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Topics

Forces on an inclined plane, Hooke's law, static friction, kinetic friction, and oscillatory motion.

Description

This simulation shows a block attached to a spring on an inclined plane. Students can vary the initial velocity, angle, spring constant, length of the incline, and both the static and kinetic coefficients of friction to investigate when the block remains at rest, when it begins to slip, and when it oscillates.

Sample Learning Goals

  1. Explain why the block can remain at rest even when gravity and the spring both act along the slope.
  2. Predict when slipping begins by comparing the parallel driving force with the maximum static friction.
  3. Relate the motion graphs to the changing force on the block.
  4. Describe how changing angle, friction, and spring constant affects the motion.

Suggested Activities

  1. Set the block at rest and increase the angle slowly. Predict the moment when the block will start to slip.
  2. Keep the angle fixed and increase the static friction. Explain why the block can remain stationary.
  3. Set friction close to zero and displace the block. Observe when the motion looks closest to oscillation.
  4. Turn on the graphs and connect the world view to the force, displacement, and velocity plots.

Version

  1. Original blog post and credits
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Teacher Notes

A productive question for this model is: What must be true for the block to stay at rest?

Encourage students to compare two quantities:

  1. The parallel driving force: the combined effect of the spring force and the component of weight along the slope.
  2. The maximum static friction: the largest frictional force available before slipping begins.

If the parallel driving force is smaller than or equal to the maximum static friction, the block can stay at rest. If it is larger, the block must slip.

Suggested sequence: prediction, run, observe, and explain. Ask students to justify each case with both the animation and the force comparison message.

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Try this first: predict whether the block will stay at rest, slip, or oscillate before you press play.

Then compare:

  1. the live motion status in the top-right corner, and
  2. the force comparison message in the bottom-left corner.

Original blog post and credits

Video Tutorial

The lesson video below can be embedded when this model is recompiled in WebEJS.

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"muLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"Yellow\"" }, { "name": "Text", "value": "\"\u03bcs = \"" }, { "name": "Font", "value": "font" } ] }, { "Name": "muSlider", "Type": "Slider", "Properties": [ { "name": "Minimum", "value": "0.0" }, { "name": "Maximum", "value": "2" }, { "name": "Format", "value": "\"0.00\"" }, { "name": "Background", "value": "\"Yellow\"" }, { "name": "Value", "value": "muStatic" }, { "name": "OnChange", "value": "muStatic=Math.max(muStatic,muKinetic); // static must be larger than kinetic\nmuStatic=Math.max(0,muStatic);\nmuStatic=Math.min(muStatic,2);\nmuSdrag =muStatic/20;\ncheckDirection();" }, { "name": "Font", "value": "font" } ] }, { "Name": "muField", "Type": "ParsedField", "Properties": [ { "name": "Format", "value": "\"0.00\"" }, { "name": "Tooltip", "value": "\"Static coefficient of friction.\"" }, { "name": "Value", "value": "muStatic" }, { "name": "OnChange", "value": "muStatic=Math.max(muStatic,muKinetic); // static must be larger than kinetic\nmuStatic=Math.max(0,muStatic);\nmuStatic=Math.min(muStatic,2);\ncheckDirection () ;" }, { "name": "Width", "value": "\"4vw\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "muKineticLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"Yellow\"" }, { "name": "Text", "value": "\"\u03bck = \"" }, { "name": "Font", "value": "font" } ] }, { "Name": "muKineticSlider", "Type": "Slider", "Properties": [ { "name": "Minimum", "value": "0.0" }, { "name": "Maximum", "value": "2" }, { "name": "Background", "value": "\"Yellow\"" }, { "name": "Value", "value": "muKinetic" }, { "name": "OnChange", "value": "muKinetic=Math.min(muStatic,muKinetic); // kinetic cann be larger than static\nmuKinetic=Math.max(0,muKinetic);\nmuKinetic=Math.min(muKinetic,2);\nmuKdrag = muKinetic/20;\ncheckDirection();" }, { "name": "Font", "value": "font" } ] }, { "Name": "muKineticField", "Type": "ParsedField", "Properties": [ { "name": "Format", "value": "\"0.00\"" }, { "name": "Tooltip", "value": "\"Kinetic coefficient of friction.\"" }, { "name": "Value", "value": "muKinetic" }, { "name": "OnChange", "value": "muKinetic=Math.min(muStatic,muKinetic); // kinetic cann be larger than static\nmuKinetic=Math.max(0,muKinetic);\nmuKinetic=Math.min(muKinetic,2);\ncheckDirection();" }, { "name": "Width", "value": "\"4vw\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "thetaLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"rgba(128,192,255,1)\"" }, { "name": "Text", "value": "\"\u03b8 = \"" }, { "name": "Font", "value": "font" } ] }, { "Name": "thetaSlider", "Type": "Slider", "Properties": [ { "name": "Minimum", "value": "0.0" }, { "name": "Maximum", "value": "90" }, { "name": "Background", "value": "\"rgba(128,192,255,1)\"" }, { "name": "Value", "value": "angleDegrees" }, { "name": "OnChange", "value": "angleDegrees=Math.max(0,angleDegrees);\nangleDegrees=Math.min(angleDegrees,90);\nangle=Math.radians(angleDegrees);\ncheckDirection();" }, { "name": "Font", "value": "font" } ] }, { "Name": "thetaField", "Type": "ParsedField", "Properties": [ { "name": "Format", "value": "\"0.0\"" }, { "name": "Tooltip", "value": "\"Incline plane angle in degrees.\"" }, { "name": "Value", "value": "angleDegrees" }, { "name": "OnChange", "value": "angleDegrees=Math.max(0,angleDegrees);\nangleDegrees=Math.min(angleDegrees,90);\nangle=Math.radians(angleDegrees);\ncheckDirection();" }, { "name": "Width", "value": "\"4vw\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "springConstantLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"RED\"" }, { "name": "Text", "value": "\"k = \"" }, { "name": "Font", "value": "font" } ] }, { "Name": "springConstantSlider", "Type": "Slider", "Properties": [ { "name": "Minimum", "value": "0.0" }, { "name": "Maximum", "value": "10.0" }, { "name": "Background", "value": "\"RED\"" }, { "name": "Value", "value": "k" }, { "name": "OnChange", "value": "k=Math.max(0,k);\nk=Math.min(k,10);\nkdrag = k/20;\ncheckDirection();" }, { "name": "Font", "value": "font" } ] }, { "Name": "springConstantField", "Type": "ParsedField", "Properties": [ { "name": "Format", "value": "\"0.00\"" }, { "name": "Tooltip", "value": "\"Spring constant in N/m.