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Figure 2: Simplified suspended jeans situation
\n", "\n", "\n", "Therefore we are in a situation which is **identical to the one seen in the mini-lecture**.Figure 3: Angle and forces in the suspended jeans situation
\n", "\n", "\n", "We can therefore **use the equation seen in the mini-lecture, which gives the tension in the cable** depending on the mass $m$ of the suspended object, the angle $\\alpha$ that the cable makes with the horizon and the gravity of earth $g$:\n", "\n", "$\n", "\\begin{align}\n", "\\lvert\\vec{T}\\rvert = \\frac{\\frac{1}{2}.m.g}{sin(\\alpha)}\n", "\\end{align}\n", "$\n", "\n", "Computing the tension in the cable will help us figure out the counterweight necessary to maintain the cable taught: intuitively, we can predict that **the higher the tension in the cable, the heavier the counterweight needed** to keep the cable taught. \n", "\n", "Now, we know that the mass of the jeans is $m =$ 3kg and that the gravity of earth is $g =$ 9.81m.s$^{-2}$, but we don't know the value of $\\alpha$. \n", "From the sketch in the original question in [Figure 1 above](#fig1), we can guess that $\\alpha$ is probably quite small, but how small?\n", "\n", "\n", "def tension_norm(g, m, alpha):\n",
" tension = (1/2 * m * g) / np.sin(alpha)\n",
" return tension\n",
"
\n",
"\n",
"m_cw = T / g
\n",
" \n",
"Of course, if you are at ease with Python you can write this as a function, which could also call the ``tension_norm`` function defined earlier instead of using ``T``...\n",
"def tension_norm_degrees(g, m, alpha):\n",
" apha_rad = degrees_to_radians(alpha)\n",
" tension = tension_norm(g, m, apha_rad)\n",
" return tension\n",
"
\n",
"\n",
"Of course the three lines in this function can be combined into just one: \n",
"\n",
"def tension_norm_degrees(g, m, alpha):\n",
" return tension_norm(g, m, degrees_to_radians(alpha))\n",
"
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" \n",
"