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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',{ref:\"intro\",staticClass:\"mb-2\"},[_vm._v(\"\\n    Banking of Curved Roads\\n  \")]),_vm._m(0),_c('h3',{ref:\"formula\",staticClass:\"mb-2\"},[_vm._v(\"\\n    Critical Speed on a Banked Road\\n  \")]),_vm._m(1),_c('h3',{ref:\"pg\",staticClass:\"mb-2\"},[_vm._v(\"\\n    MagicGraph | Critical Speed on a Banked Roadway\\n  \")]),_c('h5',{staticClass:\"mb-2\"},[_vm._v(\"\\n    Getting Started\\n  \")]),_vm._m(2),_c('h5',{staticClass:\"mb-2\"},[_vm._v(\"\\n    Icons on the MagicGraph\\n  \")]),_vm._m(3),_c('br'),_c('v-responsive',[_c('v-layout',{attrs:{\"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    Imagine a car going around a circular road with radius \\\\(r\\\\).\\n    For the car to move along a circular road without skidding,  there must be a net force acting towards the center of the circle to provide the necessary centripetal force.\\n    \"),_c('br'),_c('br'),_vm._v(\"\\n    By banking the curved road, the necessary centripetal force can be supplied by the horizontal component of the normal force.\\n  \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    For every banked curve, there is one speed at which theentire centripetal force can be supplied by the horizontal component of the normal force, and no friction is required. \"),_c('br'),_vm._v(\"\\n    This speed is known as the critical speed.\\n    \"),_c('br'),_c('br'),_vm._v(\"\\n    For a banked road of radius \\\\(r\\\\) and banking angle \\\\(\\\\theta\\\\), this critical speed is given as —\\n    $$v = \\\\sqrt{r g \\\\ \\\\tan\\\\theta}$$\\n  \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    This MagicGraph offers a visual-interactive demonstration that offers a step-by-step explanation of critical speed of a car driving on a curved road with a banking angle.\\n    \"),_c('br')])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    The naviation icons on the MagicGraph help you grasp the concept in a step-by-step manner.\"),_c('br'),_vm._v(\"\\n    Tap on \"),_c('i',{staticClass:\"next ma-1\"}),_vm._v(\" button  to go to the next step. Tap on \"),_c('i',{staticClass:\"previous ma-1\"}),_vm._v(\" button to go to the previous step.\\n  \")])\n}]\n\nexport { render, staticRenderFns }","// Import the edliy_utils\r\nimport {\r\n    createSpace,\r\n    placeLogo,\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    placeRedo,\r\n    placeUndo,\r\n    writeHTMLText,\r\n    drawPoint,\r\n    drawLine,\r\n    drawArrow,\r\n    drawAngle,\r\n    drawDash\r\n} from '../Utils';\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.image.highlight=false;\r\nJXG.Options.text.fixed=true;\r\nJXG.Options.curve.highlight=false;\r\nJXG.Options.text.cssDefaultStyle='fontFamily:Oswald;'\r\n//\r\nvar graph=createSpace(-7, 5, -2, 10);\r\ngraph.options.layer['image']=10;\r\ngraph.options.layer['arrow']=9;\r\n//Title and tetxs\r\nplaceTitle(graph, 'Driving on Banked Curves', '(Finding critical speed)');\r\nmakeResponsive(graph);\r\nplaceLogo(graph);\r\n//Creating axes\r\n//createAxes(graph);\r\n//Inserting background image\r\ngraph.create('image',['/assets/floor.svg', [-7, -2], [20, 2.3]], {fixed: true});\r\n//\r\nvar m=0;\r\nvar next = placeRedo(graph);\r\nnext.setAttribute({visible:()=>m<4});\r\n//\r\nvar prev =placeUndo(graph, 'left');\r\nprev.setAttribute({visible:()=>m>0});\r\n//\r\nnext.on('down', function(){\r\n  if(m<4){m+=1}else{m=4}\r\n  if(m==0){\r\n    im.setAttribute({fillOpacity:0.5});\r\n  }\r\n  if(m==1){\r\n    im.setAttribute({fillOpacity:0.5});\r\n  }\r\n  if(m==2){\r\n    im.setAttribute({fillOpacity:0.5});\r\n    origL.moveTo([0.5, 3.5], 200);\r\n  }\r\n  if(m==3){\r\n    im.setAttribute({fillOpacity:0.5});\r\n    origT.moveTo([2, 5.], 200);\r\n  }\r\n});\r\n//\r\nprev.on('down', function(){\r\n  if(m>0){m-=1}else{m=0}\r\n  if(m==0){\r\n    im.setAttribute({fillOpacity:0.5});\r\n  }\r\n  if(m==1){\r\n    im.setAttribute({fillOpacity:0.5});\r\n    origL.moveTo([0.5, 5.], 200);\r\n  }\r\n  if(m==2){\r\n    im.setAttribute({fillOpacity:0.5});\r\n    origT.moveTo([0.5, 5.], 200);\r\n  }});\r\n// Texts\r\n//Problem Statement\r\nwriteHTMLText(graph, -6, 7.5, 'Imagine driving a car on a banked road with radius r and angle &theta;.').setAttribute({visible:()=>m==0, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 6.5, 'Goal is to find the critical speed of the car.').setAttribute({visible:()=>m==0, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 5.5, 'Assume no friction between the car and the road.').setAttribute({visible:()=>m==0, anchorX:'left'});\r\n//\r\nwriteHTMLText(graph, -6, 7.5, 'Start with free body diagram of the car.').setAttribute({visible:()=>m==1, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 6.5, 'A free body diagram shows all the external forces acting on the body.').setAttribute({visible:()=>m==1, anchorX:'left'});\r\n//\r\nwriteHTMLText(graph, -6, 7.5, 'Balance of forces in x-direction gives:').setAttribute({visible:()=>m>1, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 6.5, 'N sin&theta; =  mv^2/r').setAttribute({visible:()=>m>1, anchorX:'left'});\r\n//\r\nwriteHTMLText(graph, -6, 5.5, 'Balance of forces in y-direction gives:').setAttribute({visible:()=>m>2, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 4.5, 'N cos&theta; = mg').setAttribute({visible:()=>m>2, anchorX:'left'});\r\n//\r\nwriteHTMLText(graph, -6, 3.5, 'Solving for v gives:').setAttribute({visible:()=>m>3, anchorX:'left'});\r\nwriteHTMLText(graph, -6, 2.5, 'v = (rg tan &theta;)^1^/^2').setAttribute({visible:()=>m>3, anchorX:'left'});\r\n//\r\nvar mg = writeHTMLText(graph, 2., 1.3, 'mg').setAttribute({visible:()=>m>0, anchorX:'middle'});\r\n//////////////////////\r\nvar cfg = writeHTMLText(graph, 4., 3.5, 'mv^2/r').setAttribute({visible:()=>m>0, anchorX:'left'});\r\n////////////////////////////\r\nvar norm = writeHTMLText(graph, -0., 5., 'N').setAttribute({visible:()=>m>0, anchorX:'left'});\r\n/////////////////////////////\r\nvar normL = writeHTMLText(graph, 0.3, 3.5, 'N sin&theta;').setAttribute({visible:()=>m>1, anchorX:'right'});\r\n////////////\r\nvar norm = writeHTMLText(graph, -0., 5., 'N').setAttribute({visible:()=>m>0, anchorX:'left'});\r\n/////////////\r\nvar normT = writeHTMLText(graph, 2., 5.5, 'N cos&theta;').setAttribute({visible:()=>m>2, anchorX:'middle'});\r\n///\r\nwriteHTMLText(graph, 0.5, 3.75, 'r').setAttribute({visible:()=>m==0, anchorX:'middle'});\r\n//////////////////\r\nvar Pt1 = drawPoint(graph, 0, 0.3);\r\nPt1.setAttribute({visible:false});\r\n/////\r\nvar Pt2 = drawPoint(graph, 2, 2.3);\r\nPt2.setAttribute({visible:false});\r\n/////////\r\nvar im = graph.create('image',['/assets/car.svg', [2, 2], [2, 2]], {rotate:45, opacity:0.65, fixed: true});\r\n//////////////////////\r\nvar curb =drawLine(graph, Pt1, Pt2);\r\ncurb.setAttribute({strokeWidth:4});\r\n//\r\n//Origin\r\nvar orig = drawPoint(graph, 2., 3.5);\r\norig.setAttribute({visible:false});\r\nvar down = drawPoint(graph, 2., 1.5);\r\ndown.setAttribute({visible:false});\r\nvar left = drawPoint(graph, 4, 3.5);\r\nleft.setAttribute({visible:false});\r\nvar norm = drawPoint(graph, 0.5, 5.0);\r\nnorm.setAttribute({visible:false});\r\n//\r\nvar origL = drawPoint(graph, 0.5, 5);\r\norigL.setAttribute({visible:false});\r\nvar origT = drawPoint(graph, 0.5, 5);\r\norigT.setAttribute({visible:false});\r\n//origL.setAttribute({visible:false});\r\n////\r\ndrawArrow(graph, orig, down).setAttribute({visible:()=>m>0, strokeColor:'red', dash:0});\r\ndrawArrow(graph, orig, left).setAttribute({visible:()=>m>0, strokeColor:'blue', dash:0});\r\ndrawArrow(graph, orig, norm).setAttribute({visible:()=>m>0, strokeColor:'green', dash:0});\r\ndrawArrow(graph, orig, origL).setAttribute({visible:()=>m>1, strokeColor:'green', dash:2});\r\ndrawArrow(graph, orig, origT).setAttribute({visible:()=>m>2, strokeColor:'green', dash:2});\r\n/////////////////\r\nvar og = drawPoint(graph, 