\"" }, { "name": "Value", "value": "k" }, { "name": "OnChange", "value": "k=Math.max(0,k);\nk=Math.min(k,10);\ncheckDirection();" }, { "name": "Width", "value": "\"4vw\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "springConstantUnitLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"RED\"" }, { "name": "Text", "value": "\"N/m\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "lengthLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"BLACK\"" }, { "name": "Tooltip", "value": "\"Length\"" }, { "name": "Foreground", "value": "\"WHITE\"" }, { "name": "Text", "value": "\"L = \"" }, { "name": "Font", "value": "font" } ] }, { "Name": "lengthSlider", "Type": "Slider", "Properties": [ { "name": "Minimum", "value": "0.5" }, { "name": "Maximum", "value": "2" }, { "name": "Background", "value": "\"BLACK\"" }, { "name": "Value", "value": "L" }, { "name": "Foreground", "value": "\"WHITE\"" }, { "name": "OnChange", "value": "L=Math.max(0.1,L);\nL=Math.min(L,10);\nLdrag = L;\nbumperX=L;\n\ncheckDirection();" }, { "name": "Font", "value": "font" } ] }, { "Name": "lengthField", "Type": "ParsedField", "Properties": [ { "name": "Format", "value": "\"0.00\"" }, { "name": "Tooltip", "value": "\"Length of incline plane in meters.\"" }, { "name": "Value", "value": "L" }, { "name": "OnChange", "value": "L=Math.max(0.1,L);\nL=Math.min(L,10);\nbumperX=L;\ncheckDirection();" }, { "name": "Width", "value": "\"4vw\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "lengthUnitLabel", "Type": "Label", "Properties": [ { "name": "Background", "value": "\"Black\"" }, { "name": "Foreground", "value": "\"WHITE\"" }, { "name": "Text", "value": "\"m\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "controlPanel2", "Type": "Panel", "Expanded": "true", "Properties": [ { "name": "Display", "value": "\"inline-flex\"" } ], "Children": [ { "Name": "bounceCheckBox", "Type": "CheckBox", "Properties": [ { "name": "Checked", "value": "bounce" }, { "name": "Tooltip", "value": "\"Bounce at ends of incline.\"" }, { "name": "Text", "value": "\"bounce\"" }, { "name": "Font", "value": "font" } ] }, { "Name": "world", "Type": "CheckBox", "Properties": [ { "name": "Checked", "value": "world" }, { "name": "OnCheckOff", "value": "Width1 = \"0%\";\ndisabled=false;\n\nif (showGraphV) \n Width2 = \"100%\";\nelse if (showGraphX)\n Width3 = \"100%\";\nelse if (showGraphF)\n Width4 = \"100%\";\n \n" }, { "name": "Background", "value": "\"Orange\"" }, { "name": "Tooltip", "value": "\"world view\"" }, { "name": "Text", "value": "\"world\"" }, { "name": "Disabled", "value": "disabledworld" }, { "name": "OnCheckOn", "value": "if (showGraphV)\n Width1 = Width2 = \"50%\";\nelse if (showGraphX)\n Width1 = Width3 = \"50%\";\nelse if (showGraphF)\n Width1 = Width4 = \"50%\";\nelse\n Width1 = \"100%\";" }, { "name": "Font", "value": "font" } ] }, { "Name": "vvst", "Type": "CheckBox", "Properties": [ { "name": "Checked", "value": "showGraphV" }, { "name": "OnCheckOff", "value": "Width2 = \"0%\";\n\nif ((!showGraphX) && (!showGraphF))\n{\n world = true;\n disabledworld=true;\n Width1 = \"100%\";\n} \n" }, { "name": "Background", "value": "\"MAGENTA\"" }, { "name": "Tooltip", "value": "\"Show velocity graph.\"" }, { "name": "Text", "value": "\"v vs t\"" }, { "name": "Disabled", "value": "disabled" }, { "name": "OnCheckOn", "value": "if (world) \n Width1 = Width2 = \"50%\";\nelse\n Width2 = \"100%\";\n \nWidth3 = \"0%\";\nWidth4 = \"0%\"; \n\ndisabledworld = showVectors = showGraphF = showGraphX = false;\n" }, { "name": "Font", "value": "font" } ] }, { "Name": "xvst", "Type": "CheckBox", "Properties": [ { "name": "Checked", "value": "showGraphX" }, { "name": "OnCheckOff", "value": "Width3 = \"0%\";\n\nif ((!showGraphV) && (!showGraphF))\n{\n world = true;\n disabledworld=true;\n Width1 = \"100%\";\n} \n" }, { "name": "Background", "value": "\"Blue\"" }, { "name": "Tooltip", "value": "\"Show position graph.