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","sourcesContent":["export * 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=009ddc36&prod&lang=scss&\"","var render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',[_vm._v(\"First Law\")]),_vm._m(0),_c('p',[_vm._v(\"\\n      The Mathematical statements might not seem very intuitive. So let us look at some real\\n      life examples of the First Law and Inertia.\\n    \")]),_vm._m(1),_c('h3',[_vm._v(\"Second Law\")]),_vm._m(2),_c('p',[_vm._v(\"\\n      There are however some cases where the mass of a system does not remain constant (like in a rocket\\n      which continuously uses up its fuel) and in such cases we cannot use \\\\(\\\\textbf{F}=m\\\\textbf{a}\\\\)\\n    \")]),_c('h3',[_vm._v(\"Third Law\")]),_vm._m(3),_vm._m(4),_c('h3',[_vm._v(\"MagicGraph | Find Tension in the String\")]),_c('v-responsive',[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}}),_c('div',{attrs:{\"justify-center\":\"\"}},[_c('p',[_vm._v(\"\\n            Floor and pully are assumed to be frictionless.\\n          \")]),_c('p',[_vm._v(\"\\n            Bucket has a mass \\\\(m_1\\\\) and the kettlebell has a mass \\\\(m_2\\\\).\\n          \")]),_c('p',[_vm._v(\"\\n            Determine the tension in the string.\\n          \")]),_c('p',{attrs:{\"id\":\"step1\"}},[_vm._v(\"\\n \\n          \")]),_c('p',{attrs:{\"id\":\"step2\"}},[_vm._v(\"\\n \\n          \")]),_c('p',{attrs:{\"id\":\"step3\"}},[_vm._v(\"\\n \\n          \")]),_c('p',{attrs:{\"id\":\"step3-1\"}},[_vm._v(\"\\n \\n          \")]),_c('p',{attrs:{\"id\":\"step3-2\"}},[_vm._v(\"\\n \\n          \")]),_c('p',{attrs:{\"id\":\"step3-3\"}},[_vm._v(\"\\n \\n          \")])])])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      Newton's first law states that:\\n      \"),_c('br'),_c('i',[_vm._v(\"\\\"An object does not change its state of motion unless\\n        acted upon by an external force.\\\"\\n      \")]),_c('br'),_vm._v(\"This means that an object which is at rest will continue to be at rest\\n      and a moving object will keep moving if no external force is applied on it.\\n      Mathematically, we can say that:\\n      $$\\\\textbf{F}_{net}=0 \\\\iff \\\\frac{d\\\\textbf{v}}{dt}=0$$\\n      The concept of inertia is very closely related to the first law. In fact\\n      sometimes the first law is called the \"),_c('i',[_vm._v(\"Principle of Inertia\")])])\n},function (){var _vm=this,_c=_vm._self._c;return _c('ol',[_c('li',[_vm._v(\"\\n        When you get off a moving bus, you should run along the\\n        bus for sometime otherwise you will fall. This is because\\n        when your feet touch the ground, they stop moving but the\\n        upper body keeps moving due to the First Law. Hence one must\\n        run alongside the bus for a while before stopping slowly\\n      \")]),_c('li',[_vm._v(\"\\n        You must've also observed that people lean forward when a bus\\n        stops. This is also due to inertia of the upper body.\\n      \")]),_c('li',[_vm._v(\"\\n        If you were to visit the International Space Station, you would notice that stopping in space is\\n        much more difficult. This is because in outer space, there is no gravity to act against our motion.\\n      \")])])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      Newton's Second Law quantitatively defines Force but before we get there, lets first look\\n      at the qualitative definition of Force which we get from The First Law:\\n      \"),_c('br'),_c('i',[_vm._v(\"\\\"Force is that physical cause which changes the state of rest or motion of a body\\\" \")]),_c('br'),_vm._v(\" This definition comes from the First Law. Now we will see the Second Law:\\n      \"),_c('br'),_c('i',[_vm._v(\"\\\"The rate of change of momentum of a body is directly proportional to the applied force and\\n        occurs in the same direction as the direction of the force applied.\\\" \")]),_vm._v(\"\\n      Mathematically,\\n      $$\\\\textbf{F}=\\\\frac{d\\\\textbf{p}}{dt}$$\\n      Using \\\\(\\\\textbf{p}=m\\\\textbf{v}\\\\) in the above equation,\\n      $$\\\\textbf{F}=m\\\\frac{d\\\\textbf{v}}{dt}+\\\\textbf{v}\\\\frac{dm}{dt}$$\\n      In most cases, mass of our system remains constant, so the above\\n      equation reduces to the famous \\\\(\\\\textbf{F}=m\\\\frac{d\\\\textbf{v}}{dt}=m\\\\textbf{a}\\\\)\\n    \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n      Newton's third law is pretty simple. It states that:\\n      \"),_c('br'),_c('i',[_vm._v(\"\\\"Every action has an equal and opposite reaction\\\"\")]),_c('br'),_vm._v(\"Now lets see some examples to understand this:\\n    \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('ol',[_c('li',[_vm._v(\"\\n        A rocket moves up because the gases which come out of it exert a force equal to the force\\n        applied by the rocket on the gas.\\n      \")]),_c('li',[_vm._v(\"When a gun is fired the shooter feels a recoil. This is due to the Third Law.\")])])\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\n    box1: function () {\r\n      JXG.Options.point.showInfoBox=false;\r\n      JXG.Options.point.highlight=false;\r\n      JXG.Options.text.highlight=false;\r\n      JXG.Options.line.highlight=false;\r\n      JXG.Options.polygon.highlight=false;\r\n      JXG.Options.text.fixed=true;\r\n      JXG.Options.curve.highlight=false;\r\n      JXG.Options.text.cssDefaultStyle='fontFamily:Oswald;'\r\n    var brd3 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-10, 10, 10, -10],\r\n    keepaspectratio: true, axis:false, ticks:{visible:false},\r\n    grid:true, showCopyright:false, showNavigation:false,\r\n    pan:{enabled:false}, zoom:{enabled:false}});\r\n    brd3.options.layer['image'] =14;\r\n    makeResponsive(brd3);\r\n    placeTitle(brd3, 'Newton\\'s Second Law', '(Calculate Forces & Acceleration)');\r\n    placeGravity(brd3, [5, 5],[5, 3], 'g');\r\n//brd3.create('text', [-6, 9., '<b> Free Body Diagram <b>'],{CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(32*brd3.canvasWidth/500.)}, fixed:true});\r\n//EXTREME POINT\r\nvar Pt1 = brd3.create('point', [-10,0],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar Pt2 = brd3.create('point', [-10, 0],{face:'o' , name:'Pt22D', size:0,withLabel:false, fixed:false});\r\n\r\nvar line = brd3.create('segment', [Pt1,Pt2],{visible: false, strokeWidth:1,dash:1, strokeColor:'black', fixed:true});\r\nvar table = brd3.create('glider', [-10,-4, line], {visible: false, face: 'o' , size:3, name:'', strokeColor:'black'});\r\n\r\n\r\n//ORANGE TABLE\r\nbrd3.create('polygon', [[-10,-15],\r\n                         [0,-15],\r\n                         [0,0],\r\n                         [function(){return table.X()}, function(){return table.Y()}]],\r\n                        {vertices:{visible:false, fixed:true}, borders:{visible:false}, fillColor: '#ffa42a', fillOpacity:1.0});\r\n\r\n//ANGLE\r\nfunction angle(){\r\n    return Math.atan(10/Math.abs(table.Y()))\r\n};\r\nbrd3.create('text', [-2, -2, function(){return \"&alpha;= \"+ (angle()*180/Math.PI).toFixed(1)}], {fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\nvar circc=brd3.create('arc', [[0,0],[function(){return -2*Math.sin(angle())},function(){return -2*Math.cos(angle())}], [0,-2]],{visible:true, strokeWidth:1, strokeColor:'black', dash:1, center:{visible:false}, radiuspoint:{visible:false}, anglepoint:{visible:false}});\r\n\r\n//SLIDING AND HANGING ELEMENTS\r\n\r\nvar Pt3 = brd3.create('point', [0,0],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar Pt4 = brd3.create('point', [function(){return table.X()}, function(){return table.Y()}],{face:'o' , name:'Pt22D', size:0,withLabel:false, fixed:false});\r\nvar line2 = brd3.create('segment', [Pt3,Pt4],{visible: false, strokeWidth:1,dash:1, strokeColor:'black', fixed:true});\r\nvar slidingBox = brd3.create('glider', [-6,0, line2], {visible: false, face: 'o' , size:3, name:'', strokeColor:'black'});\r\nvar slidingBoxIm = brd3.create('image', ['/assets/fbd/kettlebell.svg', [function(){return slidingBox.X()-0.875},function(){return slidingBox.Y()}], [1.75,1.75]],{fixed: true, highlight:false});\r\nbrd3.create('image', ['/assets/fbd/hands.svg',[()=>slidingBox.X()-2, ()=>slidingBox.Y()+2], [2, 2]],{rotate:-90});\r\nvar hangingBox = brd3.create('point', [0.5,-4],{face:'o' , name:'Pt22D', size:0,withLabel:false, fixed:false});\r\nvar hangingBoxIm = brd3.create('image', ['/assets/fbd/bucket.svg', [function(){return hangingBox.X()-0.4},function(){return hangingBox.Y()}], [1.75,1.75]], {fixed: true, highlight:false});\r\n//CORDS\r\nvar Pt5 = brd3.create('point', [0,0.8],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar Pt6 = brd3.create('point', [function(){return slidingBox.X()},function(){return slidingBox.Y()+0.8}],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar li1 = brd3.create('segment', [Pt5,Pt6], {strokeColor: 'blue'});\r\n//\r\nvar Pt7 = brd3.create('point', [1,0.5],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar Pt8 = brd3.create('point', [function(){return hangingBox.X()+0.5},function(){return hangingBox.Y()+1}],{face:'o' , name:'Pt2D', size:0,withLabel:false, fixed:false});\r\nvar li2 = brd3.create('segment', [Pt7,Pt8], {strokeColor: 'blue'});\r\n//ROTATE PULLEY\r\nvar pulley = brd3.create('point', [0,0],{face:'o' , name:'pulley', size:0,withLabel:false, fixed:true});\r\nvar p2 = brd3.create('point', [0.5,0.5], {visible:false, size:8, name:'offset', opacity:0.3});\r\nvar p3 = brd3.create('point', [0.5,0.5], {visible:false, size:8, name:'p3', opacity:0.3});\r\nvar pulleyIm = brd3.create('image', ['/assets/fbd/pulley.svg',[0, 0],[1,1]], {fixed: true});\r\nvar tRot = brd3.create('transform', [function(){return hangingBox.Y()}, p3], {type:'rotate'});\r\ntRot.bindTo(pulleyIm);\r\n//SLIDERS\r\n//var mass = brd3.create('slider', [[3,5], [6,5], [1, 5, 10]],{visible:false});\r\n//var Mass = brd3.create('slider', [[3,4], [6,4], [1, 5, 10]],{visible:false});\r\n//brd3.create('text', [1, 6.1, '&mu;'], {fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//brd3.create('text', [1, 5.4, \"bucket's <br> mass (m_1)\"], {fixed: true, fontSize:function(){return 16*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'},{visible:false});\r\n//brd3.create('text', [1, 4.0, \"kettlebell's <br> mass (m_2)\"], {fixed: true, fontSize:function(){return 16*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'},{visible:false});\r\n//brd3.create('text', [1, 4.8, ''], {fixed: true, fontSize:function(){return 16*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//brd3.create('text', [1, 3.8, ''], {fixed: true, fontSize:function(){return 16*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//brd3.create('text', [7, 5, '[kg]'], {fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n//brd3.create('text', [7, 4, '[kg]'], {fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\r\n//Arrows sliding Box\r\nvar p0arrowS = brd3.create('point', [function(){return slidingBox.X()},function(){return slidingBox.Y()+0.8}],{visible: function(){if(i>=2 ){return true} else{return false}}, name:'', size:0, fixed:true, label:{offset:[0, -20], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\n\r\nvar pWeightX = brd3.create('point', [function(){return p0arrowS.X()-2*Math.cos(angle())*Math.sin(angle())},function(){return p0arrowS.Y()-2*Math.cos(angle())*Math.cos(angle())}],{visible: false,name:'Wx', size:0, fixed:true, label:{offset:[0, -20], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar pWeightY = brd3.create('point', [function(){return p0arrowS.X()+2*Math.sin(angle())*Math.cos(angle())},function(){return