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Diffstat (limited to 'Engineering_Physics_by_Rajendran/Chapter1.ipynb')
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diff --git a/Engineering_Physics_by_Rajendran/Chapter1.ipynb b/Engineering_Physics_by_Rajendran/Chapter1.ipynb new file mode 100755 index 00000000..3f1a5138 --- /dev/null +++ b/Engineering_Physics_by_Rajendran/Chapter1.ipynb @@ -0,0 +1,492 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:be338ef971644a9f5f4678fb763a92b7fd97bf3ce5a24c5818759072b8dab2d8"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "1: Elasticity"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.1, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=3; #length of wire(m)\n",
+ "A=6.25*10**-5; #cross sectional area(m**2)\n",
+ "delta_L=3*10**-3; #increase in length(m)\n",
+ "F=1.2*10**3; #force(N)\n",
+ "\n",
+ "#Calculation\n",
+ "Y=F*L/(A*delta_L); #young's modulus(N/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"young's modulus is \",Y/10**10,\"*10**10 N/m**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "young's modulus is 1.92 *10**10 N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "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",
+ "Y=2*10**11; #young's modulus(N/m**2)\n",
+ "L=2.75; #length of wire(m)\n",
+ "d=1*10**-3; #diameter(m)\n",
+ "M=1; #applied load(kg)\n",
+ "g=9.8; #acceleration due to gravity(N)\n",
+ "\n",
+ "#Calculation\n",
+ "T=M*g; #tension(N)\n",
+ "delta_L=T*L/(math.pi*(d/2)**2*Y); #increase in length of wire(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"increase in length of wire is\",round(delta_L*10**4,5),\"*10**-4 m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "increase in length of wire is 1.71569 *10**-4 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.3, Page number 31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "F=0.3; #force(N)\n",
+ "d=5*10**-3; #displacement(m)\n",
+ "L=6*10**-2; #length of solid(m)\n",
+ "B=6*10**-2; #breadth of solid(m)\n",
+ "h=2*10**-2; #height of solid(m)\n",
+ "\n",
+ "#Calculation\n",
+ "s=F/(L*B); #shear stress(N/m**2)\n",
+ "theta=d/h; #shear strain\n",
+ "rm=s/theta; #rigidity modulus(N/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"shear stress is\",round(s,2),\"N/m**2\"\n",
+ "print \"shear strain is\",theta\n",
+ "print \"rigidity modulus is\",round(rm,2),\"N/m**2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "shear stress is 83.33 N/m**2\n",
+ "shear strain is 0.25\n",
+ "rigidity modulus is 333.33 N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.4, Page number 32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=2.5*10**10; #rigidity modulus(N/m**2)\n",
+ "L=30*10**-2; #thickness(m)\n",
+ "A=12*10**-4; #surface area(m**2)\n",
+ "delta_L=1.5*10**-2; #displacement(m)\n",
+ "\n",
+ "#Calculation\n",
+ "F=n*A*delta_L/L; #shearing force(N)\n",
+ "\n",
+ "#Result\n",
+ "print \"shearing force is\",F/10**6,\"*10**6 N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "shearing force is 1.5 *10**6 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.6, Page number 33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Y=7.25*10**10; #young's modulus of silver(N/m**2)\n",
+ "K=11*10**10; #bulk modulus of silver(N/m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=(3*K-Y)/(6*K); #poisson's ratio\n",
+ "\n",
+ "#Result\n",
+ "print \"poisson's ratio is\",round(sigma,2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "poisson's ratio is 0.39\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.7, Page number 34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=3; #length of Cu wire(m)\n",
+ "Y=12.5*10**10; #young's modulus(N/m**2)\n",
+ "r=5*10**-4; #radius of wire(m)\n",
+ "sigma=0.26; #poisson's ratio\n",
+ "m=10; #load(kg)\n",
+ "g=9.8; #acceleration due to gravity(N)\n",
+ "\n",
+ "#Calculation\n",
+ "delta_L=m*g*L/(math.pi*r**2*Y); #extension produced(m)\n",
+ "ls=sigma*delta_L/3; #lateral strain\n",
+ "dd=ls*r*2; #decrease in diameter(m) \n",
+ "\n",
+ "#Result\n",
+ "print \"extension produced is\",round(delta_L*10**3,2),\"*10**-3 m\"\n",
+ "print \"lateral compression produced is\",round(dd*10**7,3),\"*10**-7 m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "extension produced is 2.99 *10**-3 m\n",
+ "lateral compression produced is 2.595 *10**-7 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.8, Page number 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=1; #length of wire(m)\n",
+ "d=1*10**-3; #diameter of wire(m)\n",
+ "n=2.8*10**10; #rigidity modulus of wire(N/m**2)\n",
+ "theta=math.pi/2; #angle of twisting(radian)\n",
+ "\n",
+ "#Calculation\n",
+ "C=math.pi**2*n*(d/2)**4/(4*L); #couple to be applied(Nm)\n",
+ "\n",
+ "#Result\n",
+ "print \"couple to be applied is\",round(C*10**3,5),\"*10**-3 Nm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "couple to be applied is 4.31795 *10**-3 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.9, Page number 35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=0.82*10**-3; #diameter of wire(m)\n",
+ "delta_L=1*10**-3; #length of elongation produced(m)\n",
+ "m=0.33; #load(kg)\n",
+ "g=9.8; #acceleration due to gravity(N)\n",
+ "n=2.2529*10**9; #rigidity modulus of wire(N/m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "Y=m*g/(math.pi*(d/2)**2*delta_L); #young's modulus(N/m**2)\n",
+ "sigma=(Y/(2*n))-1; #poisson's ratio\n",
+ "\n",
+ "#Result\n",
+ "print \"poisson's ratio is\",round(sigma,3)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "poisson's ratio is 0.359\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.10, Page number 36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "p1=1.01*10**5; #atmospheric pressure(N/m**2)\n",
+ "K=16*10**10; #bulk modulus(N/m**2)\n",
+ "p2=10**2; #increased pressure(N/m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "dP=p1-p2; #change in pressure(N/m**2)\n",
+ "dV=dP/K; #fractional change of volume\n",
+ "\n",
+ "#Result\n",
+ "print \"change in volume of steel bar is\",round(dV*10**7,1),\"*10**-7 V m**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "change in volume of steel bar is 6.3 *10**-7 V m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.11, Page number 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Y=1.013*10**10; #young's modulus of bar(N/m**2)\n",
+ "b=2*10**-2; #breadth of bar(m)\n",
+ "l=1; #length of bar(m)\n",
+ "d=1*10**-2; #depth of bar(m)\n",
+ "m=2; #load(kg)\n",
+ "g=9.8; #acceleration due to gravity(N)\n",
+ "\n",
+ "#Calculation\n",
+ "y=m*g*l**3/(4*Y*b*d**3); #depression produced in bar(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"depression produced in bar is\",round(y,6),\"m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depression produced in bar is 0.024186 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 1.12, Page number 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=1.2*10**-2; #radius of cantilever(m)\n",
+ "l=1.5; #length of cantilever(m)\n",
+ "Y=19.5*10**10; #young's modulus(N/m**2)\n",
+ "m=2; #load(kg)\n",
+ "g=9.8; #acceleration due to gravity(N)\n",
+ "\n",
+ "#Calculation\n",
+ "y=4*m*g*l**3/(3*Y*math.pi*(r**4)); #depression produced in cantilever(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"depression produced in cantilever is\",round(y*10**3,3),\"*10**-3 m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depression produced in cantilever is 6.943 *10**-3 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |