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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',[_vm._v(\"Gravitational Force\")]),_c('p',[_vm._v(\"\\n    In 1665, Sir Issac Newton made a conclusion that any two bodies in this universe attract each other by virtue\\n    of their masses and this force of attraction is called gravitational force. Although this force is very weak\\n    for elementary particles, it is very important in the study of large objects. It helps us to study planetary orbits, motion of\\n    planets and their moons.\\n    It is the gravitational force due to which moons revolve around their planets and earth attracts every object towards its center.\\n    In 1687, Newton put forth a law called Newton’s Law of Gravitation.\\n  \")]),_c('h3',[_vm._v(\"Newton's Law of Gravitation\")]),_c('p',[_vm._v(\"\\n    According to Newton's law of gravitation, every particle in the universe attracts other particle with a force\\n    directly proportional to the product of the masses between the two particles and inversely\\n    proportional to the square of distance between them.\\n  \")]),_vm._m(0),_c('p',[_vm._v(\"\\n    Gravitational force is conservative in nature and is independent of the medium between the two particles. This\\n    law is only valid for point masses. However, for external points, even large spherical bodies act as\\n    particles in terms of the gravitational forces between them and their masses can be assumed to be\\n    concentrated at their centers.\\n  \")]),_c('h3',[_vm._v(\"Vector Form\")]),_c('p',[_vm._v(\"\\n    Direction of force between the two objects is directed along the line joining them. Newton’s law\\n    of gravitation can also be written in vector form which will tell us about the direction of the two\\n    forces.\\n  \")]),_c('v-img',{attrs:{\"src\":\"/assets\\\\Gravitaion_image_1.jpg\",\"width\":\"400px\"}}),_vm._m(1),_c('br'),_c('p',[_vm._v(\"\\n    $$\\\\mathbf{\\\\hat{r}_{21}}=\\\\frac{\\\\mathbf{r_2}-\\\\mathbf{r_1}}{|\\\\mathbf{r_2}-\\\\mathbf{r_1}|}$$\\n    Therefore,\\n    $$\\\\mathbf F_{21}=-G\\\\frac{m_1m_2}{{|\\\\mathbf{r_2}-\\\\mathbf{r_1}|}^3} \\\\mathbf{r_2}-\\\\mathbf{r_1}$$\\n    Force on object 1 due to object 2 i.e, \\\\(\\\\mathbf F_{12}\\\\) is given as,\\n    $$\\\\mathbf F_{12}= G\\\\frac{m_1m_2}{{|\\\\mathbf{r_2}-\\\\mathbf{r_1}|}^3} \\\\mathbf{r_2}-\\\\mathbf{r_1}$$\\n    It can also be seen that \\\\(\\\\mathbf F_{12} =-\\\\mathbf F_{21}\\\\).\\n  \")]),_c('br'),_c('br'),_vm._m(2),_c('h3',{ref:\"playgraph\"},[_vm._v(\"\\n    MagicGraph | Law of Gravitation\\n  \")]),_c('v-responsive',[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    Thus, if m\"),_c('sub',[_vm._v(\"1\")]),_vm._v(\" and m\"),_c('sub',[_vm._v(\"2\")]),_vm._v(\" are the masses of the two bodies, and r is the distance between them,\\n    magnitude of the gravitational force \\\\(F\\\\) is given as,\\n    $$F \\\\propto \\\\frac{m_1m_2}{r^2} $$\\n    or\\n    $$ F= G\\\\frac{m_1m_2}{r^2}$$\\n    where \\\\(G\\\\) is the proportionality constant and is known as gravitational constant. It is a universal constant\\n    and its value is equal to 6.673 x 10 \"),_c('sup',[_vm._v(\"-11\")]),_vm._v(\" N m\"),_c('sup',[_vm._v(\"2\")]),_vm._v(\"/kg\"),_c('sup',[_vm._v(\"2\")]),_vm._v(\".