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| author | hardythe1 | 2015-07-03 12:23:43 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-07-03 12:23:43 +0530 |
| commit | 9d260e6fae7328d816a514130b691fbd0e9ef81d (patch) | |
| tree | 9e6035702fca0f6f8c5d161de477985cacad7672 /Engineering_Physics_by_Shyam_Rajeev/Chapter1.ipynb | |
| parent | afcd9e5397e3e1bde0392811d0482d76aac391dc (diff) | |
| download | Python-Textbook-Companions-9d260e6fae7328d816a514130b691fbd0e9ef81d.tar.gz Python-Textbook-Companions-9d260e6fae7328d816a514130b691fbd0e9ef81d.tar.bz2 Python-Textbook-Companions-9d260e6fae7328d816a514130b691fbd0e9ef81d.zip | |
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1 files changed, 621 insertions, 0 deletions
diff --git a/Engineering_Physics_by_Shyam_Rajeev/Chapter1.ipynb b/Engineering_Physics_by_Shyam_Rajeev/Chapter1.ipynb new file mode 100755 index 00000000..10f61da5 --- /dev/null +++ b/Engineering_Physics_by_Shyam_Rajeev/Chapter1.ipynb @@ -0,0 +1,621 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:2f492bc2a6dad7cae3b696b117670d34888491ec5959ea22de590b83b18e09cd"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "1: Theory of Relativity"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.1, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l0 = 50 #length of rocket ship(m)\n",
+ "l = 49.5 #length observed on ground(m)\n",
+ "c = 3*10**8 #velocity of light(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "#we know that l = l0*math.sqrt(1-((v**2)/(c**2)))\n",
+ "v = math.sqrt((c**2)*(1-((l/l0)**2))) #speed(m/sec)\n",
+ "v = v*10**-7;\n",
+ "v=math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of the rocket is\",v, \"*10**7 m/sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of the rocket is 4.233 *10**7 m/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.2, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l0 = 1; #assume length(m)\n",
+ "l = (99/100)*l0 #length observed on ground(m)\n",
+ "c = 1 #assume c = 1\n",
+ "\n",
+ "#Calculation\n",
+ "#we know that l = l0*math.sqrt(1-((v**2)/(c**2)))\n",
+ "v = math.sqrt((c**2)*(1-((l/l0)**2))) #speed(m/sec)\n",
+ "v=math.ceil(v*10**4)/10**4; #rounding off to 4 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of the rocket is\",v,\"c\"\n",
+ "print \"answer given in the book is wrong\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of the rocket is 0.1411 c\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.3, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l0 = 120 #length of spaceship(m)\n",
+ "c = 1 #assume c = 1\n",
+ "v = 0.99*c; #speed of spaceship(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "l = l0*math.sqrt(1-((v**2)/(c**2))); #length of the observer(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of the observer is\",round(l),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "length of the observer is 17.0 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.4, Page number 30 theoretical proof"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.5, Page number 31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#surface area of elliptical lamina = 1/2 (area of circular lamina)\n",
+ "\n",
+ "#Calculation\n",
+ "c = 3*10**8; #velocity of light(m/sec)\n",
+ "#((math.pi*D**2)/4)*math.sqrt(1-(v**2/c**2)) = 1/2*math.pi*D**2/4\n",
+ "#math.sqrt(1-(v**2/c**2)) = 1/2\n",
+ "v = c*math.sqrt(1-(1/4)); #velocity(m/sec)\n",
+ "v = v*10**-8;\n",
+ "v=math.ceil(v*10)/10; #rounding off to 1 decimal\n",
+ "\n",
+ "#Result\n",
+ "print \"velocity is\",v,\"*10**8 m/sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity is 2.6 *10**8 m/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.6, Page number 32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "t0 = 2*10**-8; #mean life of meson(sec)\n",
+ "c = 1; #assume c = 1\n",
+ "v = 0.8*c; #velocity of meson(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "t = t0/math.sqrt(1-(v**2/c**2)); #mean life with a particular velocity\n",
+ "\n",
+ "#Result\n",
+ "print \"mean life of meson with a velocity is\",round(t/1e-8,3),\"*10**-8 sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean life of meson with a velocity is 3.333 *10**-8 sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.7, Page number 32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "t0 = 3; #time period of pendulum(sec)\n",
+ "c = 1; #assume c = 1\n",
+ "v = 0.95*c; #velocity of observer(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "t = t0/math.sqrt(1-(v**2/c**2)); #time period measured by observer(sec)\n",
