// Numbas version: exam_results_page_options
{"name": "Numbas demo: motion on a slope", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Numbas demo: motion on a slope", "tags": [], "metadata": {"description": "<p>Given the gradient of a slope and the coefficient of friction for a mass resting on it,&nbsp;use the equations of motion to calculate how it moves.</p>\n<p>Includes a GeoGebra rendering of the model.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><em>In this question,&nbsp;a GeoGebra applet shows a diagram of the given mathematical model. The student can see how the system behaves over time, to&nbsp;compare against their intuition and calculations.</em></p>\n<p>A mass of $\\var{mass}\\,\\mathrm{kg}$ is resting on a plane inclined at $\\var{incline}^{\\circ}$ to the horizontal. The distance along the plane from the ground to the mass is $\\var{distance}\\mathrm{m}$.</p>\n<p>A gravitational force&nbsp;of $9.8\\,\\mathrm{N/kg}$ is acting on the mass, and the coefficient of friction between the plane and the mass is $\\mu = \\var{c_friction}$.</p>\n<p>{geogebra_applet('xn3p5x73',[[\"height\",height],[\"c_\\{friction\\}\",c_friction],[\"mass\",mass]],[])}</p>", "advice": "<p>Either construct&nbsp;the intersection of two circles centred at $\\mathbf{a}$ and $\\mathbf{b}$, or use the Regular Polygon tool.</p>\n<p>(I could embed another GeoGebra applet here)</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"incline": {"name": "incline", "group": "Setup", "definition": "precround(degrees(arctan(height/50)),1)", "description": "<p>Angle of the inclined plane.</p>", "templateType": "anything"}, "t_ground": {"name": "t_ground", "group": "Answer", "definition": "if(acceleration=0,0,sqrt(-2*distance/acceleration))", "description": "", "templateType": "anything"}, "a_gravity": {"name": "a_gravity", "group": "Acceleration", "definition": "dot(gravity,slope)", "description": "", "templateType": "anything"}, "c_friction": {"name": "c_friction", "group": "Setup", "definition": "random(0.01 .. 0.5#0.01)", "description": "<p>Coefficient of friction between the mass and the plane.</p>", "templateType": "randrange"}, "acceleration": {"name": "acceleration", "group": "Acceleration", "definition": "if(acceleration_naive<0,acceleration_naive,0)", "description": "", "templateType": "anything"}, "a_friction": {"name": "a_friction", "group": "Acceleration", "definition": "let(f,dot(matrix([[0,1],[-1,0]])*slope,gravity)*c_friction,\n  min(f,-a_gravity)\n)", "description": "", "templateType": "anything"}, "height": {"name": "height", "group": "Setup", "definition": "random(10..40)", "description": "<p>Height of the mass at $t=0$</p>", "templateType": "anything"}, "distance": {"name": "distance", "group": "Setup", "definition": "45", "description": "", "templateType": "anything"}, "acceleration_naive": {"name": "acceleration_naive", "group": "Acceleration", "definition": "a_gravity+a_friction", "description": "", "templateType": "anything"}, "slope": {"name": "slope", "group": "Acceleration", "definition": "vector(cos(radians(incline)),sin(radians(incline)))", "description": "", "templateType": "anything"}, "gravity": {"name": "gravity", "group": "Acceleration", "definition": "vector(0,-9.8)", "description": "", "templateType": "anything"}, "mass": {"name": "mass", "group": "Setup", "definition": "random(5..35#5)", "description": "<p>Mass of the object.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["height", "c_friction", "mass", "incline", "distance"]}, {"name": "Acceleration", "variables": ["slope", "gravity", "a_gravity", "a_friction", "acceleration_naive", "acceleration"]}, {"name": "Answer", "variables": ["t_ground"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the total force acting on the mass, along the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>There are two forces acting on the mass: gravity and friction.</p>"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the force due to gravity, in the direction of the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.</p>", "minValue": "mass*a_gravity", "maxValue": "mass*a_gravity", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the force due to friction, in the direction of the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.</p>", "minValue": "mass*a_friction", "maxValue": "mass*a_friction", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "mass*acceleration", "maxValue": "mass*acceleration", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What happens to the mass next?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>It moves down the slope.</p>", "<p>It moves up the slope.</p>", "<p>It remains stationary.</p>"], "matrix": "if(acceleration=0,[0,1,0],[1,0,0])"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>At what time&nbsp;does the mass reach the ground? Enter your answer in seconds to 2 decimal places, or $0$ if the mass never reaches the ground.</p>", "minValue": "t_ground", "maxValue": "t_ground", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}