// Numbas version: exam_results_page_options
{"name": "Vector addition: tip-to-tail method", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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": "Vector addition: tip-to-tail method", "tags": ["angle from reference", "Graphical methods", "Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "<p>Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('jwussezq', [['f_a', forceA],['f_b', forceB],['f_c', forceC]])}</p>\n<p><strong></strong>Three forces act on &nbsp;point <em>A</em>: &nbsp; <span style=\"color: green;\">$A$ = {FA} {units[1]} at {alpha}&deg;</span>, <span style=\"color: blue;\">$B$&nbsp;= {FB} {units[1]} at {beta}&deg;&nbsp;</span> and, <span style=\"color: red;\">$C$ &nbsp;= {FC} {units[1]} at {gamma}&deg;</span>.</p>\n<p>Estimate the magnitude and direction of the resultant force&nbsp;$R$&nbsp;using the&nbsp;tip-to-tail method.</p>\n<p><span data-jme-visible=\"debug\">Force A: {fa} {units[1]}&nbsp;at {alpha} = {forceA}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">Force B: {fb} {units[1]}&nbsp;at {beta} = {forceB}</span></p>\n<p><span data-jme-visible=\"debug\">Force C: {fc}{units[1]} at {gamma} = {forceC}</span></p>\n<p><span data-jme-visible=\"debug\">Resultant: {R}{units[1]} &nbsp;at {rho} &nbsp;= {forceR}</span></p>\n<ol>\n<li>Move the tips of forces <span style=\"color: green;\">$A$</span>, <span style=\"color: blue;\">$B$</span>, and <span style=\"color: red;\">$C$</span> in this diagram to the&nbsp;correct magnitudes and directions. When this has been done correctly the dotted vector will become solid.</li>\n<li>Pick up&nbsp;vectors <span class=\"green\">$A$</span>, <span class=\"blue\">$B$</span> and <span class=\"red\">$C$</span>&nbsp; by their tails, and move them into a tip to tail arrangement. When this has been correctly done the resultant force $R$ will appear.</li>\n</ol>\n<p>Based on this diagram, estimate the magnitude and direction of the resultant.</p>", "advice": "<p>Vector Addition: &nbsp;</p>\n<p>When the forces have been moved to a tip-to=tail arrangement, the magnitude and direction can be read off the polar diagram.</p>\n<p>$\\Sigma F_x = &nbsp;R_x&nbsp;\\qquad &nbsp;R=\\sqrt{R_x^2 + R_y^2}\\\\\\\\&nbsp;\\Sigma F_y = &nbsp;R_y &nbsp;\\qquad \\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right)$</p>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"FA": {"name": "FA", "group": "Inputs", "definition": "random(20..80#5)", "description": "<p>Magnitude of force A</p>", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Inputs", "definition": "(random(-180..180#15))\n", "description": "<p>direction of force A</p>", "templateType": "anything", "can_override": false}, "ForceC": {"name": "ForceC", "group": "Outputs", "definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))", "description": "<p>Force C as a vector</p>", "templateType": "anything", "can_override": false}, "ForceR": {"name": "ForceR", "group": "Outputs", "definition": "ForceA+ForceB+ForceC", "description": "<p>Resultant as a vector</p>", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "random(20..80#5)", "description": "<p>Magnitude of Force B</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "description": "", "templateType": "anything", "can_override": false}, "rho": {"name": "rho", "group": "Outputs", "definition": "degrees(direction(ForceR))", "description": "<p>direction of resultant</p>", "templateType": "anything", "can_override": false}, "gamma": {"name": "gamma", "group": "Inputs", "definition": "(random(-180..180#15))", "description": "<p>Direction of force C in degrees</p>", "templateType": "anything", "can_override": false}, "FC": {"name": "FC", "group": "Inputs", "definition": "random(20..80#5)", "description": "<p>Magnitude of force C</p>", "templateType": "anything", "can_override": false}, "ForceA": {"name": "ForceA", "group": "Outputs", "definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))", "description": "<p>force A&nbsp;as a vector</p>", "templateType": "anything", "can_override": false}, "ForceB": {"name": "ForceB", "group": "Outputs", "definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))", "description": "<p>Force B as a vector</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Inputs", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Outputs", "definition": "abs(ForceR)", "description": "<p>Magnitude of resultant</p>", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "Inputs", "definition": "(random(-180..180#15))", "description": "<p>Direction of force B</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(alpha-beta) >= 15 and abs(beta-gamma) >= 15  and  abs(gamma-alpha) >= 15 and r <=100 and r > 10", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["alpha", "gamma", "beta", "FA", "FB", "FC", "units", "debug"]}, {"name": "Outputs", "variables": ["ForceA", "ForceB", "ForceC", "ForceR", "rho", "R"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])"}}, "preamble": {"js": "", "css": ".red{color:red;}\n.blue{color:blue;}\n.green{color:green;}"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnitude", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$R$ =&nbsp;[[0]]&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(R,units[1])", "right": "3", "close": "6", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle:  // a qty string corrected to standard angle\n  student_angle[2]  + student_angle[1] * student_angle[0] + student_units\n\n\nstudent_angle:\n  [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n  [1,-1][indices(studentAnswer[1],[true])[0]],      // ccw = 1 cw = -1\n  [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n  studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n  [interpreted_angle, studentAnswer[1], studentAnswer[2]]\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],  \n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n                concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number,answer,index],\n        zip([0],[interpreted_angle],[1])\n    )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\theta$ &nbsp;= [[0]] measured [[1]]&nbsp;from the&nbsp;[[2]]. &nbsp;</p>\n<p></p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "Direction", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "precround(qty(rho,'deg'),0)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "5", "right_tol": "2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y Axis", "-x Axis", "-y Axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}