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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',{ref:\"ia\"},[_vm._v(\"\\n Free Body Diagram\\n \")]),_vm._m(0),_c('h3',{ref:\"ja\"},[_vm._v(\"\\n Purpose of a Free Body Diagram\\n \")]),_c('p',[_vm._v(\"\\n In mechanics, a free-body diagram is commonly used in an exercise known as balance of forces and moments.\\n Balance of forces or moments is used for calculating unknown internal or reactionary forces.\\n This exercise requires accounting for all the forces and moments acting on an object.\\n Drawing a free-body diagram is the first step in this exercise and is used to visualize all the external forces and moments acting on the object.\\n \")]),_c('h3',{ref:\"ka\"},[_vm._v(\"\\n Example: Free Body Diagram of an Inclined Wooden Plank\\n \")]),_c('p',[_vm._v(\"\\n In this example, we will consider a massless wooden plank that is resting on a wall. The plank is in contact with two external objects: the floor and the wall.\\n To construct the free body diagram of the plank, we will remove these surrounding objects and replace them by the forces exerted by them on the plank.\\n \")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/FBD-1.png\",\"max-height\":\"350px\",\"max-width\":\"350px\",\"contain\":\"\"}})],1),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',{staticStyle:{\"text-align\":\"center\"}},[_vm._v(\"\\n Figure 1(a): Goal is to draw the FBD of a plank inclined against a brick wall\\n \")])]),_c('br'),_c('p',[_vm._v(\"\\n First, we remove the wall and replace it by the force exerted by it on the plank. Note that the contact between the plank and the wall is assumed frictionless.\\n So, the wall does not exert any frictional force on the plank.\\n The resultant configuration is shown in Figure 1(b).\\n \")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/FBD-2.png\",\"max-height\":\"350px\",\"max-width\":\"350px\",\"contain\":\"\"}})],1),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',{staticStyle:{\"text-align\":\"center\"}},[_vm._v(\"\\n Figure 1(b): First, we replace the wall by the force it exerts on the plank.\\n \")])]),_c('br'),_c('p',[_vm._v(\"\\n Next, we remove the floor and replace it by the force exerted by it on the plank. This completes the FBD for the plank.\\n The resultant configuration is shown in Figure 1(c).\\n \")]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('v-img',{attrs:{\"src\":\"/assets/FBD-3.png\",\"max-height\":\"350px\",\"max-width\":\"350px\",\"contain\":\"\"}})],1),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',{staticStyle:{\"text-align\":\"center\"}},[_vm._v(\"\\n Figure 1(c): Next, we replace the floor by the force it exerts on the plank.\\n \")])]),_c('h3',{ref:\"pg\"},[_vm._v(\"\\n MagicGraph | Monkey on a Plank\\n \")]),_vm._m(1),_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 A free-body diagram is a simplified graphical illustration that shows all the external forces acting on a body or a system of bodies.\\n A free-body diagram is also known as 'FBD' — the commonly used shorthand notation for it. \"),_c('br'),_vm._v(\"\\n To obtain the free-body diagram of a body, we isolate that body from its surrounding objects and replace those objects by the forces they exert on the body.\"),_c('br'),_vm._v(\"\\n Note that while drawing the free-body diagram of a system of bodies,\\n we consider only the external forces on the system — that is, the forces or moments exerted by bodies outside of the system.\\n \"),_c('br'),_vm._v(\"\\n Below are the two steps that we need to follow in order to draw the free body diagram of an object.\\n \"),_c('ul',{staticClass:\"a\"},[_c('li',[_c('h5',[_vm._v(\"Step 1 \")])]),_vm._v(\"\\n First identify all the surrounding objects that are in contact with the body or the system of bodies.\\n\\n \"),_c('li',[_c('h5',[_vm._v(\"Step 2 \")])]),_vm._v(\"\\n Then replace the surrounding objects one by one by the forces exerted by them on the body.\\n Each force on the body is indicated by a vector arrow showing the direction and point of application of the force.\\n \")])])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n Monkey \"),_c('i',[_vm._v(\"Mo\")]),_vm._v(\" is being chased by a angry bull \"),_c('i',[_vm._v(\"Bo\")]),_vm._v(\". \"),_c('br'),_vm._v(\" To save himself from the bull, Monkey \"),_c('i',[_vm._v(\"Mo\")]),_vm._v(\" climbs up a wooden plank that is inclined against a brick wall. \"),_c('br'),_vm._v(\"\\n Bull \"),_c('i',[_vm._v(\"Bo\")]),_vm._v(\" can't climb up the plank so, in an effort to bring monkey \"),_c('i',[_vm._v(\"Mo\")]),_vm._v(\" down, he charges at the plank. \"),_c('br'),_vm._v(\"\\n Your goal is to draw the free-body diagram of the plank accounting for all the external forces acting on it.