p0arrowS.Y()-2*Math.sin(angle())*Math.sin(angle())}],{visible: false,name:'W', size:0, fixed:true, label:{offset:[0, -20], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar pWeight = brd3.create('point', [function(){return p0arrowS.X()},function(){return p0arrowS.Y()-2}],{visible: function(){if(i>=2 ){return true} else{return false}},name:'W_2', size:0, fixed:true, label:{offset:[0, -5],fontSize:function(){return 18*brd3.canvasHeight/800}}});\r\nvar k =0;\r\nvar normal = brd3.create('point', [function(){return p0arrowS.X()-2*Math.sin(angle())*Math.cos(angle())},function(){return p0arrowS.Y()+2*Math.sin(angle())*Math.sin(angle())}],{visible: function(){if(i>=2 ){return true} else{return false}}, name:'N', size:0, fixed:true, label:{offset:[0, 25], fontSize:function(){return 18*brd3.canvasHeight/800}}});\r\nvar arrowNormal = brd3.create('arrow', [p0arrowS, normal] , {visible: function(){if(i>=2 ){return true} else{return false}} });\r\n\r\nvar arrowGravityX = brd3.create('arrow', [p0arrowS, pWeightX] , {visible: false});\r\nvar arrowGravityY = brd3.create('arrow', [p0arrowS, pWeightY] , {visible: false});\r\nvar arrowGravity = brd3.create('arrow', [p0arrowS, pWeight] , {visible: function(){if(i>=2 ){return true} else{return false}}});\r\n\r\nvar pTension1 = brd3.create('point', [function(){return p0arrowS.X()+2*Math.sin(angle())},function(){return p0arrowS.Y()+2*Math.cos(angle())}],{visible: function(){if(i>=2){return true} else{return false}}, name:'T_2', size:0, fixed:true, label:{offset:[0, 30], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar arrowTension = brd3.create('arrow', [p0arrowS, pTension1], {visible: function(){if(i>=2 ){return true} else{return false}}});\r\narrowTension.setLabel('T_2 is the tension in the rope.')\r\narrowTension.label.setAttribute({visible:false, offset:[0, 15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\narrowTension.on('over', function () {k=2; this.label.setAttribute({visible:true});});\r\narrowTension.on('out', function () {k=0; this.label.setAttribute({visible:false});});\r\n\r\n//Arrows hanging box\r\nvar p0arrow = brd3.create('point', [function(){return hangingBox.X()+0.5},function(){return hangingBox.Y()+0.5}],{visible: function(){if(i>=1 ){return true} else{return false}}, name:'', size:0, fixed:true, label:{offset:[0, -20], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar pWeight2 = brd3.create('point', [function(){return p0arrow.X()},function(){return p0arrow.Y()-2}],{visible: function(){if(i>=1 ){return true} else{return false}}, name:'W_1', size:0, fixed:true, label:{offset:[0, -10], fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar arrowGravity2 = brd3.create('arrow', [p0arrow, pWeight2] , {visible: function(){if(i>=1 ){return true} else{return false}}});\r\nvar pTension2 = brd3.create('point', [function(){return p0arrow.X()},function(){return p0arrow.Y()+2}],{visible: function(){if(i>=1 ){return true} else{return false}}, name:'T_1', size:0, fixed:true, label:{offset:[0, 10], fontSize:function(){return 20*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'}});\r\nvar arrowTension2 = brd3.create('arrow', [p0arrow, pTension2] , {visible: function(){if(i>=1 ){return true} else{return false}}});\r\narrowTension2.setLabel('T is the tension in the rope (act upwards)')\r\narrowTension2.label.setAttribute({visible:false, offset:[0, 15], CssStyle:'fontFamily:Oswald', fontSize:12});\r\narrowTension2.on('over', function () {k=1; this.label.setAttribute({visible:true});});\r\narrowTension2.on('out', function () {k=0; this.label.setAttribute({visible:false});});\r\narrowGravity2.setLabel('W_1 is the weight of the bucket (= m_1g). ')\r\narrowGravity2.label.setAttribute({visible:false, offset:[0, -25], CssStyle:'fontFamily:Oswald', fontSize:12});\r\narrowGravity2.on('over', function () {this.label.setAttribute({visible:true});});\r\narrowGravity2.