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* from \"-!../../../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../../../node_modules/sass-loader/dist/cjs.js??ref--8-oneOf-1-3!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=style&index=0&id=3099059a&prod&lang=scss&\"","var render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('p',[_vm._v(\"\\n We have studied about different forms of energy in previous modules and that energy can change from one form\\n to another. But the sum of different kinds of energy in an isolated system always remains conserved. For\\n example, Universe is an isolated system and the total energy in the universe remains conserved.\\n \")]),_c('h3',[_vm._v(\"What is the principle of conservation of energy?\")]),_c('p',[_vm._v(\"\\n The principle of conservation of energy states that energy can neither be created nor be destroyed. It can only\\n transform from one form to another.\\n \")]),_c('h3',[_vm._v(\"Principle of Conservation of Energy for a Body Sliding Down a Hill\")]),_c('p',[_vm._v(\"\\n Consider a body of mass m freely falling under gravity from a height h above the surface of the earth as\\n shown in the figure given below. We will calculate kinetic energy (K), potential energy (U) and total energy\\n of the body at three different instants, when the body is at point A (at topmost point i.e., at height h), B\\n (after the body has fallen through a distance x), and C (when the body has finally reached the ground) and\\n see that the total energy (sum of kinetic energy and potential energy) is same at all instants which shows\\n that it is conserved.\\n \")]),_c('p',[_c('b',[_vm._v(\"At point A,\")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/PointA.png\",\"max-height\":\"450px\",\"max-width\":\"450px\"}})],1),_vm._v(\"\\n $$\\n \\\\begin{equation} \\\\label{eq2}\\n \\\\begin{split}\\n \\\\text{Kinetic energy}&= K = 0 \\\\;\\\\;\\\\;\\\\;\\\\;\\\\; (\\\\because \\\\text{initial velocity u=0 at topmost point})\\n \\\\\\\\ \\\\text{Potential energy }&=U = mgh\\n \\\\\\\\ \\\\text{Total energy} &= K + U\\n \\\\\\\\ &= 0 + mgh =mgh\\n \\\\end{split}\\n \\\\end{equation}\\n $$\\n \")],1),_c('p',[_c('b',[_vm._v(\"At point B,\")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/PointB.png\",\"max-height\":\"450px\",\"max-width\":\"450px\"}})],1),_c('br'),_vm._v(\"From third equation of motion we know, \\\\(v^2=u^2+2as\\\\) .Therefore, substituting \\\\(u=0\\\\) and \\\\(s=x\\\\) in this\\n equation we get,\\n $$\\n \\\\begin{equation} \\\\label{eq3}\\n \\\\begin{split}\\n \\\\text{}\\n \\\\\\\\ \\\\text{Velocity at point B} &= \\\\sqrt{2gx}\\n \\\\\\\\ \\\\text{Kinetic energy}&= \\\\frac{1}{2}mv^2\\n =\\\\frac{1}{2} \\\\times m \\\\times 2gx = mgx\\n \\\\\\\\ \\\\text{Potential energy }&= mg(h-x)\\n \\\\\\\\ \\\\text{Total energy} &= K + U\\n \\\\\\\\ &= mgx + mg(h-x) = mgh\\n \\\\end{split}\\n \\\\end{equation}\\n $$\\n \")],1),_c('p',[_c('b',[_vm._v(\"At point C,\")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/PointC.png\",\"max-height\":\"450px\",\"max-width\":\"450px\"}})],1),_c('br'),_vm._v(\"From equation \\\\(v^2=u^2+2as\\\\),\\n $$\\n \\\\begin{equation} \\\\label{eq4}\\n \\\\begin{split}\\n \\\\text{}\\n \\\\\\\\ \\\\text{Velocity at point C} &= \\\\sqrt{2gh} \\\\;\\\\;\\\\;\\\\;\\\\;\\\\; (\\\\because \\\\text u=0 \\\\; and \\\\; s=h)\\n \\\\\\\\ \\\\text{Kinetic energy}&=\\\\frac{1}{2}mv^2\\n =\\\\frac{1}{2} \\\\times m \\\\times (\\\\sqrt{2gh})^2 =mgh\\n\\n \\\\\\\\ \\\\text{Potential energy }&=0 \\\\;\\\\;\\\\;\\\\;\\\\;\\\\;\\\\;\\\\;\\\\; (\\\\because \\\\text{h is 0})\\n \\\\\\\\ \\\\text{Total energy} &= K + U\\n \\\\\\\\ &= mgx +0 = mgh\\n \\\\end{split}\\n \\\\end{equation}\\n $$\\n \")],1),_c('p',[_vm._v(\"Therefore, in all the three cases the total energy is equal to \\\\(mgh\\\\), and thus it remains conserved.\")]),_vm._m(0),_c('p'),_c('h3',[_vm._v(\"MagicGraph | Conservation of Energy\")]),_c('v-responsive',[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',[_vm._v(\" Follow this link \"),_c('a',{staticClass:\"icn\",attrs:{\"href\":\"https://edliy.com/magic\"}},[_c('i',{staticClass:\"fa fa-external-link-square\"})]),_vm._v(\" to learn how MagicGraphs help students accelerate their learning curve.