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diff --git a/Principles_of_physics/chapter1.ipynb b/Principles_of_physics/chapter1.ipynb new file mode 100755 index 00000000..af9f2d94 --- /dev/null +++ b/Principles_of_physics/chapter1.ipynb @@ -0,0 +1,537 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:aa8849d14e0b72277789cfe0c1cc3e7e66ca9061ac47dccbae27561c50c68d32"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 1 Motion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.1 Page no 17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "d=180 #Distance of satellite above the surface of earth in km\n",
+ "t=90 #Time taken to complete one revolution of the earth in minutes\n",
+ "r=6400 #Radius of the earth in kms\n",
+ "\n",
+ "#Calculations\n",
+ "R=(r+d)*1000\n",
+ "T=t*60\n",
+ "v=(2*3.14*R)/T\n",
+ "a=(v**2/R)\n",
+ "\n",
+ "#Output\n",
+ "print\"Orbital speed is \",round(v,0),\"m/s\" \n",
+ "print\"Centripetal acceleration is \",round(a,1),\"m/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Orbital speed is 7652.0 m/s\n",
+ "Centripetal acceleration is 8.9 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.2 Page no 17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=0.05 #Mass of the stone in kg\n",
+ "r=0.4 #Radius of the string in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "vh=math.sqrt(9.8*r)\n",
+ "vl=math.sqrt((2/m)*(((1/2.0)*m*vh**2)+(m*9.8*2*r)))\n",
+ "\n",
+ "#Output\n",
+ "print\"Minimum speed when the stone is at the top of the circle is \",round(vh,2),\"m/s\" \n",
+ "print\"Minimum speed when the stone is at the bottom of the circle is \",round(vl,2),\"m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum speed when the stone is at the top of the circle is 1.98 m/s\n",
+ "Minimum speed when the stone is at the bottom of the circle is 4.43 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.3 Page no 17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=0.2 #Mass of the ball in kg\n",
+ "r=1.5 #Radius of vertical circle in m\n",
+ "q=35 #Angle made by the ball in degrees\n",
+ "v=6 #Velocity of the ball in m/s\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "T=(m*((v**2/r)+(9.8*math.cos(q*3.14/180.0))))\n",
+ "at=9.8*math.sin(q*3.14/180.0)\n",
+ "ar=(v**2/r)\n",
+ "a=math.sqrt(at**2+ar**2)\n",
+ "\n",
+ "#Output\n",
+ "print\"Tension in the string is \",round(T,1),\"N\" \n",
+ "print\"Tangential acceleration is \",round(at,2),\"m/s**2\" \n",
+ "print\"Radial acceleration is \",ar,\"m/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in the string is 6.4 N\n",
+ "Tangential acceleration is 5.62 m/s**2\n",
+ "Radial acceleration is 24.0 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.4 Page no 17"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "#A small ball is released from height of 4r measured from the bottom of the loop, where r is the radius of the loop\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "ar=(6*9.8)\n",
+ "at=(9.8*math.sin(90*3.14/180.0))\n",
+ "\n",
+ "#Output\n",
+ "print\"Radial acceleration is \",ar,\"m/s**2\"\n",
+ "print\"Tangential acceleration is \",round(at,1),\"m/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Radial acceleration is 58.8 m/s**2\n",
+ "Tangential acceleration is 9.8 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.5 Page no 18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "l=0.95 #Length of the strring in m\n",
+ "m=0.15 #Mass of the bob in kg\n",
+ "r=0.25 #Radius of the circle in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "h=math.sqrt(l**2-r**2)\n",
+ "t=2*3.14*math.sqrt(h/9.8)\n",
+ "\n",
+ "#Output\n",
+ "print\"The period of rotation is \",round(t,2),\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The period of rotation is 1.92 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.6 Page no 18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "N=40.0 #Minimum speed of rotor in rpm\n",
+ "r=2.5 #Radius of rotor in m\n",
+ "\n",
+ "#Calculations\n",
+ "t=60/N\n",
+ "u=(9.8*t**2)/(4.0*3.14**2*r)\n",
+ "\n",
+ "#Output\n",
+ "print\"The coefficient of limiting friction between the object and the wall of the rotor is \",round(u,3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The coefficient of limiting friction between the object and the wall of the rotor is 0.224\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.7 Page no 18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "a=30 #Angle of inclination in degrees\n",