\"" }, { "name": "Foreground", "value": "\"White\"" }, { "name": "Text", "value": "\"x vs t\"" }, { "name": "Disabled", "value": "disabled" }, { "name": "OnCheckOn", "value": "if (world)\n Width1 = Width3 = \"50%\"; \nelse \n Width3 = \"100%\";\n \nWidth2 = \"0%\";\nWidth4 = \"0%\"; \ndisabledworld = showVectors = showGraphF = showGraphV = false;\n\n" }, { "name": "Font", "value": "font" } ] }, { "Name": "forceVsT", "Type": "CheckBox", "Properties": [ { "name": "Checked", "value": "showGraphF" }, { "name": "OnCheckOff", "value": "Width4 = \"0%\";\n\nif ((!showGraphX) && (!showGraphV))\n{\n world = true;\n disabledworld=true;\n Width1 = \"100%\";\n} \n\n" }, { "name": "Background", "value": "\"GREEN\"" }, { "name": "Tooltip", "value": "\"Show total force graph.\"" }, { "name": "OnChange", "value": "showVectors=showGraphF;" }, { "name": "Text", "value": "\"force vs t\"" }, { "name": "Disabled", "value": "disabled" }, { "name": "OnCheckOn", "value": "if (world)\n Width1 = Width4 = \"50%\";\nelse\n Width4 = \"100%\";\n\nWidth2 = \"0%\";\nWidth3 = \"0%\"; \ndisabledworld = showGraphV = showGraphX = false;" }, { "name": "Font", "value": "font" } ] }, { "Name": "playPauseButton", "Type": "TwoStateButton", "Properties": [ { "name": "OffClick", "value": "%_pause%" }, { "name": "TextOn", "value": "\"\u25ba\"" }, { "name": "State", "value": "_isPaused" }, { "name": "Tooltip", "value": "\"Starts and stops the simulation.\"" }, { "name": "TextOff", "value": "\"\u275a\u275a\"" }, { "name": "Disabled", "value": "motionDone" }, { "name": "OnClick", "value": "trMessage=null;\nif (x<=maxX && x>=minX) _play();\nelse if (x>maxX && v<=0) _play();\nelse if (x=0) _play();\nelse displayAlert();" }, { "name": "Font", "value": "fontb" } ] }, { "Name": "stepButton", "Type": "Button", "Properties": [ { "name": "OnRelease", "value": "trMessage=null;\nif (x<=maxX && x>=minX)_step();\nelse if (x>maxX && v<=0)_step();\nelse if (x=0)_step();\nelse displayAlert();" }, { "name": "Tooltip", "value": "\"Step\"" }, { "name": "Text", "value": "\"\u275a\u25ba\"" }, { "name": "Disabled", "value": "motionDone" }, { "name": "Font", "value": "fontb" } ] }, { "Name": "resetButton", "Type": "Button", "Properties": [ { "name": "OnRelease", "value": "%_reset%" }, { "name": "Tooltip", "value": "\"Reset\"" }, { "name": "Text", "value": "\"\u21bb\"" }, { "name": "Font", "value": "fontb" } ] } ] } ] }, { "Name": "displayPanel", "Type": "Panel", "Expanded": "false", "Properties": [ { "name": "Width", "value": "%Width%" } ], "Children": [ { "Name": "drawingPanel", "Type": "DrawingPanel", "Expanded": "true", "Properties": [ { "name": "Enabled", "value": "true" }, { "name": "OnDoubleClick", "value": "toggleFullScreen();" }, { "name": "SquareAspect", "value": "true" }, { "name": "MaximumY", "value": "L*Math.sin(Math.max(angle, Math.PI/5))+0.05*L+0.05*L" }, { "name": "MaximumX", "value": "L*Math.cos(angle)+0.05*L" }, { "name": "TRMessage", "value": "%slippingMsg%" }, { "name": "MinimumX", "value": "-0.05*L" }, { "name": "MinimumY", "value": "-0.04*L" }, { "name": "AutoScaleY", "value": "false" }, { "name": "AutoScaleX", "value": "false" }, { "name": "Height", "value": "\"90vh\"" }, { "name": "BLMessage", "value": "%forceBalanceText%" }, { "name": "Width", "value": "%Width1%" }, { "name": "TLMessage", "value": "%trMessage%" }, { "name": "BRMessage", "value": "%ttext%" } ], "Children": [ { "Name": "ground", "Type": "Shape2D", "Properties": [ { "name": "FillColor", "value": "\"GREEN\"" }, { "name": "SizeX", "value": "4*L" }, { "name": "RelativePosition", "value": "\"NORTH\"" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "L" } ] }, { "Name": "muKineticDragGroup", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "X", "value": "0" }, { "name": "Y", "value": "0.45" } ], "Children": [ { "Name": "muKdragable", "Type": "Shape2D", "Properties": [ { "name": "SizeX", "value": "15" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "muKdrag" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "15" }, { "name": "PixelSize", "value": "true" }, { "name": "DrawFill", "value": "false" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "//vdrag= Math.round(vdrag);\nvar position = _view.drawingPanel.getInteraction().getInteractionPoint();\n//xi = position[0];\n//yi = position[1];\n//vdrag= Math.round(position[0]*10)/10;\nmuKdrag= Math.round(_info.point[0]*100)/100;\nif (muKdrag <0) muKdrag = 0;\nif (muKdrag >0.1) muKdrag = 0.1;\nmuKinetic = muKdrag*20;\n\ncheckDirection();\n" } ] }, { "Name": "group222", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "X", "value": "muKdrag" }, { "name": "Y", "value": "0" } ], "Children": [ { "Name": "muKtext", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"Orange\"" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0.01" }, { "name": "Text", "value": "\"\u03bck = \"+muKinetic.toFixed(2)" }, { "name": "Font", "value": "\"normal normal 2vw \"" } ] } ] } ] }, { "Name": "muStaticdraggroup22", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "X", "value": "0" }, { "name": "Y", "value": "0.5" } ], "Children": [ { "Name": "muSdragable", "Type": "Shape2D", "Properties": [ { "name": "SizeX", "value": "15" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "muSdrag" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "15" }, { "name": "PixelSize", "value": "true" }, { "name": "DrawFill", "value": "false" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "//vdrag= Math.round(vdrag);\nvar position = _view.drawingPanel.getInteraction().getInteractionPoint();\n//xi = position[0];\n//yi = position[1];\n//vdrag= Math.round(position[0]*10)/10;\nmuSdrag= Math.round(_info.point[0]*100)/100;\nif (muSdrag <0) muSdrag = 0;\nif (muSdrag >0.1) muSdrag = 0.1;\nmuStatic =muSdrag*20;\n\ncheckDirection();\n" } ] }, { "Name": "group22", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "X", "value": "muSdrag" }, { "name": "Y", "value": "0" } ], "Children": [ { "Name": "muS_text", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"Orange\"" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0.01" }, { "name": "Text", "value": "\"\u03bcs = \"+muStatic.toFixed(2)" }, { "name": "Font", "value": "\"normal normal 2vw \"" } ] } ] } ] }, { "Name": "LDragGroup", "Type": "Group2D", "Expanded": "true", "Properties": [], "Children": [ { "Name": "Ldragable", "Type": "Shape2D", "Properties": [ { "name": "SizeX", "value": "15" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "Ldrag" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "15" }, { "name": "PixelSize", "value": "true" }, { "name": "DrawFill", "value": "false" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "\n//var position = _view.drawingPanel.getInteraction().getInteractionPoint();\n\nLdrag= Math.round(_info.point[0]*10)/10;\nif (Ldrag <0.5) Ldrag = 0.5;\nif (Ldrag >2) Ldrag = 2;\nL = Ldrag*1;\nbumperX=L;\ncheckDirection();\n" } ] }, { "Name": "group2222", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "X", "value": "L" }, { "name": "Y", "value": "0" } ], "Children": [ { "Name": "muLtext2", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"Black\"" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "X", "value": "0.1" }, { "name": "Y", "value": "0.05" }, { "name": "Text", "value": "\"L = \"+L.toFixed(2)+\"m\"" }, { "name": "Font", "value": "\"normal normal 2vw \"" }, { "name": "EnabledPosition", "value": "\"ENABLED_ANY\"" } ] } ] } ] }, { "Name": "coordinates", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "Transformation", "value": "angle" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0" }, { "name": "Visibility", "value": "showVectors" } ], "Children": [ { "Name": "xArrow", "Type": "Arrow2D", "Properties": [ { "name": "SizeX", "value": "2*blockSize" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "1.5*blockSize" }, { "name": "SizeY", "value": "0" }, { "name": "LineWidth", "value": "2" } ] }, { "Name": "yArrow", "Type": "Arrow2D", "Properties": [ { "name": "SizeX", "value": "0" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "1.5*blockSize" }, { "name": "SizeY", "value": "2*blockSize" }, { "name": "LineWidth", "value": "2" } ] }, { "Name": "x", "Type": "Text2D", "Properties": [ { "name": "X", "value": "2*blockSize+0.03" }, { "name": "Y", "value": "1.5*blockSize" }, { "name": "Text", "value": "\"x\"" }, { "name": "PixelSize", "value": "true" }, { "name": "Font", "value": "font" } ] }, { "Name": "y", "Type": "Text2D", "Properties": [ { "name": "X", "value": "0" }, { "name": "Y", "value": "3.5*blockSize+0.03" }, { "name": "Text", "value": "\"y\"" }, { "name": "PixelSize", "value": "true" }, { "name": "Font", "value": "font" } ] } ] }, { "Name": "inclineReferenceFrame", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "Transformation", "value": "angle" }, { "name": "X", "value": "0.0" }, { "name": "Y", "value": "0.0" } ], "Children": [ { "Name": "spring", "Type": "Spring2D", "Properties": [ { "name": "Radius", "value": "blockSize/5" }, { "name": "SizeX", "value": "-L+x+blockSize/2" }, { "name": "X", "value": "L" }, { "name": "LineColor", "value": "\"RED\"" }, { "name": "Y", "value": "blockSize/4" }, { "name": "SizeY", "value": "0" }, { "name": "LineWidth", "value": "2" } ] }, { "Name": "incline", "Type": "Segment2D", "Properties": [ { "name": "SizeX", "value": "L" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "0" }, { "name": "LineWidth", "value": "2" } ] }, { "Name": "bottomBumper", "Type": "Shape2D", "Properties": [ { "name": "FillColor", "value": "\"BLACK\"" }, { "name": "MovesGroup", "value": "false" }, { "name": "SizeX", "value": "0.01*L" }, { "name": "RelativePosition", "value": "\"EAST\"" }, { "name": "ShapeType", "value": "\"ROUND_RECTANGLE\"" }, { "name": "X", "value": "0.01*L" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "blockSize/2" } ] }, { "Name": "topBumper", "Type": "Shape2D", "Properties": [ { "name": "FillColor", "value": "\"Black\"" }, { "name": "MovesGroup", "value": "false" }, { "name": "SizeX", "value": "0.01*L" }, { "name": "RelativePosition", "value": "\"SOUTH_WEST\"" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "bumperX" }, { "name": "Y", "value": "bumperY" }, { "name": "SizeY", "value": "blockSize/2" }, { "name": "OnDrag", "value": "angle += Math.atan2(bumperY,bumperX);\nangle = Math.max(0,angle);\nangle = Math.min(Math.PI/2,angle);\nangleDegrees = Math.degrees(angle); // added by lookang\nbumperX = L;\nbumperY = 0;\ncheckDirection();" }, { "name": "EnabledPosition", "value": "\"ENABLED_ANY\"" } ] }, { "Name": "block", "Type": "Shape2D", "Properties": [ { "name": "Sensitivity", "value": "0" }, { "name": "FillColor", "value": "\"rgba(128,192,255,1)\"" }, { "name": "MovesGroup", "value": "false" }, { "name": "SizeX", "value": "blockSize" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "x" }, { "name": "LineColor", "value": "\"BLACK\"" }, { "name": "Y", "value": "y" }, { "name": "SizeY", "value": "blockSize/2" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "y = 0;\n//x = _view.block.getX();\nx=Math.max(blockSize/2,x);\nx=Math.min(x,L-blockSize/2);\nv = 0;\nt = 0;\ncheckDirection();" } ] }, { "Name": "blockForces", "Type": "Group2D", "Expanded": "false", "Properties": [ { "name": "X", "value": "x" }, { "name": "Y", "value": "y+blockSize/4" }, { "name": "Visibility", "value": "showVectors" } ], "Children": [ { "Name": "gravity", "Type": "Arrow2D", "Properties": [ { "name": "SizeX", "value": "(-m*g*Math.sin(angle))*arrowScale" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "(-m*g*Math.cos(angle))*arrowScale" } ] }, { "Name": "friction", "Type": "Arrow2D", "Properties": [ { "name": "SizeX", "value": "frictionForce*arrowScale" }, { "name": "X", "value": "0" }, { "name": "LineColor", "value": 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"name": "LineWidth", "value": "2" } ] }, { "Name": "velocitydraggroup2", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "X", "value": "x+blockSize/2" }, { "name": "Y", "value": "y+blockSize" } ], "Children": [ { "Name": "velocity_drag22", "Type": "Shape2D", "Properties": [ { "name": "SizeX", "value": "15" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "vdrag" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "15" }, { "name": "PixelSize", "value": "true" }, { "name": "DrawFill", "value": "false" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "//vdrag= Math.round(vdrag);\n//var position = _view.drawingPanel.getInteraction().getInteractionPoint();\n//xi = position[0];\n//yi = position[1];\n//vdrag= Math.round(position[0]*10)/10;\n//vdrag= Math.round((_info.point[0]-(x+blockSize/2))*100)/100;\nvdrag= Math.round((_info.point[0]-(x+blockSize/2))*100)/100;\n\nif (vdrag <-0.5) vdrag = -0.5;\nif (vdrag >0.5) vdrag = 0.5;\nv =vdrag*10;\nv=Math.max(-99,v);\nv=Math.min(v,99);\ncheckDirection();\n" } ] }, { "Name": "velocityarrow", "Type": "Arrow2D", "Properties": [ { "name": "MarkEnd", "value": "\"TRIANGLE\"" }, { "name": "SizeX", "value": "vdrag" }, { "name": "LineColor", "value": "\"Magenta\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0" }, { "name": "SizeY", "value": "0" }, { "name": "LineWidth", "value": "2" }, { "name": "Offset", "value": "\"SOUTH_WEST\"" } ] }, { "Name": "group2", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "X", "value": "vdrag" }, { "name": "Y", "value": "0" } ], "Children": [ { "Name": "v22", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"Magenta\"" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0.05" }, { "name": "Text", "value": "\"v = \"+ v.toFixed(2) +\"m/s\"" }, { "name": "Font", "value": "\"normal normal 2vw \"" }, { "name": "EnabledPosition", "value": "\"ENABLED_ANY\"" } ] } ] } ] }, { "Name": "kdraggroup", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "X", "value": "0" }, { "name": "Y", "value": "blockSize/4+0.1" } ], "Children": [ { "Name": "kdrag", "Type": "Shape2D", "Properties": [ { "name": "SizeX", "value": "15" }, { "name": "ShapeType", "value": "\"RECTANGLE\"" }, { "name": "X", "value": "kdrag" }, { "name": "SizeY", "value": "15" }, { "name": "PixelSize", "value": "true" }, { "name": "DrawFill", "value": "false" }, { "name": "EnabledPosition", "value": "\"ENABLED_X\"" }, { "name": "OnDrag", "value": "var position = _view.drawingPanel.getInteraction().getInteractionPoint();\n\nkdrag = Math.round(_info.point[0]*1000)/1000;\n\nif (kdrag <0) kdrag = 0;\nif (kdrag >0.5) kdrag = 0.5;\nk = kdrag*20;\n\ncheckDirection();\n" } ] }, { "Name": "group23", "Type": "Group2D", "Expanded": "true", "Properties": [ { "name": "X", "value": "kdrag" }, { "name": "Y", "value": "0" } ], "Children": [ { "Name": "ktexte", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"Red\"" }, { "name": "RelativePosition", "value": "\"SOUTH\"" }, { "name": "X", "value": "0" }, { "name": "Y", "value": "0.05" }, { "name": "Text", "value": "\"k = \"+ k.toFixed(2) +\"N/m\"" }, { "name": "Font", "value": "\"normal normal 2vw \"" }, { "name": "EnabledPosition", "value": "\"ENABLED_ANY\"" } ] } ] } ] } ] }, { "Name": "thetagroup", "Type": "Group2D", "Expanded": "false", "Properties": [], "Children": [ { "Name": "thethatextdrag", "Type": "Text2D", "Properties": [ { "name": "FillColor", "value": "\"rgba(0,0,192,1)\"" }, { "name": "X", "value": "1.1" }, { "name": "Y", "value": "0.1" }, { "name": "Text", "value": "\"\u03b8 = \" + angleDegrees.toFixed(1)+\"\u00b0\"" }, { "name": "EnabledPosition", "value": "\"ENABLED_ANY\"" }, { "name": "Font", "value": "\"normal normal 2vw\"" } ] } ] } ] }, { "Name": "vPlottingPanel", "Type": "PlottingPanel", "Expanded": "false", 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"Width", "value": "%Width3%" } ], "Children": [ { "Name": "xpositionTrail", "Type": "Trail2D", "Properties": [ { "name": "Maximum", "value": "200" }, { "name": "LineColor", "value": "\"Blue\"" }, { "name": "InputX", "value": "t" }, { "name": "InputY", "value": "x" }, { "name": "NoRepeat", "value": "true" }, { "name": "LineWidth", "value": "2" } ] } ] }, { "Name": "forcePlottingPanel", "Type": "PlottingPanel", "Expanded": "false", "Properties": [ { "name": "Gutters", "value": "[50,0,0,50]" }, { "name": "XFixedTick", "value": "0" }, { "name": "OnDoubleClick", "value": "toggleFullScreen();" }, { "name": "MaximumX", "value": "20*dt" }, { "name": "YFixedTick", "value": "0" }, { "name": "YAutoTicks", "value": "false" }, { "name": "XTickStep", "value": "0.1" }, { "name": "TitleY", "value": "\"force (N)\"" }, { "name": "YTickStep", "value": "0.5" }, { "name": "AutoScaleY", "value": "true" }, { "name": "TitleX", "value": "\"time (s)\"" }, { "name": "AutoScaleX", "value": "true" }, { "name": 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\n \n\n
\n

