// Numbas version: finer_feedback_settings
{"name": "Moment of a couple", "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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "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": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "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": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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": "<p>Only marked close if the student actually has the right sign.</p>", "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. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Moment of a couple", "tags": ["Couple", "Mechanics", "mechanics", "Moments", "moments", "perpendicular distance", "Perpendicular distance", "Statics", "statics", "Verignon's Theorem"], "metadata": {"description": "<p>Find the moment of a couple formed by two equal and opposite forces.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet}</p>\n<p>{setAxisVisible(applet,false)}</p>\n<p>Determine the moment of the couple formed by the two&nbsp;{F} {units[1]} forces shown. &nbsp;Grid units are in [{units[0]}].</p>", "advice": "<p>The moment of a couple is found by multiplying the magnitude of force by the perpendicular distance between the lines of action of the two forces. The direction is determined by inspection. &nbsp;You will need to determine the perpendicular distance using the known locations of the two points, the direction of the force, geometry and trigonometry as we have done before.</p>\n<p>$ M = F \\cdot d_\\perp$</p>\n<p>$ M = (\\var{F}\\,&nbsp; \\var{units[1]} ) (\\var{abs(siground(moment/F,4))}\\,&nbsp; \\var{units[0]} ) = \\var{siground(abs(answer),4)}$&nbsp; {if(moment&nbsp;&gt;0,'Counterclockwise','Clockwise')}</p>\n<p>Alternately, you get the same result by finding the moment of one force about a point on the line of action of the other one. &nbsp;</p>\n<p>So, for example, take the moment of the force at $A$ about point $B$ using Verignon's Theorem. The signs in the equation below are determined by the direction of the component moments, using the sign convention that counterclockwise moments are positive. &nbsp;The sign of the resulting moment indicates its direction and it should agree with your expectations&nbsp;from&nbsp;inspection of the diagram.</p>\n<p>$ M = \\pm F_x d_y \\pm F_y d_x $</p>\n<p>$ M = \\pm\\, ( \\var{d(Force[0] )} \\, \\var{units[1]} ) ( \\var{d(r[1])} \\, \\var{units[0]} &nbsp;) \\pm\\, ( \\var{d(Force[1] )} \\, \\var{units[1]} ) ( \\var{d(r[0])} \\, \\var{units[0]} &nbsp;)$</p>\n<p>$M = \\var{siground(answer,4)}$</p>\n<p>$M = \\var{siground(abs(answer),4)} $&nbsp;{if(moment&nbsp;&gt;0,'Counterclockwise','Clockwise')}&nbsp;</p>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"F": {"name": "F", "group": "inputs", "definition": "random(10..400#10)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "inputs", "definition": "vector(random(-8..8),random(-6..6))", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "inputs", "definition": "random(5..355#5 except [90,-90,180])", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "results", "definition": "A-B + vector(0,0,0)", "description": "<p>position vector</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "inputs", "definition": "vector(random(-8..8),random(-6..6))", "description": "", "templateType": "anything", "can_override": false}, "Force": {"name": "Force", "group": "results", "definition": "vector(f cos(radians(theta)),f sin(radians(theta)),0)", "description": "<p>Force vector</p>", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "results", "definition": "d(moment) qty(units[1])qty(units[0])", "description": "<p>rounded value of moment as quantity</p>", "templateType": "anything", "can_override": false}, "moment": {"name": "moment", "group": "results", "definition": "cross(r,force)[2]", "description": "<p>Magnitude of moment</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "random(['in','lb'],['m','kN'],['cm','N'])", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[ A: A, B: B, '\u03b8': radians(theta), show: [definition: 'false', visible: false]]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('whx4ybuq', params )", "description": "", "templateType": "anything", "can_override": false}, "dperp": {"name": "dperp", "group": "results", "definition": "abs(moment)/F", "description": "<p>perpendicular distance</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(r) > 2 //  nice size\nand dperp/abs(r) < 0.96 // cos angle  makes angle > 15\u00b0\nand dperp/abs(r) > 0.18 // cos angle  makes angle < 80\u00b0\nand A[0] <> B[0] and A[1] <> B[1] // not on same vertical or horizontal axis", "maxRuns": 100}, "ungrouped_variables": ["params", "applet"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "theta", "units", "F"]}, {"name": "results", "variables": ["r", "Force", "moment", "answer", "dperp"]}], "functions": {"d": {"parameters": [["v", "number"]], "type": "number", "language": "jme", "definition": "siground(abs(v),4)"}, "setAxisVisible": {"parameters": [["app", "ggbapplet"], ["visible", "boolean"]], "type": "anything", "language": "javascript", "definition": "app.promise.then(function(d) {\n  d.app.setAxesVisible(visible,visible);});\nreturn new Numbas.jme.types.ggbapplet(app);\n\n"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n    var app = question.scope.variables.applet.app;  \n    app.setVisible(\"show\", true,false);\n    app.setValue(\"show\", 1);\n  }\n  catch(err){}  \n})", "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": "<p>$M$ =&nbsp;[[0]]&nbsp;[[1]]</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "mag", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "abs(answer)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Clockwise", "Counterclockwise"], "matrix": "[if(moment<0,5,0),if(moment>0,5,0)]"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}