// Numbas version: exam_results_page_options {"name": "23. Moment of Inertia", "metadata": {"description": "
Homework set. Basic concepts of Area Moment of Inertia.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Moment of Inertia: Basic Shapes from the MOI Table", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "Only marked close if the student actually has the right sign.
", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. if correct answer is 100 N and close is ±1%,Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.
\nThe parallel axis theorem is not required for any of these shapes. One situation requires subtracting a triangle from a rectangle however.
\nDistinguish between centroidal and non-centroidal moments of inertia.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "{geogebra_applet('ndkfbkp9',['b': b, 'h': h, 'i': index, 'Z': Z])}
\nA {shape} ({dimensions}) and its centroid are shown.
", "advice": "\nUse the information in the table below.
\n", "rulesets": {}, "variables": {"b": {"name": "b", "group": "inputs", "definition": "random(-8..8 except 0)", "description": "horizontal dimension of rectangles and triangles
", "templateType": "anything"}, "h": {"name": "h", "group": "inputs", "definition": "random(-8..8 except 0)", "description": "vertical dimension of rectangles and triangles
", "templateType": "anything"}, "r": {"name": "r", "group": "inputs", "definition": "b", "description": "radius of circle or semicircles.
", "templateType": "anything"}, "index": {"name": "index", "group": "inputs", "definition": "random(1..14)", "description": "selects the shape -- see resources for diagram
", "templateType": "anything"}, "shape": {"name": "shape", "group": "Description", "definition": "if(index=1,'circle',if(index<=4,'rectangle',if(index <=10,'triangle',if(index<=12,'semicircle','quarter-circle'))))", "description": "", "templateType": "anything"}, "dimensions": {"name": "dimensions", "group": "Description", "definition": "if(isCircular,\n \"$r = \\\\var{abs(b units) }$\",\n \"$\\\\var{abs(b units)} \\\\times \\\\var{abs(h units)}$\"\n) ", "description": "", "templateType": "anything"}, "isCircular": {"name": "isCircular", "group": "Description", "definition": "index = 1 or index > 10", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "inputs", "definition": "qty(random(['in', 'ft', 'mm', 'cm','m']))", "description": "", "templateType": "anything"}, "Ix": {"name": "Ix", "group": "Solution", "definition": "siground([ 0,pir4/4, \n bh3/3, bh3/12, bh3/3, \n bh3/12, bh3/12, bh3/36, bh3/36, bh3/12,bh3/36,\n pir4/8,pir4/8,\n pir4/16,pir4/16][index],4)", "description": "0 is placeholder for zero-indexed array.
", "templateType": "anything"}, "PIR4": {"name": "PIR4", "group": "Solution", "definition": "pi r^4 * units * units * units * units", "description": "", "templateType": "anything"}, "bh3": {"name": "bh3", "group": "Solution", "definition": "abs(b h^3) * units * units * units * units", "description": "", "templateType": "anything"}, "hb3": {"name": "hb3", "group": "Solution", "definition": "abs(h b^3) * units * units * units * units", "description": "", "templateType": "anything"}, "Iy": {"name": "Iy", "group": "Solution", "definition": "siground([0, pir4/4,\n hb3/3, hb3/3, hb3/12,\n hb3/4, hb3/12, hb3/4, hb3/12, hb3/36, hb3/36,\n pir4/8,pir4/8,\n pir4/16,pir4/16][index],4)", "description": "", "templateType": "anything"}, "centroidalaxis": {"name": "centroidalaxis", "group": "Solution", "definition": "[[],both,neither, x, y, neither, neither, x, x, y, both, x, y, neither, neither][index]\n ", "description": "marking matrix for centroidal axis [x,y,both,neither]
", "templateType": "anything"}, "x": {"name": "x", "group": "Solution", "definition": "[10,0,0,0]", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Solution", "definition": "[0,10,0,0]", "description": "", "templateType": "anything"}, "both": {"name": "both", "group": "Solution", "definition": "[0,0,10,0]", "description": "", "templateType": "anything"}, "neither": {"name": "neither", "group": "Solution", "definition": "[0,0,0,10]", "description": "", "templateType": "anything"}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "\"applet()\"", "description": "disabled calling the javascript applet
", "templateType": "anything"}, "Z": {"name": "Z", "group": "inputs", "definition": "8", "description": "ZOOM
", "templateType": "anything"}}, "variablesTest": {"condition": "abs(b)> 2 and abs(h) > 2", "maxRuns": 100}, "ungrouped_variables": ["applet"], "variable_groups": [{"name": "inputs", "variables": ["h", "r", "b", "index", "units", "Z"]}, {"name": "Description", "variables": ["shape", "dimensions", "isCircular"]}, {"name": "Solution", "variables": ["Ix", "PIR4", "bh3", "hb3", "Iy", "centroidalaxis", "x", "y", "both", "neither"]}], "functions": {"NotUsed": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n filename: 'resources/question-resources/basicShapes.ggb',\n width: 250,\n height: 250\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n var app = d.app;\n question.applet = d;\n \n function setGGBPoint(g_name, n_name = g_name) {\n // moves point in GGB to location of Numbas Vector Variable\n // g_name = geogebra point, n_name = numbas vector\n var pt = question.scope.evaluate(n_name).value\n app.setFixed(g_name,false,false);\n app.setCoords(g_name, pt[0], pt[1]);\n app.setFixed(g_name,true,true);\n }\n \n function setGGBNumber(g_name, n_name = g_name) {\n // Sets number in GGB to a Numbas Variable\n var n = question.scope.evaluate(n_name).value;\n app.setValue(g_name,n);\n }\n \n app.setValue(\"Z\",5); //zoom\n setGGBNumber(\"b\");\n setGGBNumber(\"h\");\n setGGBNumber(\"i\",\"index\")\n\n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Determine the moment of inertia of the {shape} with respect to the $x$ and $y$ axis.
\n$I_x$ = [[0]] $I_y$ = [[1]]
\nAre either of these values centroidal moments of inertia?
\n[[2]]
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ix", "marks": "20", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Ix", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Iy", "marks": "20", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Iy", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "1_n_2", "useCustomName": true, "customName": "centroidal", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["$I_x$", "$I_y$", "Both", "Neither"], "matrix": "centroidalaxis"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Moment of Inertia: rectangles", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "Only marked close if the student actually has the right sign.
", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. if correct answer is 100 N and close is ±1%,Find moment of inertia wrt the x- and y- axes for a shape made up of two rectangles.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('b3fxtwx6',[['A',A],['B',B]])}
\nUse the formula below for the moment of inertia of a rectangle about an axis passing through its base to find the moment of inertia of the composite shape about both the x- and y- axes. Grid units are [{unit}]. \\[I = \\dfrac{b h^3}{3}\\]
", "advice": "To find $I_x$ consider the shape to be made of a $ (\\var{b_1} \\times \\var{h_1})$ rectangle and a $(\\var{b_2} \\times \\var{h_2})$ {if(removed_x,'removed','')} rectangle.
\n$ \\quad I_x = \\dfrac{ (\\var{b_1}) (\\var{h_1})^3}{3} \\, \\var{if(removed_x, '–' , '+')} \\,\\dfrac{ (\\var{b_2}) (\\var{h_2})^3}{3} = \\var{siground(ix units, 4)} \\\\$
\nTo find $I_y$ consider the shape to be made of a $ (\\var{b_3} \\times \\var{h_3})$ rectangle and a $(\\var{b_4} \\times \\var{h_4})$ {if(removed_y,'removed','')} rectangle.
\n$\\quad I_y = \\dfrac{ (\\var{b_3}) (\\var{h_3})^3}{3} \\, \\var{if(removed_y, '–' , '+')} \\,\\dfrac{ (\\var{b_4}) (\\var{h_4})^3}{3}= \\var{siground(Iy units,4)}$
", "rulesets": {}, "variables": {"Iy": {"name": "Iy", "group": "Unnamed group", "definition": "MOI(b_3,h_3) + if(removed_y,-1,1) MOI(b_4,h_4)", "description": "", "templateType": "anything"}, "removed_x": {"name": "removed_x", "group": "Unnamed group", "definition": "not(add)", "description": "remove
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", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "Only marked close if the student actually has the right sign.
", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. if correct answer is 100 N and close is ±1%,Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('wsef7939',[['A',A],['B',B],['C',C]])}
\nConsider the composite shape shown. Grid units are [{units}].
\nDetermine the total area of the shape, and its Moment of Inertia and Radius of Gyration with respect to the x-axis.
\n", "advice": "Consider the shape to be made of three parts.
\nArea:
\n$A_1 = b_1 h_1 = \\var{A1}$
\n$A_2 = \\frac{1}{2} b_2 h_2= \\var{A2}$
\n$A_3 = \\frac{1}{2} b_3 h_3= \\var{A3}$ {if(removed,'Removed','')}
\n$A = \\Sigma A_i = \\var{A_t}$
\nMoment of inertia wrt x-axis:
\n$\\begin{align}I_x &= \\Sigma I_x \\\\ &= \\frac{b_1 h_1^3}{3} + \\frac{b_2 h_2^3 }{12} + \\var{if(removed,'–','')} \\frac{b_3 h_3^3}{12}\\\\&= (\\var{siground(I1x,4)}) + (\\var{siground(I2x,4)}) + (\\var{if(removed,'–','')}\\var{ siground(I3x,4)})\\\\&= \\var{siground(I_t,4)}\\end{align}$
\nRadius of gyration wrt x-axis:
\n$k_x = \\sqrt{\\dfrac{I_x}{A}} = \\var{siground(kx,4)}$
", "rulesets": {}, "variables": {"A_t": {"name": "A_t", "group": "derived geometry", "definition": "A1+ A2 + if(removed,-1,1) A3", "description": "", "templateType": "anything"}, "A2": {"name": "A2", "group": "derived geometry", "definition": "B2 H2 /2", "description": "", "templateType": "anything"}, "h2": {"name": "h2", "group": "derived geometry", "definition": "qty(B[1],units)", "description": "part 2 left triangle
", "templateType": "anything"}, "expression": {"name": "expression", "group": "derived geometry", "definition": "random([\n \"\\\\frac\\{1\\}\\{2\\}\",\n \"\\\\sin(x)\",\n \"2 + \\\\hat\\{x\\}\"\n])", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "derived geometry", "definition": "qty(abs(C[0]),units)\n", "description": "base of left triangle x(c) is always < 0
", "templateType": "anything"}, "A3": {"name": "A3", "group": "derived geometry", "definition": "B3 h3/2", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "inputs", "definition": "random('in','ft','mm','cm','m')", "description": "", "templateType": "anything"}, "I3x": {"name": "I3x", "group": "answers", "definition": "(b3 * h3 * h3 * h3)/12", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "inputs", "definition": "vector(random(-9..-1),0)", "description": "this point determines the triangle to the left of the y axis
", "templateType": "anything"}, "debug": {"name": "debug", "group": "inputs", "definition": "false", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "inputs", "definition": "vector(random(C[0]..10 except B[0] ),random(1..B[1]))", "description": "This points sets the coordinates of the second triangle, at (x,0) and (x(b),y)
", "templateType": "anything"}, "I1x": {"name": "I1x", "group": "answers", "definition": "b1 * h1 * h1 * h1/3", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "derived geometry", "definition": "qty(B[0],units)", "description": "base of rectangle 1
", "templateType": "anything"}, "I_t": {"name": "I_t", "group": "answers", "definition": "I1x + I2x + if(removed,-1,1) I3x", "description": "total moment of inertia wrt x axis
", "templateType": "anything"}, "B": {"name": "B", "group": "inputs", "definition": "vector(random(1..8),random(1..9))", "description": "top right corner of the rectangle
", "templateType": "anything"}, "kx": {"name": "kx", "group": "answers", "definition": "qty(sqrt(scalar(I_t/A_t)),units)", "description": "", "templateType": "anything"}, "h3": {"name": "h3", "group": "derived geometry", "definition": "qty(A[1],units)", "description": "", "templateType": "anything"}, "h1": {"name": "h1", "group": "derived geometry", "definition": "qty(B[1],units)", "description": "height of rectangle 1
\n", "templateType": "anything"}, "axis": {"name": "axis", "group": "inputs", "definition": "random('x','y')", "description": "", "templateType": "anything"}, "I2x": {"name": "I2x", "group": "answers", "definition": "(b2 * h2 * h2 * h2)/12\n", "description": "", "templateType": "anything"}, "A1": {"name": "A1", "group": "derived geometry", "definition": "B1 H1", "description": "area of rectangle 1
", "templateType": "anything"}, "removed": {"name": "removed", "group": "derived geometry", "definition": "if(A[0]\n$A$ = [[0]] {A_t}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Area", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "abs(A_t)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Moment of Inertia", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n$I_x =$ [[0]] {siground(I_t,4)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$I_x$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "I_t", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Radius of gyration", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$k_x =$ [[0]] {siground(kx,4)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$k_x$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "kx", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "Only marked close if the student actually has the right sign.
", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. if correct answer is 100 N and close is ±1%,