0, 0.3);\r\nog.setAttribute({visible:false});\r\nvar start = drawPoint(graph, 2, 0.3);\r\nstart.setAttribute({visible:false});\r\nvar end = drawPoint(graph, 2, 2.3);\r\nend.setAttribute({visible:false});\r\n//////////////\r\ndrawAngle(graph, end ,og, start).setAttribute({name:'&theta;',strokeColor:'black', radius:1, center:{visible:false}, radiusPoint:{visible:false}, anglePoint:{visible:false}});\r\n//\r\nvar Pt1 = drawPoint(graph, -1, -3);\r\nPt1.setAttribute({visible:false});\r\nvar Pt2 = drawPoint(graph, -1, 8);\r\nPt2.setAttribute({visible:false});\r\ndrawDash(graph, Pt1, Pt2).setAttribute({visible:()=>m==0, strokeColor:'grey',dash:1});\r\n//\r\nvar Pt3 = drawPoint(graph, -1, 3.5);\r\nPt3.setAttribute({visible:false});\r\nvar Pt4 = drawPoint(graph, 2, 3.5);\r\nPt4.setAttribute({visible:false});\r\ndrawDash(graph, Pt3, Pt4).setAttribute({visible:()=>m==0, strokeColor:'grey'});\r\n},\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3 ref=\"intro\" class=\"mb-2\">\r\n      Banking of Curved Roads\r\n    </h3>\r\n    <p>\r\n      Imagine a car going around a circular road with radius \\(r\\).\r\n      For the car to move along a circular road without skidding,  there must be a net force acting towards the center of the circle to provide the necessary centripetal force.\r\n      <br><br>\r\n      By banking the curved road, the necessary centripetal force can be supplied by the horizontal component of the normal force.\r\n    </p>\r\n    <h3 ref=\"formula\" class=\"mb-2\">\r\n      Critical Speed on a Banked Road\r\n    </h3>\r\n    <p>\r\n      For every banked curve, there is one speed at which theentire centripetal force can be supplied by the horizontal component of the normal force, and no friction is required. <br>\r\n      This speed is known as the critical speed.\r\n      <br><br>\r\n      For a banked road of radius \\(r\\) and banking angle \\(\\theta\\), this critical speed is given as &mdash;\r\n      $$v = \\sqrt{r g \\ \\tan\\theta}$$\r\n    </p>\r\n    <h3 ref=\"pg\" class=\"mb-2\">\r\n      MagicGraph | Critical Speed on a Banked Roadway\r\n    </h3>\r\n    <h5 class=\"mb-2\">\n      Getting Started\n    </h5>\r\n    <p>\r\n      This MagicGraph offers a visual-interactive demonstration that offers a step-by-step explanation of critical speed of a car driving on a curved road with a banking angle.\r\n      <br>\r\n    </p>\r\n    <h5 class=\"mb-2\">\n      Icons on the MagicGraph\n    </h5>\r\n    <p>\r\n      The naviation icons on the MagicGraph help you grasp the concept in a step-by-step manner.<br>\r\n      Tap on <i class=\"next ma-1\" /> button  to go to the next step. Tap on <i class=\"previous ma-1\" /> button to go to the previous step.\r\n    </p>\r\n    <br>\r\n    <v-responsive>\r\n      <v-layout 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: 'CurvedRoad',\r\n  created () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Banking on a Curved Road';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    /*let newTopics = [\r\n      {title: 'Parallel Lines', img:'/assets/number-1.svg', action: () => this.goto('intro')},\r\n      {title: 'Transversal', img:'/assets/number-2.svg', action: () => this.goto('trans')},\r\n      {title: 'Pair of Angles', img:'/assets/number-3.svg', action: () => this.goto('angles')},\r\n      {title: 'MagicGraph',img:'/assets/touch.svg', action: () => this.goto('pg')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);*/\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newMath =true;\r\n    this.$store.commit('navigation/replacePhys', newMath);\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: 'Banking on a Curved Road',\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 about banking on a curved road'}\r\n                ]\r\n        }\r\n   },\r\n}\r\n</script>\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=b8d60ee2&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\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":""}