\")])])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_c('b',[_vm._v(\"Note \")]),_vm._v(\" — In all the calculations above, we have ignored the effect of frictional force or any other\\n opposing\\n force. The above calculations are valid strictly in vacuum. However, the principle of\\n conservation of energy always holds, because in the case when the body is not in vacuum, certain part of the\\n mechanical energy of the ball gets converted to heat energy and other forms of energy but the total sum of\\n all\\n forms of energy always remains constant.\\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 placeDash\r\n} from '../../../common/edliy_utils-energy';\r\nconst Boxes = {\r\nbox1: function () {\r\n JXG.Options.board.minimizeReflow = 'none';\r\n JXG.Options.text.highlight =false;\r\n JXG.Options.text.fixed =true;\r\n JXG.Options.text.highlight =false;\r\n JXG.Options.text.cssStyle='fontFamily:Oswald',\r\n JXG.Options.image.highlight =false;\r\n JXG.Options.polygon.highlight =false;\r\n JXG.Options.line.highlight =false;\r\n JXG.Options.point.highlight =false;\r\n JXG.Options.curve.highlight =false;\r\n JXG.Options.slider.highlight =false;\r\n JXG.Options.point.showInfoBox =false;\r\n var brd1 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-1, 15, 19, -5],\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\n\r\n brd1.suspendUpdate();\r\n\r\n brd1.options.layer['image'] =14;\r\n makeResponsive(brd1);\r\n //Title and subtitle\r\n //var title1 = brd1.create('text', [9, 13, ' Conservation of Energy '],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(28*brd1.canvasWidth/500.)}},);\r\n placeTitle(brd1, 'Conservation of Energy', ' ');\r\n //Sliders\r\n //var mass = brd1.create('slider',[[13,11],[16,11],[10,100,120]], {snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'m', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n //placeSlider(brd1, )\r\n var mass =placeSlider(brd1, 0, 12, 10, 100, 120, 5, ' m', ' kg');\r\n //mass.setAttribute({unitLabel:'kg'});\r\n var velocity = placeSlider(brd1, 0, 10, 0, 0, 10, 5, ' v', ' m/s');\r\n //brd1.create('slider',[[13,10],[16,10],[0,0,10]], {snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'v', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n var posX = placeSlider(brd1, 0, 8, 0, 0, 16, 16, ' x', ' m');\r\n posX.setAttribute({face:'^'});\r\n //brd1.create('slider',[[13,9],[16,9],[0,0,19]], {snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'x', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n\r\n //var txtMass = brd1.create('text', [18.5, 11, 'kg'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtVelocity = brd1.create('text', [18.2, 10, 'm/s'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtPosition = brd1.create('text', [18, 9, 'm'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\n //RollerCoaster function\r\n var rollerCoaster = brd1.create('functiongraph',\r\n [function(x){ if(x<= 8 ) {return 3*Math.cos(Math.PI*x*0.2) + 3}\r\n else if(x>8 && x<=10){return -(x-9)*(x-9) + 3*Math.cos(Math.PI*8*0.2) + 4}\r\n else if(x>10 && x <= 14.2) {return Math.cos(Math.PI*x*0.5-2.12)*1 + 3.4}\r\n else if (x>14 && x <15.7) {return Math.sin(Math.PI*x*0.5 -1.26)*2 +2 }\r\n else {return 0}\r\n }, -5, 25 ], {strokeColor: 'black', strokeWidth: 3, fillColor: '#C0C0C0', fillOpacity:0.5}\r\n );\r\n\r\n\r\n //Drag Me Cart\r\n var defY = 0.25;\r\n var cart = brd1.create('point', [function(){return posX.Value()}, function(){ if(posX.Value()<= 8 ) {return 3*Math.cos(Math.PI*posX.Value()*0.2) + 3 + defY}\r\n else if(posX.Value()>8 && posX.Value()<=10){return -(posX.Value()-9)*(posX.Value()-9) + 3*Math.cos(Math.PI*8*0.2) + 4 + defY}\r\n else if(posX.Value()>10 && posX.Value() <= 14.2) {return Math.cos(Math.PI*posX.Value()*0.5-2.12)*1 + 3.4 + defY}\r\n else if (posX.Value()>14 && posX.Value() <15.7) {return Math.sin(Math.PI*posX.Value()*0.5 -1.26)*2 +2 + defY}\r\n else {return 0 + defY}\r\n }],{color: 'red', face:'o' , name:'', size:function(){return 7*brd1.canvasHeight/800}, fixed:false, visible:true, label:{offset:[0, 20], anchorX:'middle', fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n\r\n\r\n //var cartImg = brd1.create('image', ['assets/cart.svg', [function(){return cart.X() -0.6}, function(){return cart.Y() +0.1}], [1,1]], {visible: true, fixed: true});\r\n\r\n //Energy\r\n var height = function(){ return (cart.Y() - defY)};\r\n var PE = function(){ return mass.Value()*9.81*height()};\r\n var ME = function(){return 0.5*mass.Value()*velocity.Value()*velocity.Value() + mass.Value()*9.81*6};\r\n var KE = function(){return ME() - PE()};\r\n var instantVelocity = function(){return Math.sqrt(2*KE()/mass.Value())};\r\n\r\n //Tetxs\r\n var txtHeight = brd1.create('text', [10, 7, function(){return 'h = ' + height().toFixed(2)+' m'}],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(18*brd1.canvasWidth/500.)