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n//HAND\r\nvar hand = brd3.create('image', ['/assets/fbd/hand2.svg', [-4,0.5], [1.5,1.5]], {visible: function(){if(i>=4){return true} else{return false}}, fixed: false, rotate: 90});\r\n\r\n//ARC\r\nvar centro = brd3.create('point', [0.4,0.3],{visible: false});\r\nvar final = brd3.create('point', [1,0.5],{visible: false});\r\nvar ppio = brd3.create('point', [0,0.8],{visible: false});\r\nvar circc1=brd3.create('arc', [centro,final,ppio],{fixed: true, visible:true, strokeWidth:2, strokeColor:'blue', dash:0, center:{visible:false}, radiuspoint:{visible:false}, anglepoint:{visible:false}});\r\n\r\n//REDO AND UNDO\r\nvar redo = brd3.create('image', ['/assets/fbd/redo.svg', [3.4,-8.5], [1.2,1.2]], {visible: true, fixed: true});\r\nvar undo = brd3.create('image', ['/assets/fbd/undo.svg', [2,-8.5], [1.2,1.2]], {visible: true, fixed: true});\r\n\r\nvar i =0;\r\nvar maxSteps = 3;\r\n\r\nfunction updateStepTexts(){\r\n    if (i<=0){\r\n        return;\r\n    }\r\n    if(i>=1){\r\n        document.getElementById('step1').innerHTML = \"\" + text1.plaintext;\r\n\r\n    }\r\n    if(i>=2){\r\n        document.getElementById('step2').innerHTML = \"\" + text2.plaintext;\r\n\r\n    }\r\n    if(i>=3){\r\n        document.getElementById('step3').innerHTML = \"\" + text3_0.plaintext;\r\n        document.getElementById('step3-1').innerHTML = \"\" + text3_1.plaintext;\r\n\t\tdocument.getElementById('step3-2').innerHTML = \"\" + text3_2.plaintext;\r\n        document.getElementById('step3-3').innerHTML = \"\" + text3_3.plaintext;\r\n    }\r\n}\r\n\r\nredo.on('down',function(){\r\n    i = i+1;\r\n    if (i > 3){\r\n        i = 3;\r\n    }\r\n    updateStepTexts();\r\n});\r\n\r\nundo.on('down',function(){\r\n    i=i-1;\r\n    if (i < 0){\r\n        i = 0;\r\n    }\r\n    document.getElementById('step1').innerHTML = \"\";\r\n    document.getElementById('step2').innerHTML = \"\";\r\n\tdocument.getElementById('step3').innerHTML = \"\";\r\n    document.getElementById('step3-1').innerHTML = \"\";\r\n    document.getElementById('step3-2').innerHTML = \"\";\r\n    document.getElementById('step3-3').innerHTML = \"\";\r\n    updateStepTexts();\r\n});\r\n\r\n\r\n//FIRST STEP\r\nvar text1 = brd3.create('text', [-9, -3, \"<b> Step 1 </b>: Apply Newton's 2^n^d law on the bucket<br>  &sum;F_y = m_1a <br> T - W_1 = m_1(-a) <br> T_1 - m_1g = -m_1a <br> T_1 = m_1(g - a) \"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\r\n//SECOND STEP\r\nvar text2 = brd3.create('text', [-5, -3, \"<b>Step 2 </b>: Apply Newton's 2^n^d law on the kettlebell <br> &sum;F_x = m_2a <br> T_2 = m_2a\"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\r\n//THIRD STEP\r\nvar text3_0 = brd3.create('text', [-7, -3, \"<b>Step 3 </b>: Pulley is frictionless. So T_1 = T_2 = T\"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\nvar text3_1 = brd3.create('text', [-7, -3,  \" m_1(g - a) = m_2a\"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\nvar text3_2 = brd3.create('text', [-7, -3,  \"a = m_1g/(m_1+m_2)\"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\nvar text3_3 = brd3.create('text', [-7, -3,  \"T = m_2a = m_1m_2g/(m_1+m_2)\"], {visible: false, fixed: true, fontSize:function(){return 18*brd3.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\r\n//MOVEMENT\r\nhand.on('up', function(){\r\n    if(tension()>weightSLidingBoxX()){\r\n       return slidingBox.moveTo([-0.3,0],1000),\r\n              hangingBox.moveTo([0.5,-8],1000),\r\n\r\n              pTension2.setAttribute({visible: false}),\r\n              p0arrow.setAttribute({visible: false}),\r\n              arrowTension2.setAttribute({visible: false}),\r\n              arrowGravity2.setAttribute({visible: false}),\r\n              pWeight2.setAttribute({visible:false}),\r\n\r\n              p0arrowS.setAttribute({visible:false}),\r\n              