2.56 Micrometer Trap Force Brian Computation (1).ipynb

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 "metadata": {
  "name": "2.56 Micrometer Trap Force Brian Computation"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "Optical Tweezers Trap Force Measurement"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "May 15th, 2014 </br>\nBrian Perrett, Kyle Eichenberger, Samuel Estrella </br>\nAdvanced Projects Lab"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<table>\n    <tr>\n        <td>\n            <strong>Microsphere Size</strong>\n        </td>\n        <td>\n            $2.56\\mu m$\n        </td>\n    </tr>\n    <tr>\n        <td>\n            <strong>Beam Strength</strong>\n        </td>\n        <td>\n            $4.6mW$\n        </td>\n    </tr>\n    <tr>\n        <td>\n            <strong>Measurements Per Second</strong>\n        </td>\n        <td>\n            $200$\n        </td>\n    </tr>\n    <tr>\n        <td>\n            <strong>$\\Delta t$ between measurements</strong>\n        </td>\n        <td>\n            $.005s$\n        </td>\n    </tr>\n</table>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Import Data from .csv file...  Add them to arrays."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_pos = []\ny_pos = []\n\n###########################\nimport csv\nwith open('C:/Users/Brian/Google Drive/Sophomore/Physics/Advanced Projects Lab 491/2.56 micrometer tracking 5-14-14/2.56 micrometer parsed.csv') as f:\n    reader = csv.reader(f)\n    for row in reader:\n        x_pos.append(float(row[0]))\n        y_pos.append(float(row[1]))\n###########################\n\n# convert lists to arrays for simplified calculations\nx_pos = array(x_pos)\ny_pos = array(y_pos)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Convert from $\\mu m$ to $m$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_pos = x_pos*10**(-6)\ny_pos = y_pos*10**(-6)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$\\frac {1}{2} k_b T = \\frac {1}{2} k <x^2>$"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<ul>\n<li>\nUsing the equipartition Theorem and equating it to the potential energy of the trap, we can solve for k\n</li>\n</ul>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "to compute the variance we must solve..."
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$variance=\\overline{(x_{mean}-x_t)^2}$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_mean = mean(x_pos)\ny_mean = mean(y_pos)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_var = mean((x_mean - x_pos)**2)\ny_var = mean((y_mean - y_pos)**2)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "print(\"The x variation is \" + str(x_var))\nprint(\"The y variation is \" + str(y_var))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "The x variation is 6.92133033795e-16\nThe y variation is 2.57011754526e-15\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<table>\n<tr>\n    <td>\n        x var\n    </td>\n    <td>\n        6.92133E-16 m\n    </td>\n</tr>\n<tr>\n    <td>\n        y var\n    </td>\n    <td>\n        2.57012E-15\n    </td>\n</tr>\n</table>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$\\ \\frac {k_b T}{<x^2>} = k $"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "kb = 1.3806488e-23\nT = 298",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_strength = (kb*T)/x_var\ny_strength = (kb*T)/y_var",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Let's convert from standard units to piconewtons per micrometer"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_strength = x_strength*(10**12)/(10**6)\ny_strength = y_strength*(10**12)/(10**6)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x_strength # piconewtons/micrometer",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": "5.9444257434757573"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "y_strength # piconewtons/micrometer",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": "1.6008347289755338"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<table>\n<th>\n    direction\n</th>\n<th>\n    k\n</th>\n<tr>\n    <td>\n        x trap strength\n    </td>\n    <td>\n        $5.94 \\frac {pN}{\\mu m}$\n    </td>\n</tr>\n<tr>\n    <td>\n        y trap strength\n    </td>\n    <td>\n        $1.60 \\frac {pN}{\\mu m}$\n    </td>\n</tr>\n</table>"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}