About this Simulation

\n

\n This simulation models the motion of a block attached to a spring on an inclined plane.\n You can change the angle of the slope, the spring constant, and the friction coefficients,\n then observe whether the block stays at rest, slips, or oscillates.\n

\n

\n The model helps learners compare the forces acting along the incline. In particular, it shows\n how the spring force, the component of gravity down the slope, and friction work together to\n determine the motion. By exploring different settings, you can connect the world view to the\n displacement, velocity, and force graphs.\n

\n\n

Learning Objectives

\n
    \n
  • Understand how the angle of incline changes the component of weight along the slope.
    • \n
  • Explain when static friction is able to keep the block at rest.
    • \n
  • Investigate how spring constant and friction affect slipping and oscillation.
    • \n
  • Relate the motion of the block to the displacement, velocity, and force graphs.
    • \n
  • Describe energy changes between gravitational potential, elastic potential, and kinetic energy.
    • \n
\n\n
\n Try this first: Before pressing play, predict whether the block will stay at rest,\n slip, or oscillate.\n
\n
\n\n
\n

How to Explore

\n
    \n
  1. Set the block in a starting position and predict what will happen before pressing play.
    2. \n
  2. Adjust the incline angle and observe how the motion changes.
    3. \n
  3. Change the static and kinetic friction coefficients to compare sticking and slipping.
    4. \n
  4. Change the spring constant to see how strongly the block is pulled back toward equilibrium.
    5. \n
  5. Turn on the graphs and compare the animation with the plotted quantities.
    6. \n
\n
\n\n
\n

Thinking Questions for Active Learning

\n\n
\n
1. If the block is initially at rest, what must be true for it to remain at rest?
\n \n
\n The net force along the incline must be zero. Static friction must be able to balance the combined effect\n of the spring force and the component of gravity along the slope.\n
\n
\n\n
\n
2. How does increasing the angle of the incline affect the tendency of the block to slip?
\n \n
\n Increasing the angle increases the component of weight acting down the slope, so slipping becomes more likely.\n
\n
\n\n
\n
3. What is the difference between static friction and kinetic friction in this simulation?
\n \n
\n Static friction acts when the block is not slipping and can adjust up to a maximum value. Kinetic friction acts\n once the block is already sliding and usually has a smaller, nearly constant value.\n
\n
\n\n
\n
4. When does the block begin to oscillate instead of simply slipping down the slope?
\n \n
\n Oscillation is seen most clearly when friction is very small and the spring provides a restoring force that pulls\n the block back toward equilibrium.\n
\n
\n\n
\n
5. How does increasing the spring constant change the motion of the block?
\n \n
\n A larger spring constant gives a stronger restoring force for the same displacement, which usually makes the motion quicker\n and can reduce the oscillation period.\n
\n
\n\n
\n
6. What happens to the motion when friction is very small or zero?
\n \n
\n Less energy is lost, so the block can oscillate more clearly and the motion becomes closer to an ideal spring-block oscillator.\n
\n
\n\n
\n
7. How is the force graph related to the displacement of the block?
\n \n
\n The spring force changes with displacement, so the force graph changes as the block moves farther from or closer to equilibrium.\n
\n
\n\n
\n
8. At which parts of the motion is the kinetic energy greatest?
\n \n
\n The kinetic energy is greatest when the block is moving fastest, usually near the equilibrium position.\n
\n
\n\n
\n
9. When is the elastic potential energy in the spring greatest?
\n \n
\n The elastic potential energy is greatest when the spring is stretched or compressed the most.\n
\n
\n\n
\n
10. How does the equilibrium position change when the incline angle changes?
\n \n
\n Changing the incline changes the component of gravity along the slope, so the position where the forces balance also changes.\n
\n
\n
\n\n
\n

Teacher-Only Suggested Use

\n

\n Ask students to predict first, then test the prediction using the simulation, and finally explain their result\n using the force comparison shown on screen.\n

\n
    \n
  • Case 1: Choose values where static friction keeps the block at rest.
    • \n
  • Case 2: Reduce static friction until slipping just begins.
    • \n
  • Case 3: Reduce friction further and explore oscillation.
    • \n
  • Case 4: Turn on graphs and connect the visual motion to the plotted quantities.
    • \n
\n
\n
\n\n" } ] } ] } ], "RootProperties": [] }, "metadata": { "APP": "WebEJS", "CreatedWith": "WebEJS : The web version of Easy JavaScript Simulations", "MoreInfo": "WebEJS 1.1", "version": "https://www.um.es/fem/wikis/webejs/" } }