// Numbas version: exam_results_page_options
{"name": "Cantilever beam", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\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:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"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": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "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": [{"ungrouped_variables": [], "name": "Cantilever beam", "functions": {"format": {"definition": "string(siground(q,4))", "language": "jme", "parameters": [["q", "quantity"]], "type": "string"}}, "variable_groups": [{"variables": ["L", "A", "B", "units", "FA", "magA", "MagC", "theta_c", "FC", "M", "debug"], "name": "Input"}, {"variables": ["OA", "OC", "OB", "MA", "MC", "MB", "MO", "FO", "dirO", "angle_from_ref"], "name": "output"}], "tags": [], "rulesets": {}, "statement": "<p>{geogebra_applet('dpvndcem',[['A',A],['B',B],['L',L],['units','\"'+units[1]+'\"'],['fa',FA], ['fc',FC], ['M',M]])}</p>\n<p style=\"padding-left: 30px;\"></p>\n<p>A&nbsp;beam of length <em>L</em> = {L} {units[1]} is supported by a fixed (cantilever) support at&nbsp;<em>O. </em>Detemine the reactions at <em>O</em>&nbsp;when the beam supports loads:&nbsp;</p>\n<p><em>A</em> = {magA} {units[0]},&nbsp;<em>B</em>&nbsp;= {abs(M)} {units[0]}-{units[1]} and <em>C</em>&nbsp;= {magC} {units[0]}, as shown.</p>\n<p></p>", "extensions": ["geogebra", "quantities", "weh"], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.</p>"}, "advice": "<p>Draw a free body diagaram of the beam, then apply the equations of equilibrium.</p>\n<p></p>\n<p>$\\Sigma M = 0$</p>\n<p style=\"padding-left: 30px;\">$M_O + M_A + M_B + M_C = 0$</p>\n<p style=\"padding-left: 30px;\">$M_A = d_1 A_y$ = ({OA}) ({qty(abs(FA[1]),units[0])}) =&nbsp;{abs(MA)} <em> {if(sign(MA)&gt;0,'counterclockwise','clockwise')}</em></p>\n<p style=\"padding-left: 30px;\">$M_B =$ {abs(MB)} <em>{if(sign(MB)&gt;0,'counterclockwise','clockwise')}</em></p>\n<p style=\"padding-left: 30px;\">$M_C = L&nbsp;C_y$ = ({OC}) ({format(qty(abs(FC[1]),units[0]))}) =&nbsp;{format(abs(MC))} <em>{if(sign(MC)&gt;0,'counterclockwise','clockwise')}</em></p>\n<p style=\"padding-left: 30px;\">$ M_O = - (&nbsp;\\var{format(MA)} + \\var{format(MB)} + \\var{format(MC)} ) = \\var{format(abs(MO))}$&nbsp;<em>{if(sign(MO)&gt;0,'counterclockwise','clockwise')}</em></p>\n<p style=\"padding-left: 30px;\"><em>&nbsp;</em></p>\n<p>$\\Sigma F_x = 0$</p>\n<p style=\"padding-left: 30px;\">$O_x + A_x + C_x = 0$</p>\n<p style=\"padding-left: 30px;\">$O_x = 0 - C_x &nbsp;= &nbsp;\\var{format(qty(abs(FO[0]), units[0]))}$&nbsp;<em>{if(sign(FO[0])&gt;=0,'right','left')}</em></p>\n<p style=\"padding-left: 30px;\"><em>&nbsp;</em></p>\n<p>$\\Sigma F_y = 0$</p>\n<p style=\"padding-left: 30px;\">$O_y + A_y + C_y = 0$</p>\n<p style=\"padding-left: 30px;\">$O_y = - (A_y + C_y) &nbsp;= - ( \\var{FA[1]} + \\var{siground(FC[1],4)} )= \\var{format(qty(abs(FO[1]), units[0]))} $ &nbsp;<em>{if(sign(FO[1])&gt;=0,'up','down')}</em></p>\n<p style=\"padding-left: 30px;\"><em>&nbsp;</em></p>\n<p>Resolve $O_x$ and $O_y$ to get</p>\n<p>Force $O = \\var{format(qty(abs(FO), units[0]))} $ at an angle of {format(dirO)} from the positve x-axis.</p>", "variablesTest": {"maxRuns": 100, "condition": "B-A > 0.2"}, "parts": [{"marks": 0, "prompt": "<p>Determine the magnitude and direction of the moment at the fixed support at <em>O</em>.</p>\n<p>$M_O$ =&nbsp;[[0]]&nbsp;&nbsp;[[1]] &nbsp;<span data-jme-visible=\"debug\">{format(MO)}</span></p>", "customName": "", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "showCorrectAnswer": true, "sortAnswers": false, "showFeedbackIcon": true, "gaps": [{"marks": "4", "customName": "", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "settings": {"close": "1.0", "C2": "50", "correctAnswer": "abs(MO)", "right": "0.2", "C1": "75", "C3": "25"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "engineering-answer"}, {"marks": 0, "matrix": "[if(sign(MO)>0,2,0),if(sign(MO)<0,2,0),if(sign(MO)=0,2,0)]", "minMarks": 0, "maxMarks": 0, "customName": "", "displayType": "dropdownlist", "customMarkingAlgorithm": "", "shuffleChoices": false, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "displayColumns": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "showCellAnswerState": true, "choices": ["Counterclockwise", "Clockwise", "Neither"], "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "1_n_2"}], "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"marks": 0, "prompt": "<p>Determine the magnitude and direction of the reaction force at <em>O</em>.</p>\n<p><em>O</em> =&nbsp;[[0]]&nbsp;&nbsp; at an angle of [[2]]&nbsp;measured from the&nbsp;[[1]].</p>\n<p data-jme-visible=\"debug\">{format(qty(abs(FO),units[0]))} at {format(dirO)</p>", "customName": "", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "showCorrectAnswer": true, "sortAnswers": false, "showFeedbackIcon": true, "gaps": [{"marks": "4", "customName": "", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "settings": {"close": "1.0", "C2": "50", "correctAnswer": "qty(abs(FO),units[0])", "right": "0.2", "C1": "75", "C3": "25"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "engineering-answer"}, {"marks": "0", "customName": "", "customMarkingAlgorithm": "", "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toString() +'.');"}}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "settings": {"dummy": "'ignore'"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "drop-down-axis-reference"}, {"marks": "4", "customName": "", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "settings": {"restrict_angle": true, "close": "1.0", "C2": "50", "right": "0.2", "C1": "75", "correct_quantity": "dirO", "C3": "25"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "angle-quantity-from-reference"}], "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "variables": {"dirO": {"definition": "qty(degrees(atan2(FO[1],FO[0])),'deg')", "name": "dirO", "group": "output", "templateType": "anything", "description": ""}, "units": {"definition": "random('mm','m')", "name": "units", "group": "Input", "templateType": "anything", "description": ""}, "L": {"definition": "if(units[1]='ft',random(2..12#2),random(1..5))", "name": "L", "group": "Input", "templateType": "anything", "description": ""}, "FA": {"definition": "MagA vector(0,random(1,-1))", "name": "FA", "group": "Input", "templateType": "anything", "description": ""}, "A": {"definition": "random(0.2..0.8#0.1)", "name": "A", "group": "Input", "templateType": "anything", "description": ""}, "OA": {"definition": "qty(A L, units[1])", "name": "OA", "group": "output", "templateType": "anything", "description": "<p>distance from O to A</p>"}, "M": {"definition": "random(100..500#25) random(1,-1)", "name": "M", "group": "Input", "templateType": "anything", "description": "<p>The magnitude of the moment.</p>"}, "MA": {"definition": "qty(cross(vector(scalar(OA),0,0),vector(FA[0],\n    FA[1],0))[2],\nunits[0] + \" \" + units[1])\n\n", "name": "MA", "group": "output", "templateType": "anything", "description": "<p>Moment of force A about point O.</p>"}, "MagC": {"definition": "random(10..150#10)", "name": "MagC", "group": "Input", "templateType": "anything", "description": ""}, "debug": {"definition": "false", "name": "debug", "group": "Input", "templateType": "anything", "description": "<p>d</p>"}, "theta_c": {"definition": "random(0..355#5 except [0,90,180,270])", "name": "theta_c", "group": "Input", "templateType": "anything", "description": ""}, "OB": {"definition": "qty(B L, units[1])", "name": "OB", "group": "output", "templateType": "anything", "description": "<p>distance from O to B</p>"}, "MO": {"definition": "-(MA + MB + MC)", "name": "MO", "group": "output", "templateType": "anything", "description": "<p>The reaction moment at O.</p>"}, "OC": {"definition": "qty(L, units[1])", "name": "OC", "group": "output", "templateType": "anything", "description": "<p>distance from O to C</p>"}, "magA": {"definition": "random(10..150#10)", "name": "magA", "group": "Input", "templateType": "anything", "description": ""}, "MB": {"definition": "qty(M,units[0] + \" \" + units[1])\n", "name": "MB", "group": "output", "templateType": "anything", "description": "<p>The concentrated moment.</p>"}, "MC": {"definition": "qty(cross(vector(scalar(OC),0,0),\n    vector(FC[0],FC[1],0))[2],\n  units[0] + \" \" + units[1])\n  \n  \n  ", "name": "MC", "group": "output", "templateType": "anything", "description": "<p>Moment of force C&nbsp;about point O.</p>"}, "angle_from_ref": {"definition": "let(ang,scalar(dirO),\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "name": "angle_from_ref", "group": "output", "templateType": "anything", "description": ""}, "FO": {"definition": "-(FA+FC)", "name": "FO", "group": "output", "templateType": "anything", "description": "<p>The resultant force at O as a vector.</p>"}, "FC": {"definition": "magC vector(cos(radians(theta_C)),sin(radians(theta_C)))", "name": "FC", "group": "Input", "templateType": "anything", "description": ""}, "B": {"definition": "random(A..0.9#0.1)", "name": "B", "group": "Input", "templateType": "anything", "description": ""}}, "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Keith Tarnowski", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3425/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Keith Tarnowski", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3425/"}]}