pWeightY.setAttribute({visible:false}),\r\n              arrowGravityY.setAttribute({visible:false}),\r\n              pWeight.setAttribute({visible:false}),\r\n              arrowGravity.setAttribute({visible:false}),\r\n\r\n              pTension1.setAttribute({visible:false}),\r\n              arrowTension.setAttribute({visible:false}),\r\n\r\n              normal.setAttribute({visible:false}),\r\n              arrowNormal.setAttribute({visible:false}),\r\n\r\n              textAcc.setAttribute({visible:true}),\r\n              textWy.setAttribute({visible:true}),\r\n              textTension.setAttribute({visible:true}),\r\n              textWBucket.setAttribute({visible:true})\r\n\r\n    }\r\n    else if(tension()<weightSLidingBoxX() && angle()!= Math.PI/2 ){\r\n        return slidingBox.moveTo([-8*Math.sin(angle()),-8*Math.cos(angle())],1000),\r\n               hangingBox.moveTo([0.5,-1],1000),\r\n               pTension2.setAttribute({visible: false}),\r\n              p0arrow.setAttribute({visible: false}),\r\n              arrowTension2.setAttribute({visible: false}),\r\n              arrowGravity2.setAttribute({visible: false}),\r\n              pWeight2.setAttribute({visible:false}),\r\n\r\n              p0arrowS.setAttribute({visible:false}),\r\n              pWeightX.setAttribute({visible:false}),\r\n              arrowGravityX.setAttribute({visible:false}),\r\n              pWeightY.setAttribute({visible:false}),\r\n              arrowGravityY.setAttribute({visible:false}),\r\n              pWeight.setAttribute({visible:false}),\r\n              arrowGravity.setAttribute({visible:false}),\r\n\r\n              pTension1.setAttribute({visible:false}),\r\n              arrowTension.setAttribute({visible:false}),\r\n\r\n              normal.setAttribute({visible:false}),\r\n              arrowNormal.setAttribute({visible:false})\r\n\r\n    }\r\n\r\n});\r\n\r\n//RESET BUTTON\r\nvar reset = brd3.create('image', ['/assets/fbd/reset.svg',[-10,2.5],[1.2,1.2]], {visible: function(){if(i>=4){return true} else{return false}}, fixed: true});\r\n\r\n\r\nreset.on('down',function(){\r\n    mass.moveTo([4.3334,0],10),\r\n    Mass.moveTo([4.3334,0],10),\r\n    hangingBox.moveTo([0.5,-4],10),\r\n    slidingBox.moveTo([-6,0],10),\r\n    table.moveTo([-10,-4],10),\r\n    hand.moveTo([-4,0.5],10),\r\n\r\n    pTension2.setAttribute({visible: true}),\r\n    p0arrow.setAttribute({visible: true}),\r\n    arrowTension2.setAttribute({visible: true}),\r\n    arrowGravity2.setAttribute({visible: true}),\r\n    pWeight2.setAttribute({visible:true}),\r\n\r\n    p0arrowS.setAttribute({visible:true}),\r\n    pWeightY.setAttribute({visible:true}),\r\n    arrowGravityY.setAttribute({visible:true}),\r\n    pWeight.setAttribute({visible:true}),\r\n    arrowGravity.setAttribute({visible:true}),\r\n\r\n    pTension1.setAttribute({visible:true}),\r\n    arrowTension.setAttribute({visible:true}),\r\n\r\n    normal.setAttribute({visible:true}),\r\narrowNormal.setAttribute({visible:true})});\r\n\r\n      },\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3>First Law</h3>\r\n    <p>\n      Newton's first law states that:\r\n      <br><i>\"An object does not change its state of motion unless\r\n        acted upon by an external force.\"\r\n      </i>\r\n      <br>This means that an object which is at rest will continue to be at rest\r\n      and a moving object will keep moving if no external force is applied on it.\r\n      Mathematically, we can say that:\r\n      $$\\textbf{F}_{net}=0 \\iff \\frac{d\\textbf{v}}{dt}=0$$\r\n      The concept of inertia is very closely related to the first law. In fact\r\n      sometimes the first law is called the <i>Principle of Inertia</i>\n    </p>\r\n    <p>\n      The Mathematical statements might not seem very intuitive. So let us look at some real\r\n      life examples of the First Law and Inertia.