+ "t=3 #Time in s\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "a=(9.8*math.sin(a*3.14/180.0))\n",
+ "v=(0+a*t)\n",
+ "\n",
+ "#Output\n",
+ "print\"Speed of the block after \",t,\"s is \",round(v,1),\"m/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of the block after 3 s is 14.7 m/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.8 Page no 19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=10.0 #Mass of the block in kg\n",
+ "F1=40 #Horizontal force to start moving in N\n",
+ "F2=32 #Horizontal force to move with constant velocity in N\n",
+ "\n",
+ "#Calculations\n",
+ "u1=(F1/(m*9.8))\n",
+ "u2=(F2/(m*9.8))\n",
+ "\n",
+ "#Output\n",
+ "print\"Coefficient of static friction is \",round(u1,3)\n",
+ "print\"Coefficient of kinetic friction is \",round(u2,4)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Coefficient of static friction is 0.408\n",
+ "Coefficient of kinetic friction is 0.3265\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.9 Page no 19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=(3,12) #Masses of the blocks in kg\n",
+ "q=50 #Angle made by the string in degrees\n",
+ "a=3 #Acceleration of 12kg block in m/s^2\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "T=m[0]*(9.8+a)\n",
+ "u=(m[1]*(9.8*math.sin(q*3.14/180.0)-a)-T)/(m[1]*9.8*math.cos(q*3.14/180.0))\n",
+ "\n",
+ "#Output\n",
+ "print\"Tension in the string is \",T,\"N\" \n",
+ "print\"The coefficient of kinetic friction is \",round(u,3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tension in the string is 38.4 N\n",
+ "The coefficient of kinetic friction is 0.207\n"
+ ]
+ }
+ ],
+ "prompt_number": 54
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.e.1 Page no 9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "w=50 #Weight in N\n",
+ "a=(40,50) #Angles made by two cables in degrees\n",
+ "\n",
+ "#Calculations\n",
+ "#Solving two equations obtained from fig. 1.10 on page no.10\n",
+ "#-T1cos40+T2cos50=0\n",
+ "#T1sin40+T2sin50=50\n",
+ "import math\n",
+ "A = array([[math.cos(a[1]*3.14/180.0),-math.cos(a[0]*3.14/180.0)], \n",
+ " [math.sin(a[0]*3.14/180.0),math.sin(a[1]*3.14/180.0)]])\n",
+ "b = array([0,50])\n",
+ "X = solve(A, b)\n",
+ "T2=X[1]\n",
+ "print \"T2=\",round(T2,1),\"N\"\n",
+ "T1=(math.cos(a[1]*3.14/180.0)/math.cos(a[0]*3.14/180.0))*T2\n",
+ "print \"T1\",round(T1,1),\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "T2= 32.7 N\n",
+ "T1 27.4 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.e.5 Page no 13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=100.0 #Mass of block in kg\n",
+ "F=500 #Force in N\n",
+ "q=30 #Angle made with the horizontal in degrees\n",
+ "u=0.4 #Coefficient of sliding friction\n",
+ "\n",
+ "#Calculations\n",
+ "R=m*9.8\n",
+ "f=(u*R)\n",
+ "a=(F*math.cos(q*3.14/180.0)-f)/m\n",
+ "\n",
+ "#Output\n",
+ "print\"The acceleration of the block is \",round(a,2),\"m/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The acceleration of the block is 0.41 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 56
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.e.6 Page no 14"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=(20.0,80.0) #Masses of blocks in kg\n",
+ "F=1000 #Force with which 20kg block is pulled in N\n",
+ "\n",
+ "#Calculations\n",
+ "a=F/(m[0]+m[1])\n",
+ "T=F-(m[0]*a)\n",
+ "\n",
+ "#Output\n",
+ "print\"The acceleration produced is \",a,\"m/s^2\" \n",
+ "print\"The tension in the string connecting the blocks is \",T,\"N\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The acceleration produced is 10.0 m/s^2\n",
+ "The tension in the string connecting the blocks is 800.0 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1.e.8 Page no 15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "w=588 #Weight of the person in N\n",
+ "a=3 #Acceleration in m/s^2\n",
+ "b=180\n",
+ "\n",
+ "#Calculations\n",
+ "m=(w/9.8)\n",
+ "P=(w+(m*a))\n",
+ "p=w-b\n",
+ "\n",
+ "#Output\n",
+ "print\"Weight of the person when the elevator is accelerated upwards is \",P,\"N\"\n",
+ "print\"Weight of the person when the elevator is accelerated upwards is \",p,\"N\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Weight of the person when the elevator is accelerated upwards is 768.0 N\n",
+ "Weight of the person when the elevator is accelerated upwards is 408 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |