Vaja_2.ipynb

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      "name": "Vaja 2.ipynb",
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      "cell_type": "markdown",
      "source": [
        "# Vaja 2: Kinematika točke\n",
        "\n",
        "## Naravni koordinatni sistem\n",
        "Koordinatni sistem se premika skupaj z opazovano točko.\n",
        "\n",
        "## Polarni koordinatni sistem\n",
        "$r(t)$ in $\\phi(t)$"
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 1\n",
        "Zaradi neravnin na cesti voznica avtomobila zavira z enakomernim pojemkom. Njena hitrost na dnu (točka A) je 100 km/h, na vrhu (točka C) pa 50 km/h. Dolžina ceste med točkama A in C je 120 m. Če sopotniki v točki A občutijo skupni pospešek 3 m/s$^2$, ter če je radij ukrivljenosti v točki C enak 150 m, izračunajte:\n",
        " - radij ukrivljenosti $\\rho$ v točki A,\n",
        " - skupni pospešek na točki prevoja B,\n",
        " - skupni pospešek v točki C."
      ],
      "metadata": {
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    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
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      "execution_count": null,
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    {
      "cell_type": "code",
      "source": [
        "v_A = 100/3.6\n",
        "v_C = 50/3.6\n",
        "l_AC = 120\n",
        "rho_C = 150\n",
        "a_A = 3\n",
        "\n",
        "a_t = (v_C**2-v_A**2) / (2*l_AC)\n",
        "a_t"
      ],
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    {
      "cell_type": "code",
      "source": [
        "a_nA = np.sqrt(a_A**2 - a_t**2)\n",
        "a_nA"
      ],
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    {
      "cell_type": "code",
      "source": [
        "rho_A = v_A**2/a_nA\n",
        "rho_A"
      ],
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      "source": [
        "a_B = a_t\n",
        "a_B"
      ],
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      "cell_type": "code",
      "source": [
        "a_nC = v_C**2 / rho_C\n",
        "a_C = np.sqrt(a_nC**2 + a_t**2)\n",
        "a_C"
      ],
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          "metadata": {},
          "execution_count": 8
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      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 2\n",
        "Lestev gasilskega tovornjaka je narejena tako, da se izvleče s konstantno hitrostjo $\\dot{l}=150$ mm/s, obenem pa se vrti s $\\dot{\\varphi}=2^{\\circ}$/s. V položaju lestve $\\varphi=50^{\\circ}$ in $l=4$ m določite velikost hitrosti in pospeška gasilca v točki A."
      ],
      "metadata": {
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    {
      "cell_type": "code",
      "source": [
        "R = 6\n",
        "l_ = 0.15\n",
        "phi_ = 2 * np.pi/180 \n",
        "\n",
        "phi = 50 * np.pi/180\n",
        "l=4"
      ],
      "metadata": {
        "id": "yrTAXQj8iyKA"
      },
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "v_r = l_\n",
        "v_phi = (R+l) * phi_\n",
        "\n",
        "v = np.sqrt(v_r**2 + v_phi**2)\n",
        "v "
      ],
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          "metadata": {},
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    },
    {
      "cell_type": "code",
      "source": [
        "a_r = 0 - (R+l) * phi_**2\n",
        "a_phi = (R+l) * 0 + 2 * l_ * phi_\n",
        "\n",
        "a = np.sqrt(a_r**2 + a_phi**2)\n",
        "a "
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 3\n",
        "Navpično izstreljeni raketi sledi radar. Ko je $\\varphi=60^{\\circ}$, so ostale izmerjene vrednosti naslednje:\n",
        " - $r=10000$ m,\n",
        " - $\\ddot{r}=25$ m/s$^2$,\n",
        " - $\\dot{\\varphi}=0,02$ rad/s.\n",
        "\n",
        "Izračunajte velikost hitrosti in pospeška rakete v tem položaju."
      ],
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      }
    },
    {
      "cell_type": "code",
      "source": [
        "phi = 60 *np.pi/180\n",
        "r = 10000\n",
        "r__ = 25\n",
        "phi_ = 0.02"
      ],
      "metadata": {
        "id": "Zz7N5t8olHAP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "v_phi = r * phi_\n",
        "v = v_phi / np.cos(phi)\n",
        "v"
      ],
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    {
      "cell_type": "code",
      "source": [
        "a_r = r__ - r*phi_**2 \n",
        "a = a_r / np.sin(phi)\n",
        "a"
      ],
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