\\n You may assume that the plank is massless, and monkey \"),_c('i',[_vm._v(\"Mo\")]),_vm._v(\" has a mass \\\\(m\\\\).\\n The gravity acts downward (as shown in the MagicGraph).\\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-integral';\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: [-10, 11, 10, -9],keepaspectratio: true, axis:false, ticks:false, grid:true, pan:{enabled:false}, zoom:{enabled:false}, showCopyright:false, showNavigation:false});\r\n brd1.options.layer['line'] =2;\r\n brd1.options.layer['polygon'] =2;\r\n brd1.options.layer['image'] =8;\r\n makeResponsive(brd1);\r\n // Creat titleStyle\r\n placeTitle(brd1, 'Wavelength of a Travelling Wave', 'y= A cos(k x - w t)');\r\n //SLiders\r\n var amplitud = 2;\r\n var frec =placeSlider(brd1, -2, 7.5, 1, 2, 4, 4, '  λ');\r\n frec.setAttribute({snapWidth:1.0});\r\n //brd1.create('slider',[[5,7],[8,7],[-5,2,5]], {snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'A', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n\r\n //var frec = placeSlider(brd1, 5, 7, 0, 0.25, 1, 3, ' f');\r\n //frec.setAttribute({visible:false, highline:{visible:false}, baseline:{visible:false}});\r\n //var frec=0.25;\r\n //brd1.create('slider',[[5,7],[8,7],[0,0.2,1]], {visible: false, snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'f', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n //var phi = brd1.create('slider',[[5,6],[8,6],[-10,0,10]], {visible: false, snapToGrid: false ,face:'square', size:4, strokeWidth: 2, name:'φ', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n\r\n var time1 =placeSlider(brd1, -4, -8, 0, 0, 10, 8, ' t');\r\n time1.setAttribute({unitLabel:'sec'});\r\n //brd1.create('slider',[[-7,-5],[7,-5],[0,0,10]], {visible: false, snapToGrid: false ,face:'square', size:6, strokeWidth:0,\r\n //name:'t', strokeColor:'black', fillColor: 'grey', label:{fontSize:function(){return 20*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n //Graph\r\n var graph = brd1.create('functiongraph',\r\n [function(x){ return amplitud.valueOf()*Math.cos(2*Math.PI/frec.Value()*(time1.Value() - x));}, -10, 10],\r\n {dash: 0, strokeColor: 'blue', strokeWidth: 1}\r\n );\r\n\r\n\r\n //Points\r\n function yPoints(x){return amplitud.valueOf()*Math.cos(2*Math.PI/frec.Value()*(time1.Value() - x ))}\r\n\r\n var point1 = placePoint(brd1, -9, function(){return yPoints(-9)}, 3, '#ff0000', 'black');\r\n var point2 = placePoint(brd1, -8, function(){return yPoints(-8)}, 3, '#3cb371', 'black');\r\n var point3 = placePoint(brd1, -7, function(){return yPoints(-7)}, 3, '#ffa500', 'black');\r\n var point4 =placePoint(brd1, -6, function(){return yPoints(-6)}, 3, '#ff3082', 'black');\r\n var point5 =placePoint(brd1, -5, function(){return yPoints(-5)}, 3, 'yellow', 'black');\r\n var point6 =placePoint(brd1, -4, function(){return yPoints(-4)}, 3, '#006782', 'black');\r\n var point7 =placePoint(brd1, -3, function(){return yPoints(-3)}, 3, '#966737', 'black');\r\n var point8 =placePoint(brd1, -2, function(){return yPoints(-2)}, 3, 'white', 'black');\r\n var point9 =placePoint(brd1, -1, function(){return yPoints(-1)}, 3, '#9667ff', 'black');\r\n var point10 =placePoint(brd1, -0, function(){return yPoints(-0)}, 3, 'blue', 'black');\r\n var point11 =placePoint(brd1, 1, function(){return yPoints(1)}, 3, '#9667ff', 'black');\r\n var point12 =placePoint(brd1, 2, function(){return yPoints(2)}, 3, 'white', 'black');\r\n var point13 =placePoint(brd1, 3, function(){return yPoints(3)}, 3, '#966737', 'black');\r\n var point14 =placePoint(brd1, 4, function(){return yPoints(4)}, 3, '#006782', 'black');\r\n var point15 =placePoint(brd1, 5, function(){return yPoints(5)}, 3, 'yellow', 'black');\r\n var point16 =placePoint(brd1, 6, function(){return yPoints(6)}, 3, '#ff3082', 'black');\r\n var point17 =placePoint(brd1, 7, function(){return yPoints(7)}, 3, '#ffa500', 'black');\r\n var point18 =placePoint(brd1, 8, function(){return yPoints(8)}, 3, '#3cb371', 'black');\r\n var point19 =placePoint(brd1, 9, function(){return yPoints(9)}, 3, '#ff0000', 'black');\r\n //brd1.create('point', [-9 ,function(){return yPoints(-9)}],{face:'o' , name:'pp', size:3, strokeColor: 'black', fillColor:'yellow', withLabel:false, fixed:false, visible:true, label:{fontSize:function(){return 18*brd4.