Interactive manimation worksheet: center of mass of emptying can

center of mass of emptying can.ipynb

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   "source": [
    "Credit: https://github.com/fred-fp/manim/blob/main/cm_can.py"
   ]
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   "source": [
    "from manim import *\n",
    "import numpy as np"
   ]
  },
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   "execution_count": null,
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    "config.media_width = \"80%\""
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    "%%manim -v WARNING -qm Cena1\n",
    "\n",
    "class Cena1(Scene):\n",
    "    def construct(self):\n",
    "\n",
    "        #define initial surface level and the masses of both liquids\n",
    "        surface_level = ValueTracker(3.0)\n",
    "        mass_liquid_1 = 1\n",
    "        mass_liquid_2 = 20\n",
    "\n",
    "        #create components of system 1\n",
    "        can_1 = Rectangle(color=WHITE, width=3.5, height=6, stroke_width=2).set_x(-4)\n",
    "        cm_can_1 = Dot(color=YELLOW).scale(0.5).set_x(-4)\n",
    "        \n",
    "        liquid_1 = always_redraw(lambda :\n",
    "                 Rectangle(fill_color=BLUE,\n",
    "                           fill_opacity=0.6,\n",
    "                           stroke_width=0,\n",
    "                           width=3.5,\n",
    "                           height=surface_level.get_value()*2).set_y(surface_level.get_value() - 3).set_x(-4)\n",
    "            )\n",
    "        cm_liquid_1 = always_redraw(lambda :\n",
    "                                 Dot(color=ORANGE).scale(0.5).set_y(surface_level.get_value() - 3).set_x(-4)\n",
    "                                 )\n",
    "\n",
    "        cm_total_1 = always_redraw(lambda :\n",
    "                                 Dot(color=WHITE).set_y((cm_can_1.get_y() +\n",
    "                                                         cm_liquid_1.get_y()* (mass_liquid_1 * surface_level.get_value()/3))\n",
    "                                                        /(1 + (mass_liquid_1 * (surface_level.get_value()/3)))\n",
    "                                                        ).scale(0.5).set_x(-4)\n",
    "                                 )\n",
    "\n",
    "        system_1 = Group(can_1, liquid_1)\n",
    "        centers_of_mass_1 = Group(cm_can_1, cm_liquid_1, cm_total_1)\n",
    "\n",
    "\n",
    "        #create components of system 2\n",
    "        can_2 = Rectangle(color=WHITE, width=3.5, height=6, stroke_width=2).set_x(4)\n",
    "        cm_can_2 = Dot(color=YELLOW).scale(0.5).set_x(4)\n",
    "        \n",
    "        liquid_2 = always_redraw(lambda :\n",
    "                 Rectangle(fill_color=BLUE,\n",
    "                           fill_opacity=0.6,\n",
    "                           stroke_width=0,\n",
    "                           width=3.5,\n",
    "                           height=surface_level.get_value()*2).set_y(surface_level.get_value() - 3).set_x(4)\n",
    "            )\n",
    "        cm_liquid_2 = always_redraw(lambda :\n",
    "                                 Dot(color=ORANGE).scale(0.5).set_y(surface_level.get_value() - 3).set_x(4)\n",
    "                                 )\n",
    "\n",
    "        cm_total_2 = always_redraw(lambda :\n",
    "                                 Dot(color=WHITE).set_y((cm_can_2.get_y() +\n",
    "                                                         cm_liquid_2.get_y()* (mass_liquid_2 * surface_level.get_value()/3))\n",
    "                                                        /(1 + (mass_liquid_2 * (surface_level.get_value()/3)))\n",
    "                                                        ).scale(0.5).set_x(4)\n",
    "                                 )\n",
    "\n",
    "        system_2 = Group(can_2, liquid_2)\n",
    "        centers_of_mass_2 = Group(cm_can_2, cm_liquid_2, cm_total_2)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "        #text\n",
    "        desc_cm_can = Tex(\"CM of can\", color=YELLOW).shift(UP)\n",
    "        desc_cm_liquid = Tex(\"CM of liquid\", color=ORANGE).shift(DOWN)\n",
    "        desc_cm_total = Tex(\"CM of system\", color=WHITE)\n",
    "\n",
    "        desc = Group(desc_cm_can, desc_cm_liquid, desc_cm_total)\n",
    "\n",
    "        desc_liquid_1 = MathTex(\"m_{liquid} = \", mass_liquid_1, \"m_{can}\").scale(0.7).shift(LEFT*4+UP*3.5)\n",
    "        desc_liquid_2 = MathTex(\"m_{liquid} = \", mass_liquid_2, \"m_{can}\").scale(0.7).shift(RIGHT*4+UP*3.5)\n",
    "\n",
    "        #animate\n",
    "        self.wait(0.5)\n",
    "        self.play(FadeIn(system_1),\n",
    "                  FadeIn(system_2)\n",
    "                  )\n",
    "        self.play(FadeIn(desc),\n",
    "                  FadeIn(centers_of_mass_1),\n",
    "                  FadeIn(centers_of_mass_2),\n",
    "                              FadeIn(desc_liquid_1),\n",
    "                  FadeIn(desc_liquid_2)\n",
    "                  )\n",
    "        self.play(surface_level.animate.set_value(0.), run_time = 7)\n",
    "        self.wait(1)\n",
    "        self.play(\n",
    "            *[FadeOut(mob)for mob in self.mobjects]\n",
    "        )"
   ]
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Dockerfile

FROM manimcommunity/manim:v0.10.0

COPY --chown=manimuser:manimuser . /manim