\n    </p>\r\n    <ol>\r\n      <li>\n        When you get off a moving bus, you should run along the\r\n        bus for sometime otherwise you will fall. This is because\r\n        when your feet touch the ground, they stop moving but the\r\n        upper body keeps moving due to the First Law. Hence one must\r\n        run alongside the bus for a while before stopping slowly\r\n      </li>\r\n      <li>\n        You must've also observed that people lean forward when a bus\r\n        stops. This is also due to inertia of the upper body.\r\n      </li>\r\n      <li>\n        If you were to visit the International Space Station, you would notice that stopping in space is\r\n        much more difficult. This is because in outer space, there is no gravity to act against our motion.\r\n      </li>\n    </ol>\r\n    <h3>Second Law</h3>\r\n    <p>\n      Newton's Second Law quantitatively defines Force but before we get there, lets first look\r\n      at the qualitative definition of Force which we get from The First Law:\r\n      <br><i>\"Force is that physical cause which changes the state of rest or motion of a body\" </i>\r\n      <br> This definition comes from the First Law. Now we will see the Second Law:\r\n      <br><i>\"The rate of change of momentum of a body is directly proportional to the applied force and\r\n        occurs in the same direction as the direction of the force applied.\" </i>\r\n      Mathematically,\r\n      $$\\textbf{F}=\\frac{d\\textbf{p}}{dt}$$\r\n      Using \\(\\textbf{p}=m\\textbf{v}\\) in the above equation,\r\n      $$\\textbf{F}=m\\frac{d\\textbf{v}}{dt}+\\textbf{v}\\frac{dm}{dt}$$\r\n      In most cases, mass of our system remains constant, so the above\r\n      equation reduces to the famous \\(\\textbf{F}=m\\frac{d\\textbf{v}}{dt}=m\\textbf{a}\\)\n    </p>\r\n    <p>\n      There are however some cases where the mass of a system does not remain constant (like in a rocket\r\n      which continuously uses up its fuel) and in such cases we cannot use \\(\\textbf{F}=m\\textbf{a}\\)\n    </p>\r\n    <h3>Third Law</h3>\r\n    <p>\n      Newton's third law is pretty simple. It states that:\r\n      <br><i>\"Every action has an equal and opposite reaction\"</i>\r\n      <br>Now lets see some examples to understand this:\n    </p>\r\n    <ol>\r\n      <li>\n        A rocket moves up because the gases which come out of it exert a force equal to the force\r\n        applied by the rocket on the gas.\r\n      </li>\r\n      <li>When a gun is fired the shooter feels a recoil. This is due to the Third Law.</li>\r\n    </ol>\r\n    <h3>MagicGraph | Find Tension in the String</h3>\r\n    <v-responsive>\r\n      <v-layout align-center justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n        <div justify-center>\r\n          <p>\n            Floor and pully are assumed to be frictionless.\r\n          </p>\r\n          <p>\n            Bucket has a mass \\(m_1\\) and the kettlebell has a mass \\(m_2\\).\r\n          </p>\r\n          <p>\r\n            Determine the tension in the string.\n          </p>\r\n          <p id=\"step1\">\n&nbsp;\n          </p>\r\n          <p id=\"step2\">\n&nbsp;\n          </p>\r\n          <p id=\"step3\">\n&nbsp;\n          </p>\r\n          <p id=\"step3-1\">\n&nbsp;\n          </p>\r\n          <p id=\"step3-2\">\n&nbsp;\n          </p>\r\n          <p id=\"step3-3\">\n&nbsp;\n          </p>\r\n        </div>\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.$store.commit('navigation/resetState');\r\n    let title = 'Newton\\'s Laws of Motion';\r\n    this.$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&\"; 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=009ddc36&\"\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=009ddc36&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":""}