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});;\r\n //var point2 = brd1.create('point', [-8 ,function(){return yPoints(-8)}],{face:'o' , name:'pp', size:3, strokeColor: 'black', fillColor:'yellow', withLabel:false, fixed:false, visible:true, label:{fontSize:function(){return 18*brd4.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});;\r\n //var point3 = brd1.create('point', [-7 ,function(){return yPoints(-7)}],{face:'o' , name:'pp', size:3, strokeColor: 'black', fillColor:'yellow', withLabel:false, fixed:false, visible:true, label:{fontSize:function(){return 18*brd4.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});;\r\n placeDash(brd1, [()=>point1.X(), 0],[()=>point1.X(), ()=>point1.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point2.X(), 0],[()=>point2.X(), ()=>point2.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point3.X(), 0],[()=>point3.X(), ()=>point3.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point4.X(), 0],[()=>point4.X(), ()=>point4.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point5.X(), 0],[()=>point5.X(), ()=>point5.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point6.X(), 0],[()=>point6.X(), ()=>point6.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point7.X(), 0],[()=>point7.X(), ()=>point7.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point8.X(), 0],[()=>point8.X(), ()=>point8.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point9.X(), 0],[()=>point9.X(), ()=>point9.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point10.X(), 0],[()=>point10.X(), ()=>point10.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point11.X(), 0],[()=>point11.X(), ()=>point11.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point12.X(), 0],[()=>point12.X(), ()=>point12.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point13.X(), 0],[()=>point13.X(), ()=>point13.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point14.X(), 0],[()=>point14.X(), ()=>point14.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point15.X(), 0],[()=>point15.X(), ()=>point15.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point16.X(), 0],[()=>point16.X(), ()=>point16.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point17.X(), 0],[()=>point17.X(), ()=>point17.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point18.X(), 0],[()=>point18.X(), ()=>point18.Y()], 1, 'black');\r\n placeDash(brd1, [()=>point19.X(), 0],[()=>point19.X(), ()=>point19.Y()], 1, 'black');\r\n //var segment1 = brd1.create('segment', [[function(){return point1.X()}, 0], point1], {dash: 1, dash: 1, fixed: true, strokeColor: 'black', strokeWidth:1});\r\n\r\n // var txt1 = brd1.create('text', [ function(){return point11.X()+ 0.8}, function(){return point11.Y()/2}, function(){return 'A: ' + point11.Y().toFixed(2)}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(10*brd1.canvasWidth/500.)}},);\r\n\r\n //Lambda\r\n\r\n var lambdaSeg = brd1.create('segment', [[0, function(){return Math.abs(amplitud.valueOf()) +1}],[function(){return frec.Value()}, function(){return Math.abs(amplitud.valueOf()) +1}]], {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\n var lambdaTxt = brd1.create('text', [function(){return frec.Value()/2 }, function(){return Math.abs(amplitud.valueOf()) +1.5},\r\n function(){ return ' λ = ' + (frec.Value()).toFixed(0) }],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\n\r\n //Animation\r\n function start(){\r\n time1.startAnimation(10, 500, 30);\r\n playImg.setAttribute({visible: false});\r\n pauseImg.setAttribute({visible: true});\r\n\r\n }\r\n\r\n function pause(){\r\n time1.stopAnimation(10, 500, 30);\r\n playImg.setAttribute({visible: true});\r\n pauseImg.setAttribute({visible: false});\r\n\r\n }\r\n //Play Button\r\n var playImg = brd1.create('image', ['/assets/play.svg', [-0.8, -6], [1.5, 1.5]], {visible: true, fixed: true});\r\n playImg.on('up', start);\r\n playImg.setLabel('Tap to 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 //Pause Button\r\n var pauseImg = brd1.create('image', ['/assets/pause.svg', [-0.8, -6], [1.5, 1.5]], {visible: false, fixed: true});\r\n pauseImg.on('up', pause);\r\n pauseImg.setLabel('Tap to 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 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=780447a6&\"\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=780447a6&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","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=780447a6&prod&lang=scss&\""],"sourceRoot":""}