// Numbas version: exam_results_page_options
{"name": "Equilibrium of a particle: four forces", "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": "Equilibrium of a particle: four forces", "tags": ["angle from reference", "Equlibrium", "Mechanics", "mechanics", "Particle Equilbrium", "Statics", "statics"], "metadata": {"description": "<p>Three random forces act on a particle. &nbsp;Determine the force required for equilibirum.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet} <span data-jme-visible=\"debug\">{alpha} {beta} {gamma}</span></p>\n<p><span>Four forces with magnitudes </span><span style=\"color: red;\">$A$</span> = {qty(maga,units)}, <span style=\"color: blue;\">$B$&nbsp;</span>= {qty(magb,units)}, and <span style=\"color: green;\">$C$</span> = {qty(magC,units)}, act on a particle&nbsp;in the directions shown.</p>\n<p>Determine the magnitude and direction of force $\\mathbf{D}$ required for equilibrium.</p>", "advice": "<p>Begin by drawing a free body diagram of the particle. Since the direction of force $\\mathbf{D}$ is unknown you will have to make an assumption about which way it points.</p>\n<p>Set up and solve the equilibrium equations based on your assumed direction for $\\mathbf{D}$</p>\n<p style=\"padding-left: 40px;\">$\\begin{align}<br/>\\Sigma F_x &amp;= 0\\\\<br/>A_x + B_x + C_x + D_x &amp;= 0\\\\ <br/>\\simplify[!collectNumbers]{{enground(A[0])} + &nbsp;{enground(B[0])} &nbsp;+ {enground(C[0])} - D_x} &amp;= 0 &nbsp;\\\\<br/>D_x &amp;= \\var{qty(enground(A[0] +B[0] +C[0]),units)}&amp;(1)\\\\\\\\<br/>\\Sigma F_y &amp;= 0\\\\<br/>A_y + B_y + C_y + D_y &amp;= 0\\\\<br/>\\simplify[!collectNumbers]{{enground(A[1])} + {enground(B[1])} &nbsp;+ &nbsp;{enground(C[1])} + D_y } &amp;= 0\\\\<br/>D_y &amp;= \\var{qty(- enground(A[1] +B[1] +C[1]),units)} &amp; (2)<br/>\\end{align}$</p>\n<p>If your calculations result in a negative value for $D_x$ or $D_y$, then your assumed direction is opposite of the component's actual direction.</p>\n<p>Draw a sketch showing $D_x$, $D_y$, and $D$ pointing in their actual directions and define angle $\\theta$.</p>\n<p>Resolve the components using right triangle trigonometry to find $D$ and $\\theta$. &nbsp;</p>\n<p style=\"padding-left: 40px;\">$D = \\var{enground(abs(D))}$ {units},</p>\n<p style=\"padding-left: 40px;\">$\\theta&nbsp;&nbsp;= \\var{siground(theta,4)}$&deg; measured counterclockwise from the $x$-axis.</p>\n<p><em>Your value of $\\theta$ will depend on the reference angle you choose. Choose one that makes $\\theta$ less than 90&deg; to avoid sign errors.</em></p>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "forces", "definition": "maga vector(cos(radians(alpha)),sin(radians(alpha)))\n", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "forces", "definition": "degrees(atan2(D[1],D[0]))", "description": "", "templateType": "anything", "can_override": false}, "gamma": {"name": "gamma", "group": "input", "definition": "random(180..265#5)", "description": "", "templateType": "anything", "can_override": false}, "magc": {"name": "magc", "group": "input", "definition": "random(10..100#5)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "forces", "definition": "magc vector(cos(radians(gamma)),sin(radians(gamma)))", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "input", "definition": "random(270..355#5)", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "input", "definition": "random(0..90#5)", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "input", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "magb": {"name": "magb", "group": "input", "definition": "random(10..100#5)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "input", "definition": "random('kN','N','lb')", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "forces", "definition": "magb vector(cos(radians(beta)),sin(radians(beta)))", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "forces", "definition": "-(A+B+C)\n", "description": "", "templateType": "anything", "can_override": false}, "maga": {"name": "maga", "group": "input", "definition": "random(10..100#5)", "description": "", "templateType": "anything", "can_override": false}, "magd": {"name": "magd", "group": "forces", "definition": "qty(abs(D),units)\n", "description": "", "templateType": "anything", "can_override": false}, "dx": {"name": "dx", "group": "check", "definition": "-(A[0] + B[0] + C[0])", "description": "", "templateType": "anything", "can_override": false}, "dy": {"name": "dy", "group": "check", "definition": "-(A[1] + B[1] + C[1])", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "input", "definition": "geogebra_applet('xnbz73te',params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "input", "definition": "['\u03b1': radians(alpha),'\u03b2': radians(beta) ,'\u03b3': radians(gamma) , 'maga': maga , 'magb': magb,'magc':magc ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "input", "variables": ["alpha", "beta", "gamma", "units", "maga", "magb", "magc", "debug", "applet", "params"]}, {"name": "forces", "variables": ["A", "B", "C", "D", "magd", "theta"]}, {"name": "check", "variables": ["dx", "dy"]}], "functions": {"enground": {"parameters": [["n", "number"]], "type": "number", "language": "jme", "definition": "if(abs(N) < 10^(-10), precround(n,3) , siground(n,4))"}, "graphics2": {"parameters": [["app", "ggbapplet"]], "type": "ggbapplet", "language": "javascript", "definition": "// Take an applet, set its perspective to the given string.\n// See https://wiki.geogebra.org/en/SetPerspective_Command for the format of the perspective string.\napp.promise.then(function(d) {\n  d.app.setPerspective(\"D\");// D=graphics2\n});\nreturn new Numbas.jme.types.ggbapplet(app);"}}, "preamble": {"js": "", "css": ".part:not(.dirty) > .student-answer.answered[feedback-state='wrong'] input {\nborder-color: hsl(0, 0%, 50%);\nbackground: hsl(0, 0%, 95%);\n}\n"}, "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>$D$ =&nbsp;[[3]] &nbsp;<span data-jme-visible=\"debug\" style=\"color: blue;\">({siground(magd,4)}) </span>acting at &nbsp;[[0]]&nbsp;measured [[1]]&nbsp;from the&nbsp;[[2]]. <span data-jme-visible=\"debug\" style=\"color: blue;\">({siground(theta,4)}&deg;)</span></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": "qty(round(theta*100)/100,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Sign", "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": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Reference Direction", "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": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x Axis", "+y Axis", "-x Axis", "-y Axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "magD", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}