// 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": [{"variable_groups": [{"variables": ["height", "c_friction", "mass", "incline", "distance"], "name": "Setup"}, {"variables": ["slope", "gravity", "a_gravity", "a_friction", "acceleration_naive", "acceleration"], "name": "Acceleration"}, {"variables": ["t_ground"], "name": "Answer"}], "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>", "tags": [], "ungrouped_variables": [], "parts": [{"steps": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "type": "information", "prompt": "<p>There are two forces acting on the mass: gravity and friction.</p>", "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "precision": "2", "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>", "showPrecisionHint": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "mass*a_gravity", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "mass*a_gravity", "precisionType": "dp", "allowFractions": false, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision."}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "precision": "2", "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>", "showPrecisionHint": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "mass*a_friction", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "mass*a_friction", "precisionType": "dp", "allowFractions": false, "variableReplacements": [], "precisionMessage": "<p>You have not given your answer to the correct precision.</p>"}], "scripts": {}, "marks": "3", "stepsPenalty": 0, "variableReplacementStrategy": "originalfirst", "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>", "showPrecisionHint": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "mass*acceleration", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "mass*acceleration", "precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2"}, {"variableReplacementStrategy": "originalfirst", "maxMarks": 0, "marks": 0, "shuffleChoices": false, "choices": ["<p>It moves down the slope.</p>", "<p>It moves up the slope.</p>", "<p>It remains stationary.</p>"], "prompt": "<p>What happens to the mass next?</p>", "displayColumns": 0, "showCorrectAnswer": true, "displayType": "radiogroup", "variableReplacements": [], "type": "1_n_2", "matrix": "if(acceleration=0,[0,1,0],[1,0,0])", "minMarks": 0, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "precision": "2", "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>", "showPrecisionHint": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "t_ground", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "t_ground", "precisionType": "dp", "allowFractions": false, "variableReplacements": [], "precisionMessage": "<p>You have not given your answer to the correct precision.</p>"}], "functions": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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>"}, "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>", "type": "question", "variables": {"gravity": {"group": "Acceleration", "description": "", "definition": "vector(0,-9.8)", "name": "gravity", "templateType": "anything"}, "t_ground": {"group": "Answer", "description": "", "definition": "if(acceleration=0,0,sqrt(-2*distance/acceleration))", "name": "t_ground", "templateType": "anything"}, "incline": {"group": "Setup", "description": "", "definition": "precround(degrees(arctan(height/50)),1)", "name": "incline", "templateType": "anything"}, "mass": {"group": "Setup", "description": "", "definition": "random(5..35#5)", "name": "mass", "templateType": "anything"}, "slope": {"group": "Acceleration", "description": "", "definition": "vector(cos(radians(incline)),sin(radians(incline)))", "name": "slope", "templateType": "anything"}, "a_friction": {"group": "Acceleration", "description": "", "definition": "let(f,dot(matrix([[0,1],[-1,0]])*slope,gravity)*c_friction,\n  min(f,-a_gravity)\n)", "name": "a_friction", "templateType": "anything"}, "distance": {"group": "Setup", "description": "", "definition": "45", "name": "distance", "templateType": "anything"}, "height": {"group": "Setup", "description": "", "definition": "random(10..40)", "name": "height", "templateType": "anything"}, "acceleration": {"group": "Acceleration", "description": "", "definition": "if(acceleration_naive<0,acceleration_naive,0)", "name": "acceleration", "templateType": "anything"}, "a_gravity": {"group": "Acceleration", "description": "", "definition": "dot(gravity,slope)", "name": "a_gravity", "templateType": "anything"}, "c_friction": {"group": "Setup", "description": "", "definition": "random(0.01..0.5#0.01)", "name": "c_friction", "templateType": "anything"}, "acceleration_naive": {"group": "Acceleration", "description": "", "definition": "a_gravity+a_friction", "name": "acceleration_naive", "templateType": "anything"}}, "rulesets": {}, "extensions": ["geogebra"], "name": "Numbas demo: motion on a slope", "variablesTest": {"condition": "", "maxRuns": 100}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}