}},);\r\n var txtME = brd1.create('text', [function(){return 1.5 + ME()/1000}, -1, function(){return 'T =' + ME().toFixed(1)+' J'}],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n var txtPE = brd1.create('text', [function(){return 1.5 + PE()/1000}, -2, function(){return 'U =' + PE().toFixed(1)+ ' J'}],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n var txtKE = brd1.create('text', [function(){return 1.5 + KE()/1000}, -3, function(){return 'K =' + KE().toFixed(1)+' J'}],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n var txtInstantV = brd1.create('text', [15, 7, function(){return 'v = ' + instantVelocity().toFixed(2)+ ' m/s'}],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(18*brd1.canvasWidth/500.)}},);\r\n\r\n //var txtHeight2 = brd1.create('text', [16, 8, 'm'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtME2 = brd1.create('text', [function(){return 2.8 + ME()/1000}, -1, 'J'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtPE3 = brd1.create('text', [function(){return 2.8 + PE()/1000}, -2, 'J'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtKE3 = brd1.create('text', [function(){return 2.8 + KE()/1000}, -3, 'J'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n //var txtInstantV2 = brd1.create('text', [16, 7, 'm/s'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\n var segmentME = brd1.create('segment', [[0,-1], [function(){return ME()/1000},-1]], {visible: true, fixed: true, strokeColor: 'orange', strokeWidth:function(){return 20*brd1.canvasHeight/800}});\r\n var segmentPE = brd1.create('segment', [[0,-2], [function(){return PE()/1000},-2]], {visible: true, fixed: true, strokeColor: 'blue', strokeWidth: function(){return 20*brd1.canvasHeight/800}});\r\n var segmentKE = brd1.create('segment', [[0,-3], [function(){return KE()/1000},-3]], {visible: true, fixed: true, strokeColor: 'red', strokeWidth:function(){return 20*brd1.canvasHeight/800}});\r\n\r\n //MOVEMENT\r\n function start(){\r\n posX.moveTo([16, 9], 10000);\r\n playImg.setAttribute({visible: false});\r\n pauseImg.setAttribute({visible: true});\r\n }\r\n\r\n function pause(){\r\n playImg.setAttribute({visible: true});\r\n pauseImg.setAttribute({visible: false});\r\n posX.moveTo([0, 9], 10);\r\n }\r\n\r\n //Play Button\r\n var playImg = brd1.create('image', ['/assets/play.svg', [16, -4], [1.5, 1.5]], {visible: true, fixed: true});\r\n playImg.on('up', start);\r\n playImg.setLabel('Play')\r\n playImg.label.setAttribute({visible:false, offset:[15, -15], CssStyle:'fontFamily:Oswald', fontSize:16});\r\n playImg.on('over', function () {this.label.setAttribute({visible:true});});\r\n playImg.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n //Pause Button\r\n var pauseImg = brd1.create('image', ['/assets/reloading.svg', [16, -4], [1.5, 1.5]], {visible: false, fixed: true});\r\n pauseImg.on('up', pause);\r\n pauseImg.setLabel('pause')\r\n pauseImg.label.setAttribute({visible:false, offset:[15, -15], CssStyle:'fontFamily:Oswald', fontSize:16});\r\n pauseImg.on('over', function () {this.label.setAttribute({visible:true});});\r\n pauseImg.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n brd1.unsuspendUpdate();\r\n }\r\n }\r\nexport default Boxes;\r\n","\r\n\r\n\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&\"; export default mod; export * 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&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=3099059a&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Lesson.vue?vue&type=style&index=0&id=3099059a&prod&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n script,\n render,\n staticRenderFns,\n false,\n null,\n null,\n null\n \n)\n\nexport default component.exports"],"sourceRoot":""}