\\n  \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    Consider the figure shown above. For the two masses m\"),_c('sub',[_vm._v(\"1\")]),_vm._v(\" and m\"),_c('sub',[_vm._v(\"2\")]),_vm._v(\", whose position vectors\\n    are \\\\(\\\\mathbf{r_1}\\\\) and \\\\(\\\\mathbf{r_2}\\\\)  respectively, force in vector form is given as,\\n    $$\\\\mathbf {F_{21}}=-G\\\\frac{m_1m_2}{|\\\\mathbf {r_{21}}|^2} \\\\mathbf{\\\\hat{r}_{21}}$$\\n    where,\\\\(F_{21}\\\\) is the force applied on object 2 by object 1, \\\\(G\\\\) is the gravitational\\n    constant and \\\\(\\\\hat{r}_{21}\\\\) is the unit vector from object 1 to object 2.\\n    The negative sign indicates that the force is acting in a direction opposite to the unit vector.\\n  \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    In a system of n particles, the interaction force between any two particles remains unchanged and the net gravitational force on any particle can be given as the vector sum of all individual gravitational forces acting on the body i.e, if \\\\(F\\\\) is the net force on a body, it is given as,\\n    $$ \\\\mathbf{F} = \\\\mathbf{F_{12}}+\\\\mathbf{F_{13}} +...+ \\\\mathbf{F_{1n}}  $$\\n    This is called the \"),_c('b',[_vm._v(\"principle of superposition\")]),_vm._v(\".\\n  \")])\n}]\n\nexport { render, staticRenderFns }","// Import the edliy_utils\r\nimport {\r\n    makeResponsive,\r\n    placeTitle,\r\n    placeImage,\r\n    placeInput,\r\n    placeSlider,\r\n    hoverMe,\r\n    placeRec,\r\n    hiddenPt,\r\n    fixedPt,\r\n    clearInputFields,\r\n    dragMe,\r\n    placeArrow,\r\n    placeGravity,\r\n    placeText,\r\n    placeLine,\r\n    placePoint,\r\n    placeGlider,\r\n    placeRuler,\r\n    placeLeftText,\r\n    placeSliderSwitch\r\n} from '../../../common/edliy_utils-circle';\r\nconst Boxes = {\r\nbox1: function () {\r\nJXG.Options.point.showInfoBox=false;\r\nJXG.Options.point.highlight=false;\r\nJXG.Options.text.highlight=false;\r\nJXG.Options.text.fixed=true;\r\nJXG.Options.curve.highlight=false;\r\nJXG.Options.text.cssDefaultStyle='fontFamily:Oswald;'\r\nvar brd1 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-3, 20, 20, -3],\r\n    keepaspectratio: true, axis:true, ticks:{visible:false},\r\n    grid:true, showCopyright:false, showNavigation:false,\r\n    pan:{enabled:false}, zoom:{enabled:false}});\r\nbrd1.options.layer['image']=14;\r\nbrd1.suspendUpdate();\r\n//Title\r\nmakeResponsive(brd1);\r\nplaceTitle(brd1, 'Rolling Motion of a Coin', 'Trajectory of a Point on the Coin');\r\n//Sliders\r\nbrd1.suspendUpdate();\r\n\r\nbrd1.options.layer['image'] =14;\r\n//Title and subtitle\r\n//var title1 = brd1.create('text', [8, 18, '<b> Perimeter of Circle <b>'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(28*brd1.canvasWidth/500.)}},);\r\n//var radius = brd1.create('slider',[[15,12],[20,12],[1,2.5,3]], {snapToGrid: false ,face:'circle', size:3, name:'r', strokeColor:'black', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n//placeImage(brd1,'/assets/one.svg', 2, 11.7, 0.6, 0);\r\n//placeImage(brd1,'/assets/two.svg', 2, 9.7, 0.6, 0);\r\nvar Go =placeImage(brd1,'/assets/go.svg', 9, 6, 2, 0);\r\nvar radius =placeSlider(brd1, 1, 7, 1, 1.5, 2, 4, '&nbsp; &nbsp;R');\r\nradius.setAttribute({snapWidth:0.25});\r\nplaceText(brd1, 8.5, 16, 20,  '1. Set the Location of Point \\'P\\' 2. Tap on Go button to let the coin roll')\r\n//placeText(brd1, 6, 10, 20,  '1. Set the radius using the slider. 2. Tap on the Go button to roll the circle.')\r\n//placeText(brd1, 3, 6, 20, ()=>'L =2 &pi; R ='+(2*Math.PI*radius.Value()).toFixed(2));\r\nvar segment1 = brd1.create('segment', [[0,function(){return radius.Value()}], [function(){return 4*Math.PI*radius.Value()},function(){return radius.Value()}]], {fixed: true, strokeColor: 'black', visible:false});\r\n//var ptCenter = brd1.create('glider', [0,2, segment1],{face:'o' , name:'Drag Me!', label:{fontSize:function(){return 16*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\nvar ptCenter = placeGlider(brd1, segment1, 0, 2, 3,  'red', 'black');\r\n//ptCenter.setLabel('Drag me!');\r\nvar r =placePoint(brd1, ()=>ptCenter.X(), ()=>ptCenter.Y()/2,0, 'red','black');\r\nr.setLabel('R');\r\nr.label.setAttribute({anchorX:'middle', anchorY:'middle'});\r\nvar pt1 =brd1.create('point', [function(){return ptCenter.X()},0.0], {fixed:false, visible:false, face:'circle', size:4, name:' ', label: {offset: [0,25]}, strokeColor: 'black', fillColor: '#e1e1e1'});\r\nradius.on('down', function(){ptCenter.moveTo([0,radius.Value()]); pt1.moveTo([0,0]);});\r\nvar c1 = brd1.create('circle', [ptCenter, pt1], {strokeColor: 'black', strokeWidth: 0.5, fillColor: 'orange', fillOpacity: 0.2});\r\nfunction angle1(){\r\n    return  (2*Math.PI-ptCenter.X()/radius.Value() );\r\n}\r\n\r\nvar pt3 =brd1.create('point',\r\n[function(){return ptCenter.X()+radius.Value()*Math.sin(angle1())},function(){return ptCenter.Y()-radius.Value()*Math.cos(angle1())}], {trace:true, fixed:true, visible:true, face:'circle', size:3, name:'',  strokeColor: 'black', fillColor: 'white'});\r\n\r\nplaceArrow(brd1, [()=>ptCenter.X(), ()=>ptCenter.Y()], [()=>pt3.X(), ()=>pt3.Y()], 2, 'black');\r\n//var txt1 = brd1.create('text', [3, -4,  function(){return 'ANGLE = ' + angle1()*180/Math.PI}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\nvar segment2 = brd1.create('segment', [[0,0], [function(){return pt1.X()},0]], {fixed: true, strokeWidth:4, strokeColor: 'green'});\r\n\r\nvar arc1 = brd1.create('arc', [ptCenter, pt1, pt3], {strokeColor: 'green', strokeWidth:4});\r\n\r\n\r\n//Arrow\r\nvar ptArrow1 =brd1.create('point', [function(){return pt1.X()} ,-2], {fixed:true, visible:false, face:'circle', size:4, name:' ', label: {offset: [0,25]}, strokeColor: 'black', fillColor: '#e1e1e1'});\r\nvar ptArrow2 =brd1.create('point', [0 ,-2], {fixed:false, visible:false, face:'circle', size:4, name:' ', label: {offset: [0,25]}, strokeColor: 'black', fillColor: '#e1e1e1'});\r\nvar segment2 = brd1.create('segment', [ptArrow1, ptArrow2], {fixed: true, strokeColor: 'black', visible:true, strokeWidth:1,\r\n                                                                                                                highlightStrokeWidth: 2,\r\n                                                                                                                lastArrow: {type: 2, size: 8, highlightSize: 6},\r\n                                                                                                                touchLastPoint: false,\r\n                                                                                                                firstArrow: {type: 2, size: 8}\r\n                                                                                                                });\r\n\r\nvar txtPer = brd1.create('text', [function(){return pt1.X()/2}, -1.5,  function(){return pt1.X().toFixed(2)}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\nGo.on('down', function(){ptCenter.moveTo([4*Math.PI*radius.Value(), radius.Value()], 1000)});\r\n\r\n//var ptArrow3 =brd1.create('point', [-5,0], {fixed:true, visible:false, face:'circle', size:4, name:' ', label: {offset: [0,25]}, strokeColor: 'black', fillColor: '#e1e1e1'});\r\n//var ptArrow4 =brd1.create('point', [-5, function(){return radius.Value()}], {fixed:false, visible:false, face:'circle', size:4, name:' ', label: {offset: [0,25]}, strokeColor: 'black', fillColor: '#e1e1e1'});\r\n//var segment3 = brd1.create('segment', [ptArrow3, ptArrow4], {fixed: true, strokeColor: 'black', visible:true, strokeWidth:1,\r\n//                                                                                                                highlightStrokeWidth: 2,\r\n//                                                                                                                lastArrow: {type: 2, size: 8, highlightSize: 6},\r\n                                                                                                                //touchLastPoint: false,\r\n                                                                                                                //firstArrow: {type: 2, size: 8}\r\n                                                                                                                //})\r\n//var txtRad = brd1.create('text', [-4, function(){return radius.Value()/2},  function(){return radius.Value().toFixed(2)}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\nbrd1.unsuspendUpdate();\r\n}\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3>Gravitational Force</h3>\r\n    <p>\n      In 1665, Sir Issac Newton made a conclusion that any two bodies in this universe attract each other by virtue\r\n      of their masses and this force of attraction is called gravitational force. Although this force is very weak\r\n      for elementary particles, it is very important in the study of large objects. It helps us to study planetary orbits, motion of\r\n      planets and their moons.\r\n      It is the gravitational force due to which moons revolve around their planets and earth attracts every object towards its center.\r\n      In 1687, Newton put forth a law called Newton’s Law of Gravitation.\n    </p>\r\n    <h3>Newton's Law of Gravitation</h3>\r\n    <p>\n      According to Newton's law of gravitation, every particle in the universe attracts other particle with a force\r\n      directly proportional to the product of the masses between the two particles and inversely\r\n      proportional to the square of distance between them.\n    </p>\r\n    <p>\n      Thus, if m<sub>1</sub> and m<sub>2</sub> are the masses of the two bodies, and r is the distance between them,\r\n      magnitude of the gravitational force \\(F\\) is given as,\r\n      $$F \\propto \\frac{m_1m_2}{r^2} $$\r\n      or\r\n      $$ F= G\\frac{m_1m_2}{r^2}$$\r\n      where \\(G\\) is the proportionality constant and is known as gravitational constant. It is a universal constant\r\n      and its value is equal to 6.673 x 10 <sup>-11</sup> N m<sup>2</sup>/kg<sup>2</sup>.\n    </p>\r\n    <p>\n      Gravitational force is conservative in nature and is independent of the medium between the two particles. This\r\n      law is only valid for point masses. However, for external points, even large spherical bodies act as\r\n      particles in terms of the gravitational forces between them and their masses can be assumed to be\r\n      concentrated at their centers.\n    </p>\r\n    <h3>Vector Form</h3>\r\n    <p>\n      Direction of force between the two objects is directed along the line joining them. Newton’s law\r\n      of gravitation can also be written in vector form which will tell us about the direction of the two\r\n      forces.\n    </p>\r\n    <v-img src=\"/assets\\Gravitaion_image_1.jpg\" width=\"400px\" />\r\n\r\n    <p>\n      Consider the figure shown above. For the two masses m<sub>1</sub> and m<sub>2</sub>, whose position vectors\r\n      are \\(\\mathbf{r_1}\\) and \\(\\mathbf{r_2}\\)  respectively, force in vector form is given as,\r\n      $$\\mathbf {F_{21}}=-G\\frac{m_1m_2}{|\\mathbf {r_{21}}|^2} \\mathbf{\\hat{r}_{21}}$$\r\n      where,\\(F_{21}\\) is the force applied on object 2 by object 1, \\(G\\) is the gravitational\r\n      constant and \\(\\hat{r}_{21}\\) is the unit vector from object 1 to object 2.\r\n      The negative sign indicates that the force is acting in a direction opposite to the unit vector.\n    </p>\r\n    <br>\r\n    <p>\r\n      $$\\mathbf{\\hat{r}_{21}}=\\frac{\\mathbf{r_2}-\\mathbf{r_1}}{|\\mathbf{r_2}-\\mathbf{r_1}|}$$\r\n      Therefore,\r\n      $$\\mathbf F_{21}=-G\\frac{m_1m_2}{{|\\mathbf{r_2}-\\mathbf{r_1}|}^3} \\mathbf{r_2}-\\mathbf{r_1}$$\r\n      Force on object 1 due to object 2 i.e, \\(\\mathbf F_{12}\\) is given as,\r\n      $$\\mathbf F_{12}= G\\frac{m_1m_2}{{|\\mathbf{r_2}-\\mathbf{r_1}|}^3} \\mathbf{r_2}-\\mathbf{r_1}$$\r\n      It can also be seen that \\(\\mathbf F_{12} =-\\mathbf F_{21}\\).\n    </p>\r\n    <br><br>\r\n    <p>\r\n      In a system of n particles, the interaction force between any two particles remains unchanged and the net gravitational force on any particle can be given as the vector sum of all individual gravitational forces acting on the body i.e, if \\(F\\) is the net force on a body, it is given as,\r\n      $$ \\mathbf{F} = \\mathbf{F_{12}}+\\mathbf{F_{13}} +...+ \\mathbf{F_{1n}}  $$\r\n      This is called the <b>principle of superposition</b>.\r\n    </p>\r\n    <h3 ref=\"playgraph\">\n      MagicGraph | Law of Gravitation\n    </h3>\r\n    <v-responsive>\r\n      <v-layout align-center justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n      </v-layout>\r\n    </v-responsive>\r\n  </div>\r\n</template>\r\n<script>\r\nimport Boxes from './Boxes.js'\r\nexport default {\r\n  name: 'FBD',\r\n  created: function () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Law of Gravitation';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: 'What is a Free Body Diagram?', img:'/assets/number-1.svg', action: () => this.goto('ia')},\r\n      {title: 'Purpose of FBD', img:'/assets/number-2.svg', action: () => this.goto('ja')},\r\n      {title: 'Example of FBD', img:'/assets/number-3.svg', action: () => this.goto('ka')},\r\n      {title: 'MagicGraph' ,img:'/assets/touch.svg', action: () => this.goto('graphical')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newPhys =true;\r\n    this.$store.commit('navigation/replacePhys', newPhys);\r\n    let newLeftArrow =true;\r\n    this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n    let newModule =true;\r\n    this.$store.commit('navigation/replaceModule', newModule);\r\n  },\r\n  mounted () {\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    Boxes.box1();\r\n  },\r\n  metaInfo() {\r\n  return{ title: 'Free Body Diagram',\r\n          titleTemplate: '%s - Learn interactively',\r\n          meta: [ {name: 'viewport', content: 'width=device-width, initial-scale=1'},\r\n                  {name: 'description', content: 'Learn interactively how to draw a free body diagram'}\r\n                ]\r\n        }\r\n   },\r\n}\r\n</script>\r\n<style lang=\"scss\">\r\n@import 'src/styles/edliy-box.scss';\r\n@import 'src/styles/subtopic-menu.scss';\r\n@import 'src/styles/edliy-box-about.scss';\r\n@import 'src/styles/screen-sizes.scss';\r\n</style>\r\n","import mod from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"; 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