+ "t = math.ceil(t*100)/100; #rounding off to 2 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"time period measured by observer is\",t,\"sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time period measured by observer is 9.61 sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.8, Page number 33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "t0 = 1; #life time of particle(micro sec)\n",
+ "v = 2.7*10**8; #velocity of particle(m/sec)\n",
+ "c = 3*10**8; #velocity of light(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "t0 = t0*10**-6; #life time of particle(sec)\n",
+ "t = t0/math.sqrt(1-(v**2/c**2)); #life time(sec)\n",
+ "t = round(t/1e-6,1)*10**-6; \n",
+ "x = v*t; #distance travelled before disintegration(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"life time is\",t,\"sec\"\n",
+ "print \"distance travelled before disintegration is\",x,\"m\"\n",
+ "print \"answer for distance given in the book is wrong\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "life time is 2.3e-06 sec\n",
+ "distance travelled before disintegration is 621.0 m\n",
+ "answer for distance given in the book is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.9, Page number 33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "c = 1; #assume c = 1\n",
+ "u = -0.85*c; #speed of B\n",
+ "v = 0.75*c; #speed of A\n",
+ "\n",
+ "#Calculation\n",
+ "u_dash = (u-v)/(1-(u*v/c**2)); #velocity of B with respect to A\n",
+ "u_dash = math.ceil(u_dash*10**3)/10**3; #rounding off to 3 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"velocity of B with respect to A is\",u_dash,\"c\"\n",
+ "print \"answer given in the book is wrong with respect to sign\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity of B with respect to A is -0.977 c\n",
+ "answer given in the book is wrong with respect to sign\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.10, Page number 34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "c = 1; #assume c = 1\n",
+ "u_dash = 0.9*c; #velocity of beta particle\n",
+ "v = 0.25*c; #speed of A\n",
+ "\n",
+ "#Calculation\n",
+ "u = (u_dash+v)/(1+(u_dash*v/c**2)); #speed of beta particle\n",
+ "u = math.ceil(u*10**2)/10**2; #rounding off to 2 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of beta particle is\",u,\"c\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of beta particle is 0.94 c\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.11, Page number 34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "mp = 1.6*10**-27; #mass of proton(kg)\n",
+ "me = 9.1*10**-31; #mass of electron(kg)\n",
+ "c = 3*10**8; #velocity of light(m/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "m0 = me;\n",
+ "m = mp;\n",
+ "# we know that m = m0/math.sqrt(1-(v**2/c**2));\n",
+ "A = (m0/m)**2;\n",
+ "v_square = (1-A)*(c**2);\n",
+ "v = math.sqrt(v_square); #speed of electron(m/sec)\n",
+ "v = v*10**-8;\n",
+ "v = math.ceil(v*10**7)/10**7; #rounding off to 7 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of electron is\",v,\"*10**8 m/sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of electron is 2.9999996 *10**8 m/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.12, Page number 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "m0 = 1; #assume m0 = 1\n",
+ "m = 2.25*m0;\n",
+ "\n",
+ "#Calculation\n",
+ "A = (m0/m)**2;\n",
+ "v_square = (1-A)*(c**2);\n",
+ "v = math.sqrt(v_square); #speed of a body(m/sec)\n",
+ "v = v*10**-8;\n",
+ "v = math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n",
+ "\n",
+ "#Result\n",
+ "print \"speed of the body is\",v,\"*10**8 m/sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of electron is 2.688 *10**8 m/sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.13, Page number 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "c = 1; #assume c = 1\n",
+ "v = 0.99*c; #velocity of electron\n",
+ "m0 = 9.1*10**-31; #mass(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "m = m0/math.sqrt(1-(v**2/c**2)); #mass of electron(kg)\n",
+ "m = m*10**31;\n",
+ "\n",
+ "#Result\n",
+ "print \"mass of the electron is\",int(m),\"*10**-31 kg\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mass of the electron is 64 *10**-31 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.14, Page number 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.15, Page number 36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.16, Page number 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |